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Definitions that you’ll never see again
Economics is the study of choices made by people when there is scarcity. Economics is largely about the
choices people make given the constraints they face. It is about incentives they have. It is about the trades
people make. It is about markets and competition. There is more on scarcity below.
Microeconomics – unit of analysis is the individual. Here we are looking at one person’s behavior, one
firm’s choice, do you have a job, what is the wage of pasty chefs, how many hours do your work a week,
how many juiced baseballs does Rawlings produce, etc. Here we look at the trees.
Macroeconomics – considers economy-wide aggregates. Here we are looking at the overall
unemployment rate, the overall level of output, the labor force participation rate, the average price level in
the economy, etc. Here we look at the forest.
Labor Economics – obviously the focus is on labor markets, the participants in these labor markets and
their decisions, and government policies that affect the employment and compensation of labor resources.
Our class will focus mostly on the microeconomic aspects of labor economics. I will not ask you to make
the distinction between what is microeconomic and what is macroeconomic, but if you are interested in the
categorization, see p. 7 in your textbook for a nice chart.
Why should you care about labor economics? A sermon delivered to the choir…
You will find that labor economics issues are all around you, largely because labor markets are all around
you. First off, many of you have jobs or will have jobs. It is a lucky person indeed that never participates
in a labor market. Second, the fact that you are taking this class suggests you are in college, something that
is very important to your future labor market experiences. I don’t believe there is a person reading this who
doesn’t think that going to college will result in better labor market opportunities. We’ll spend a lot of time
analyzing these types of investments. Next, seventy percent of national income is paid to laborers, much
more than the 30% that goes to capital owners. For most people, labor income is their major, if not their
only source of income. It will be important to understand. Finally, it’s rare indeed where current events
(politics too) are unrelated to labor markets. For just one example, pay attention to the flap in New Orleans
about illegal immigrants doing construction work. Education, the decision to have children, and safety
(just to name a few) all have something to do with labor economics. Read Chapter 1 for more big picture
and pep talk type stuff.
How do you “do” Economics? Economists do it with models
Not the economists I know. Economic models are simplified representations of the world (theories).
Economics is a social science, thus it attempts to explain people’s behavior. Unfortunately we can’t do too
many controlled lab-type experiments on people (as those in the natural sciences do). We can’t put people
in a test-tube and subject them to experiments like lab rats because people object to this. Consider the
experiment I have in mind to take away half of your wealth and give it to your roommate and then see who
buys more steak dinners. Or another where I double your wage and see how many hours you work. I
would guess that you wouldn’t be lining up for the first one, but I bet you would for the second (perhaps
your employers many not). Those experiments that are done in the economics realm are done are usually
done on college students and lab rats (college students are cheaper?). As such, economists try to learn
about the world by using models - making assumptions, developing a model, then testing the model
statistically to determine if it accurately predicts. If it works, we keep them, if not, we toss them out. All
social sciences use models. Models can be mathematical, graphical, or verbal.
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Desirable characteristics of models
Simple, general, useful, and long legs, high cheekbones, etc….
Simple is straightforward. It doesn’t make any sense to make up a model that you don’t understand.
General means that it applies to a number of situations. If a model only works at 9:00 AM on Thursdays
when it’s raining and the Dukes of Hazard is on TV, it’s not going to be too helpful. Useful means that is
predicts behavior correctly.
Of course, to simplify matters, we will have to make assumptions. You may take exception to some of the
assumptions we’ll make. Ultimately, in economics, we will judge our models not based on how realistic
the assumptions are, but instead based on how well they predict observed behavior. A good model is a
model that predicts behavior correctly (a useful model).
Rationality
Economists often assume that people are rational. You may disagree, but nonetheless it proves to be a
valuable assumption. If you don’t believe me, try predicting the behavior of someone who is completely
irrational. Need some inspiration? Pat Robertson? Enron? Tonya Harding? Mayor Nagin? Crack
Addicts? Methodists? But in all seriousness, even criminals and ACC basketball players have been shown
to act rationally. In economics, we’d assume that Mayor Nagin is trying to get re-elected, that Tonya
Harding is trying to win a figure skating contest, and that Enron is trying to maximize profits.
We can define rationality in the following fashion. People do the best they can based on their own values
and information, under the circumstances they face. Or stated a bit differently, people maximize their own
welfare (happiness) as they conceive it. Notice this allows for people to have different values and different
perceptions. And it doesn’t preclude people making bad choices from time to time. Assuming that people
are rational suggests that people learn from their mistakes (Lisa Simpson’s experiment comparing Bart and
her hamster).
Supposing we were trying to develop a model that predicts scores on the final exam in Econ 325, how
would an economist go about it? First, we would then think about and collect the relevant data (variables)
to include in consideration of our model. We’d ask – what types of things would effect test grades? Things
that might help would be the number of hours you studied, whether or not you did the homework, your
blood alcohol content (in which direction I don’t know), your major, sex (why?), and whether or not I was
in a good mood when I wrote the test? We wouldn’t include color of your socks (even if they are lucky),
the relative humidity, and the day of the week (should we?), as we wouldn’t expect these variables to be
important.
Golly, I wonder what is important in determining whether or not people work? Or what is important in
determining a person wages? We’ll ponder these for a couple of weeks.
Some jargon you’ll see once on the first exam, but can forget after that
Positive Statements – statements of facts, of what is, or what would occur if something else were to
happen. These must be either true or false. Example: Michael Jackson is a musician. If Al Gore shaves
off his beard, he will get more votes in election.
Normative Statements – express value judgments. They state what should be. Cannot be true or false,
just opinion. Dead give away is the word “should” or “ought”. Example: Michael Jackson should not be
allowed to work in a day care center. Al Gore should allow Chad to spend more time with his daughters.
We shall mainly be concerned, as budding economists, with positive statements. As economists, we should
talk about the statements of facts, and let you all make your own value judgments based on these facts. In
fact, most economists will agree on positive statements. Where there is disagreement is on the normative
statements.
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Some fallacies you should take a glance at but won’t be tested on
These are examples of some logical mistakes that are commonly made. Read these once.
Fallacy of composition – occurs when someone says what is true for one person must be true for the whole
(group). While it might be true for one person, it isn’t necessarily true for everyone. Example – standing
up at a football game allows one person to see better, so it must be the case that if everyone stands up,
everyone would be able to see better. If you said this, you’d be committing a fallacy of composition.
Slipping $100 under my door will improve your grade, so if everyone does, everyone will get a better grade
(If I grade on a strict curve, this statement would be fallacious. Keep the money coming, though.)
Post-hoc fallacy – occurs when someone says since event A occurred before event B, it must be the case
that event A caused event B. This is obviously not always the case. Example – you send Xmas cards
before Xmas, thus sending Xmas cards causes Xmas. If you said this, you’d be committing a post-hoc
fallacy. I walk into the bathroom before I “tinkle”, thus walking in to the bathroom causes me to tinkle.
***Selection bias – occurs when people use data that are not typical, but instead are selected in a way that
biases results. Suppose I was asked to find out how many alcoholic beverages the typical NSU student
consumes in a given evening. If I conduct the survey in the gutter outside of Last Call at 2:00 on a Friday
morning, I will get a different result than if I conduct the survey at the library (the one with the books) at
9:00 the next morning. Neither place is typical. Coke learned about this one the hard way when it came to
their taste testing of New Coke (ask a marketing major). If you ask a person how much money they spend
on movies, and you do the surveying outside a movie theatre, do you think you’ll get a higher number than
the true average? Or if you survey people’s incomes and only choose the people in line to give blood
plasma (or in Econ 325) class you might get some misleading answers.
Finally, something important? You can’t hear this enough.
Scarcity ⇒ Conflict ⇒ Choices ⇒ Opportunity costs
Scarcity – limited resources, but unlimited wants. Everyone wants to be able to allocate the productive
resources. If I were Czar of NSU, my office is getting bigger, will have more windows, and a bar (for
serving juice). Powell would have a batting cage with live pitching (perhaps Mitch Williams could serve
up some BP), I’d have 3 assistants, and Don Rickels would be my greeter. I’d also have a green room.
And certainly class wouldn’t be at 9:00. There wouldn’t be as much room for computer labs and classes
and other people’s offices, but hey those are the breaks. Waitresses on roller-skates, anyone? How about
leather recliners for my students? The first floor could be an elaborate miniature golf course. Get the
drift?
When I talk about limited resources, I mean the productive resources – those things that are used to make
stuff. These are things like labor, oil, lumber, engineers, forklifts, etc. There is only so much of this stuff
to go around, so many hours in the day. When I talk about unlimited wants, I mean that everyone wants the
right to allocate productive resources (decide how the various resources are used). It isn’t necessarily greed
(Mother Theresa would like more resources to go to poor folks in India). Very loosely, everyone wants to
decide how to use the resources the way that makes him / her the happiest.
Scarcity put our wants in conflict (my ideas vs. your ideas vs. Billy Bob Thornton’s ideas), and thus we
must make choices about how we will use our resources.
Somewhere in the middle of all this we should talk about competition. We have all of this conflict about
how we are going to use resources. My plan to put a batting cage in White is in conflict with your plan to
turn it into a roller derby arena, which is conflict with Billy Bob Thornton’s plan to make it a tattoo parlor.
How do we make the choices? Competition is the process of conflict resolution. Take for instance, A’s in
Econ 325. A's are a scarce resource. Everyone wants one and is willing to give up something of value to
obtain one. However, unfortunately, there are only so many to go around. How do I / we decide who gets
them? You all compete for them. We could have the competition occur many different ways. Competition
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determines the rules of the game. I could give them away based on height. We could have a footrace to
decide who gets the A's. We could play cricket on the dartboard in my office. Or rock scissors paper
(check out http://www.worldrps.com for some tips). Or perhaps we could have quizzes and tests – that’s
sounds like a good way. Markets will be key in the real world in the US.
Opportunity cost – the highest valued foregone alternative. To determine the opportunity cost of activity
X, answer the following: What would I have done instead if I hadn’t done X?
Every time a choice is made, an opportunity cost is incurred. What is an opportunity cost? It’s the
highest valued foregone alternative. To determine the opportunity cost of activity X, just ask yourself what would I have done instead if I hadn’t done X. The cost need not be monetary, and usually won’t be.
What’s the opportunity cost of buying a baseball hat? Maybe it’s a sandwich and a movie ticket. What is
the opportunity cost of coming to class? It is likely an hour of sleep for many of us. Maybe it was going to
the gym and working out. Maybe it is an hour of work at your job. We don’t add up all the alternatives,
only the highest valued (the one we would have chosen). The opportunity cost of an action is the real cost
we should consider. Only you know your opportunity cost, as only you can tell what activities you would
have engaged in. The rest of the semester when I talk about cost, I am referring to opportunity costs.
What is the full cost of you coming to college? What does it include? Don’t stop after tuition and books!!
What should I read?
Chapter 1
Much like every other textbook’s chapter 1, it isn’t a page turner. However, it does a pretty good
idea of painting the big picture about what the course is about.
You might find the box discussing Gary Becker interesting. If you read this, you’ll find that labor
economics has a more wide reaching scope than you think. We’ll come back to both Gary Becker
later in the course. Also notice this is written by a man named Larry Summers who I guarantee
will insult a few of you later in the course.
What’s next?
Chapter 2
This is toughest material (mathematically and technically) that we’ll do all semester. We’ll take it
slow, but the sooner you can give it a whirl, the better.
Need Supply and Demand review?
Review Lectures 3, 4, 5
I’ll post some lecture notes I put up for my Econ 211 class. You’ll find lectures 3 – 5 somewhere
on Blackboard. There a bit more technical that we’ll likely need, but take a look if you care to.
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Review of Supply
First Law of Supply – Ceteris paribus (holding other relevant factors constant), the higher the price of a
good the greater will be the quantity supplied. Or stated differently, supply curves are upward sloping.
This is symmetric. Ceteris paribus, the lower the price of the good the lower will be the quantity supplied.
A supply curve shows how suppliers (producers) will behave when facing various prices. The 1st Law of
Supply simply says that suppliers will want to produce more if they can sell for a higher price.
Changes in the “own price” imply movements along a given supply, and are referred to as “changes in
quantity supplied”. If I am looking at the market for Wayne Newton albums, the own price refers to the
price of Wayne Newton albums.
Price
Supply
P1
A movement along a supply curve.
At P0, the quantity supplied will be Q0.
At the higher price P1, there will be a
higher quantity supplied, Q1.
P0
Q0
Q1
Quantity
Surely price is an important determinant in modeling firms’ (producers’) behavior. The effect of changing
prices on firms’ production decisions in just what a supply curve captures, holding other relevant factors
constant. However, there many other relevant factors that will affect a firm’s output decision. These
factors are listed below and are called the ceteris paribus conditions for supply. When we change these
other relevant factors, we will have to draw a new supply curve.
Ceteris Paribus Conditions for Supply
1.
2.
3.
Input prices – inputs are goods that are used in the production of other goods
Technology
Everything else of relevance
Supply Curve Shifts
Any change in a ceteris paribus condition above implies a shifting of the entire supply curve. Recall
what ceteris paribus conditions are. These are the things that we hold constant when we are drawing a
supply curve. If we change one of these conditions, we have a new supply curve.
We say that this is a change in supply, or a shift in supply. When we shift the supply curve to the right, it is
called an increase in supply. A shift of the supply to the left is called a decrease in supply.
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Price
S
An increase in supply (rightward shift)
S’ Notice at each price, there will be a higher quantity supplied.
Originally, at price P, the quantity supplied is Q0. After the
shift, the quantity supplied is Q1.
P
Q0
Q1
Quantity
Price
S’
S
A decrease in supply (leftward shift)
Notice at each price, there will be a lower quantity supplied.
Originally, at price P, the quantity supplied is Q0. After the
shift, the quantity supplied is Q1.
P
Q1
Q0
Quantity
What is Different About the Supply for Labor?
1.
Relabel the price of labor as “Wage Rate”.
Wage Rate
SLABOR
W1
.
W0
Q0
2.
Q1
Quantity of Labor (Hours)
The big difference between supply curves you studied in 211 and the supply curve of labor is that the
supplier of labor is inherently linked to the locations (conditions} where they supply their labor
services. You can’t be separated from your labor services. You can’t be a sweat shop laborer without
spending time in a sweatshop. The substitution and income effects will be important. More later…
Ceteris Paribus Conditions for Labor Supply
1.
2.
3.
4.
5.
Nonwage Aspects of the Job
Nonwage Income
Other Wage Rate (Other Occupations)
Number of (Other) Qualified Suppliers
Labor / Lesiures Preferences
Consider these ceteris paribus conditions simply a preview of coming attractions. Much more as we go.
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Review of Demand
First Law of Demand - Ceteris paribus (holding other relevant factors constant), the lower the price of a
good the greater will be the quantity demanded of that good. If you’d prefer a lower brow version, what
this says is that demand curves are downward sloping.
This is symmetric. Ceteris paribus, the higher the price of a good, the lower will be the quantity of that
good demanded.
A change in the “own price” of a good implies a movement along a given demand curve. We say that this
is “a change in quantity demanded”. The “own price” is the term we mean to refer to the good whose
demand curve we are examining. Thus, if we are looking at the demand for potato chips, the own price
refers to the price of potato chips.
Price
Here, we have a movement along a demand curve. When we
are looking at the demand curve for pistachios, the price of
pistachios is called the own price. Thus, a change in the
own price from P0 to P1 causes a movement along the demand
curve from Q0 to Q1. Or stated differently, when the price of
pistachios increases, it leads to a decrease in the quantity of
pistachios demanded.
P1
P0
Demand for Pistachios
Q1
Q0
Quantity of Pistachios
In the 1st Law of Demand, we said that to draw a demand curve, we most hold all other relevant factors
constant (ceteris paribus). When we draw a demand curve, we are not allowing all this other stuff to
change. The whole point of a demand curve is to isolate the relationship between the price of the good and
the quantity demanded of that good. When one of those other relevant factors changes, we have altered this
relationship and will have to draw a new demand curve. We call these factors the ceteris paribus conditions
for demand. What are these other relevant factors?
Ceteris Paribus Conditions for Demand
1.
2.
3.
Price of other goods
a. substitutes
b. complements
Income of consumers
a. normal (superior) good
b. inferior good
Everything else of relevance, which may include
Tastes / Advertising
Potential # of consumers
Expectations of future prices
Demand curve shifts
Any change in a ceteris paribus condition above implies a shifting of the entire demand curve. Recall
what ceteris paribus conditions are. These are the things that we hold constant when we are drawing a
demand curve. If we change one of these conditions, we have a new demand curve.
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We say that this is a change in demand, or a shift in demand. When we shift the demand curve to the right
it is called an increase in demand. A shift to the left is called a decrease in demand.
Price
An increase in demand. Notice at each price, there will be
a higher quantity demanded. Originally, at price P, the
quantity demanded is Q0. After the shift, the quantity
demanded is Q1.
P
D
Q0 Q1
D’
Quantity
Price
A decrease in demand. Notice at each price, there will be
a lower quantity demanded. Originally, at price P, the
quantity demanded is Q0. After the shift, the quantity
demanded is Q1.
P
D’
Q1 Q0
D
Quantity
What’s Different About the Demand for Labor?
1.
We relabel the price of labor as the “Wage Rate”.
Wage Rate
W1
W0
DLABOR
Q1
2.
Q0
Quantity of Labor (Hours)
We’ll talk much more about the demand for labor later in the course. The big difference between
demand curves you studied in Econ 211 and the demand for labor is that the demand for labor is called
a “derived demand”. We say that the demand for a particular type of labor is derived from the demand
for the product itself. If consumers are willing to pay for some product, some firm will wish to hire
workers than can help produce that product. If there is an increase in the demand for some product, it
stands to reason that there will likely be an increase in the demand for workers than can produce that
product.
You can think of the idea of derived demand from yet another angle. Suppose there are some
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workers whose only skill is the production of sauerkraut smoothies. If no one wishes to purchase a
sauerkraut smoothie, no firm will wish to hire sauerkraut smoothies workers. No demand for the
product, no demand for the labor that produces that product.
If you discussed marginal products of labor and production functions in Econ 211 or 212, you’ve seen
a good bit of this. If not, don’t fret.
Cetris Paribus Condition for Labor Demand
1.
2.
3.
4.
Product Demand
Productivity
Prices of Other Resouces
Number of Employers
There will be much discussion of these as we go.
Horizontal and Vertical Interpretations of Supply Curves
Take a look at the picture below with a boring labor supply curve drawn. From time to time we will find it
convenient to look at this same supply curve from two different perspectives.
Horizontal interpretation of the supply curve: the idea here is to take some wage as given, and see how
many hours of labor workers wish to supply. The “horizontal” come from taking the wage as given and
moving horizontally until you hit the supply curve. For instance, consider an individuals supply curve for
labor. If your boss tells you can make $12.00 an hour and can pick how many hours you wish to work at
this wage, this would be an example where the horizontal interpretation is applicable.
Vertical interpretation of the supply curve: the idea here is to take some number of hours of labor as
given and see what is the lowest wage workers will accept (to work that many hours). The “vertical”
comes from taking the hours as given and moving vertically until you hit the supply curve. For example,
again looking at your individual supply curve, if someone asks you what wage it would take for you to
work 40 hours a week, this would a case where the vertical interpretation of the supply curve is applicable.
Don’t worry – we’ll figure out along the way which interpretation is applicable in each situation. At this
point I just want you to spend a few minutes thinking about this.
Wage Rate
SLABOR
W1
.
W0
Q0
Q1
Quantity of Labor (Hours)
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Horizontal and Vertical Interpretations of Demand Curves
It’s the same idea with demand curves. Check out the picture below.
Horizontal interpretation of the demand curve: the idea here is to take some wage as given, and see how
many hours of labor (or workers) the firm wishes to hire (demand). The “horizontal” again come from the
fact that the wage is being taken as given and then moving horizontally until you hit the demand curve. As
an example, suppose we are looking at a firm’s demand curve for a certain type of workers. Perhaps the
firm knows the going wage for receptionists is $14 an hour. We would then ask how many receptionsists
the firm wishes to hire.
Vertical interpretation of the demand curve: the idea here is to take some number of hours (or wokers)
as given and determine the highest wage firms would be willing to pay. Again the “vertical” comes from
taking the hours as given and moving vertically until you hit the demand curve. For instance, later on we’ll
be able to determine exactly how much a firm would be willing to pay for the 36th hour or labor, or even the
17th worker in a factory.
Again, you’ll see how this plays out as we go.
Wage Rate
W1
W0
DLABOR
Q1
Q0
Quantity of Labor (Hours)
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Definition of Leisure
Labor economists think of leisure in a different way that most people do. For most people leisure is
reading a book on a beach, watching TV, visiting friends and countless other things. The way economists
think of leisure (and the way you should think of leisure to score points on tests) is as any time that is not
spent working at a paid job. So we will actually consider taking a shower, watching your kids, doing
aerobics as leisure, and (scoff) washing the dishes as leisure.
Using this definition, and because there are 24 hours in a day, all 24 hours are spent on labor or leisure. If
you spend 8 hours a day working, you have 16 hours on leisure. If you work 2 hours a day, you consume
22 hours of leisure. Letting W stand for hours of work, and letting L stand for hours on leisure, we can
write:
24 = L + W
This will come in handy later.
Supply of Labor – Big Picture
We will spend quite a while working on the supply of labor. Broadly, we are trying to figure out what are
the determinants of an individual’s choice of where to work, how much to work, or even if they wish to
work.
We will be interested in a number of questions, but for now we will be focusing on the “how much” part.
Why do some people choose to work, while other people chose not to work at all? Why do some people
work overtime or work two jobs, while others work only part-time? Why do some people choose to retire
early? Why might you be working only 20 hours a week now, but plan on working 40 hours a week next
year?
The basic idea here to explore here is how much of their limited time to people want to spend on leisure,
and how much on labor. This is sometimes called the “labor / leisure tradeoff”. People enjoy leisure, but
they also enjoy consuming goods. Goods require income and labor provides a means to earn income.
Thus, another way to look at this tradeoff between labor and leisure is a tradeoff between leisure and goods
or between leisure and income.
Once we have the basics of the labor / leisure trade off under control, we can look at some other factors, but
we will first turn our attention to this labor / leisure tradeoff.
Labor / Leisure Tradeoff – Big Picture
In thinking about this tradeoff, we will look at two different sets on information.
The first will be people’s preferences between leisure and labor. Of course, everyone likes leisure, but
everyone likes consuming goods as well. People will differ in their willingness to trade leisure for income.
Some people are “workaholics”. Other people are “leisure lovers”. Moreover, their willingness to trade
leisure for income might depend on how much of each good they already have. For example, you might be
willing to give from 0 to 2 hours of work a day for $20 a day, but I doubt you would be willing to go from
22 hours of work a day to 24 hours of work today for $20. Your textbook calls this subjective information.
The analytical tool we will use to capture preferences is called an indifference curve.
The second set of information will be people’s constraints. We all start with 24 hours a day. However,
the rate at which leisure is exchanged for income (the wage rate) will differ amongst people. Thus, the
combinations of leisure and income that are attainable will differ amongst people. If you get a raise, or
have other sources of income, this may alter your choice. Your textbook calls this objective information.
The analytical tool we will use to capture constraints is called a budget line (budget constraint).
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We will use will combine information on preferences and constraints to model people’s labor supply
choices.
Indifference Curves
I think I may belabor the indifference curves a bit, but I do not want you think these came from right field.
I walked out of class after talking about this once and told a colleague “I can’t believe I talked about
indifference curves for 63 minutes.” The look on my students’ faces also seemed to say, “I can’t believe
you talked about indifference curves for 63 minutes.”
An indifference curve shows the various combinations of income and leisure time that will yield some
specific level of utility or satisfaction to the individual.1
Stated a bit differently, two points on the same indifference curve must yield the same level of utility of
satisfaction.
People invariably get shook up by the word utility. If you do not like this word, you will be fine if you
think “satisfaction”, “welfare”, or “enjoyment”.
Ultimately, we will be interested in what these indifference curves look like. With a little introspection and
we can learn quite a bit about their shape and slope and how they might differ across types of people.
Are indifference curves positively or negatively sloped?
Look at the following diagram and focus your attention on point A. The first thing to ask is what other
point(s) could possibly be on the same indifference curve as point A, bearing in mind that two points on the
same indifference curve indicate the same level of satisfaction.
Income (per day)
C
B
G
A
D
H
E
F
0
4
8
12
16
20
24
Leisure (per day)
24
20
16
12
8
4
0
Labor (per day)
First, compare point A and point B. Can they represent the same level of satisfaction and therefore be on
the same indifference curve? Clearly not, as point B has more leisure and more income than point A.
Clearly, people would prefer point B to point A. Point B would yield a higher utility level. Since A and B
cannot be on the same indifference curve, we know indifference curves will not be upward sloping.
1
We could draw indifference curves for any two goods. If our two goods were food and clothing, this
indifference curve would show combinations of food and clothing that would yield the same level of utility.
For those of you who have seen indifference curves before (like, say in Econ 311), changing the names of
the goods (to leisure and income) will not change the results in any meaningful fashion. What you learned
before is still pertinent.
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Compare point A and point C. These cannot be on the same indifference curve either, as both A and C
have the same amount of leisure, but point C has more income. People would prefer C to A. Since A and
C cannot be on the same indifference curve, we know indifference curves cannot be vertical lines.
Likewise, people will prefer point D to point A. They both have the same amount of income, but point D
has more leisure and thus D would provide more satisfaction that point A. Since A and D cannot be on the
same indifference curve, we know indifference curves cannot be horizontal lines.
By using the same arguments, we know that neither of F, G, and H can be on the same indifference curve
as A. (You should make sure you understand why.) Therefore, the indifference curve through point A
cannot be in any of the shaded parts of the graph, so it must be downward sloping. Stated a bit differently,
if indifference curves cannot be vertical, horizontal, or upward sloping, they must be downward sloping.
Another way to see this is to compare points A and E. Is it possible that these two points lie on the same
indifference curve? Point E has more leisure but less income than point A. As we go from point A to E, is
it possible that the extra leisure is just enough to compensate for the lost income? It is. So it is possible
that A and E are on the same indifference curve.
If you add some leisure, and want to stay on the same indifference curve (same level of satisfaction), you
have to take away some income.
What have we learned after all this? We have learned that indifference curves are downward sloping.
See your textbook for a slightly less verbose discussion.
Are Indifference Curves Convex, Concave, or Straight?
Knowing they are downward sloping, there are still three possibilities. Indifference curves could be
straight lines, they could be convex, or they could be concave. I have cut and pasted the picture above but
removed the unnecessary points and letters. The straight-line indifference curve is in black, the convex
indifference curve is blue (bowed inward – farthest from the origin), and the concave indifference curve in
red (bowed outward – closest to the origin).
We will start with the concave indifference curve, see what it implies about people’s tradeoff between labor
and leisure, and then decide if it makes sense.
Income (per day)
A
0
4
8
12
16
20
24
Leisure (per day)
24
20
16
12
8
4
0
Labor (per day)
3
Lecture3
1/22/2007 7:18 PM
Concave Indifference Curves?
Income (per day)
AB
C
∆Y2
D
E
∆Y1
F
0 1
4
8
12 13
16
20 21
24
Leisure (per day)
24 23
20
16
12 11
8
4 3
0
Labor (per day)
Imagine starting over at point F. The person is consuming quite a bit of leisure (21 hours) and has
relatively small income. Consider giving up one hour of leisure (moving to point E). The indifference
curve suggests that it would take a sizable increase in income (∆Y1) to compensate for the lost hour of
leisure and remain at the same level of satisfaction.
Now consider completing this process again, only this time starting at point D. The person already is now
consuming much less leisure (13 hours) and has a relatively large income. Consider giving up an hour of
leisure (moving to point C). The indifference curve suggests it would take only a small increase in income
(∆Y2) to compensate for the lost hour of leisure and remain at the same level of satisfaction.
Keep going. Imagine starting at point B. Now the person is consuming only one hour of leisure, they are
working 23 hours a day. Again, consider giving up an hour of leisure (moving to point A). The
indifference curve suggests they would give up their very last hour of leisure for a tiny change in income
and would still remain at the same level of satisfaction.
A convex indifference curve suggests that as leisure gets more and more scarce, that a person becomes less
reluctant to give up leisure! Does this sound bizarre? It sounds backwards to me. Indifference curves are
not concave.2
2
If the story above does not make sense to you, try going in the “opposite direction”. Imagine starting at
point A. The person would have very large income but no leisure. Considering moving to point B. Even
though the person has little leisure, the indifference curve would suggest that the person would be willing
to give up very little income for an extra hour of leisure. Now start at C. The person is now consuming
more leisure and has less income. Consider moving to point D. According to the indifference curve, the
person here would be willing to give up a fairly large amount of income (∆Y2) for an extra hour of leisure.
Finally, start at point E. The person is now consuming a large amount of leisure and has very littlie
income. According to the indifference curve, the person would be willing to give up a large amount of
income (∆Y1) for an extra hour of leisure. As leisure becomes more abundant, does it make sense for a
person to be willing to give up more and more income for an additional hour of leisure? No. Indifference
curves are not concave.
4
Lecture3
1/22/2007 7:18 PM
Convex Indifference Curves!
Income (per day)
A
∆Y1
B
C
∆Y2
D
E
0
3 4
8
12 13
16
20
23 24
24
21 20
16
12 11
8
4
1 0
F
Leisure (per day)
Labor (per day)
Imagine starting over at point A. The person has relatively largely income, but little leisure. Consider
giving up some income to increase leisure by another hour. The indifference curve suggests that it would a
person would be willing to give up a sizable amount of (∆Y1) in order to be able to consume an extra hour
of leisure (and remain at the same level of satisfaction).
Now consider completing this process again, only this time starting at point C. The person already has less
income and more leisure than they did at point A. Again, consider giving up some income to increase
leisure by another hour. The indifference curve suggests the person would be willing to give up a smaller
amount of income (∆Y1) to get another hour of leisure (and remain at the same level of satisfaction).
Keep going to the right along the indifference curve to point E. The person has very little income and
much leisure. The indifference curve indicates the person would be willing to give up only a tiny amount
of income to increase leisure by another hour (and remain at the same level of satisfaction).
Thus, according to a convex indifference curve, as income becomes less plentiful and leisure more
plentiful, the person would be willing to give up less income for an additional unit of leisure. I think that
makes more sense than the convex case. This story and picture are in your book (Figure 2.1). What have
we learned? Indifference curves are convex. 3
Again, if this doesn’t make much sense, you might have an easier time if you flip the story around and
think about moving from first from F to E, then from D to C , and finally from B to A. If you do this, you
will find when people have low incomes and much leisure (point F), they will be willing to trade away an
hour of leisure for a relatively small increase in income. You will also find, as leisure time becomes more
scarce and income more abundant, they will require larger increases in income to compensate for the loss in
an hour of leisure. To get the person to give up their last unit of leisure (point B), the person will require a
large increase in income. Again, this makes sense.
3
Hey, what happened to linear? A linear indifference curve would imply a constant tradeoff between
income and leisure. A person who would be willing to give up their first hour of leisure for $4 would also
be willing to give up their last hour of leisure for $4. We reject linear indifference curves by the same
argument with which we rejected concave indifference curves.
5
Lecture3
1/22/2007 7:18 PM
Marginal Rate of Substitution of Leisure for Income
The marginal rate of substitution of leisure for income MRS(L,Y) is the amount of income one must give
up to compensate for one more unit (hour) of leisure.4
The steeper the indifference curve, the larger the marginal rate of substitution, the more income someone
will give up for an additional unit of leisure.
For math lovers, the marginal rate of substitution is the absolute value of the slope of the indifference
curve.
Check out Figure 2.1 in the textbook. It is very similar to the above picture. The only difference is they
give you numbers (4 and 1) where I did not (∆Y1 and ∆Y2)
One important thing to see is that as we move to the right along an indifference curve, the indifference
curve becomes flatters, so the MRS decreases. Stated differently, as people have more and more leisure,
they are willing to give up less income for an additional unit of leisure.5
And in fact, if you wanted to know the MRS at any point on an indifference curve, all you would have to
do is draw a tangent line at that point and figure out the (absolute value) of that tangent line’s slope. See
the review of tangent lines at the end of these notes if you need a refresher.
Indifference Map
We have only drawn one indifference curve so far. If you go back to the first picture in these notes, the
only one that was drawn went through point A. We noted that point A and Point B were not on the same
indifference curve. However, point B is on some indifference curve. Every combination of leisure and
income is on some indifference curve. There are hundreds, thousands, even an infinite number of
indifference curves. Obviously, we do not want to take the time to draw them all, but we might draw a
couple to illustrate the general shape. Often a series of indifference curves are called a family of
indifference curves. I have drawn a family of indifference curves below. It is important to remember that
as we move to the northeast, the level of satisfaction associated with an indifference curve increases. Do
you know why? On which indifference curve would you rather be?
By the way, from time to time, on an exam or a homework assignment you will have to draw in an
indifference curve that is not pictured. That is ok. Based on the other indifference curves that are drawn,
you will have a very good idea of the shape of the indifference curve you will need to draw.
4
You might have noticed the interpretation of some of our changes differs depending on whether we are
moving from left to right along an indifference curve or if we are moving from right to left. When thinking
about things, doing problems, etc, you may find it more convenient to go one way rather than the other. By
all means, please do. However, when we talk about the MRS, we will always use the definition above and
always talk about the amount of income that would be given up for an additional hour of leisure.
5
If you are having a deja-vu type flashback to our discussion of why we though indifference curves are
convex, you are on the right track. We chose convex indifference curves because they are consistent with a
MRS that decreases as we move to the right along indifference curve.
A linear indifference curve would have a constant MRS, while a concave indifference curve would produce
a MRS that increased as we move to the right along an indifference curve.
6
Lecture3
1/22/2007 7:18 PM
Income (per day)
I3
I2
I1
Satisfaction Level Increases
0
4
8
12
16
20
24
Leisure (per day)
24
20
16
12
8
4
0
Labor (per day)
Different Preferences
Hey, wait a minute, I though indifference curves were about people’s preferences. All this talk about
trading off leisure for income seems like we are discussing preferences. Could it be the case that different
people have different preferences? Yes indeed. We can show different preferences with differently shaped
indifference curves.
Leisure Lovers
Below is a picture with very steep indifference curves. In order to give up just a bit of leisure, this person
would require a large amount of income. Your textbooks call this type of person a leisure-lover, but I
think it is better to think of this as someone who has a relatively high value of leisure or a relatively low
value of income. Lazy college kids? Single mom with kids? Big golf nut? Someone who really likes to
read novels? Someone who really hates his or her job in a cubicle?
Income (per day)
I3
I2
I1
0
4
8
12
16
20
24
Leisure (per day)
24
20
16
12
8
4
0
Labor (per day)
Workaholics
Below is a picture with very flat indifference curves. This person would give up a large amount of leisure
for only a modest increase in income. Your textbooks call this type of person a workaholic, but I think its
better to think of this as someone who has a relatively low value of leisure, or a relatively high value of
income. Someone who works two jobs to buy expensive shoes? Who has until Tuesday to pay of the mob?
Single computer nerd with a broken modem? Someone who really likes his or her job?
7
Lecture3
1/22/2007 7:18 PM
Income (per day)
I3
I2
I1
0
4
8
12
16
20
24
Leisure (per day)
24
20
16
12
8
4
0
Labor (per day)
Of leisure lovers and workaholics, who tends to have larger marginal rate of substitution?6
Magic Johnson once said in an interview something to the effect of him loving to play basketball so much
that he would play even if they did not pay him. At that time, would you have expected him to have a high
MRS (steep indifference curves) or a low MRS (flatter indifference curves)?7
6
Leisure lovers tend to have a higher MRS. Notice leisure lovers have steeper indifference curves and thus
are willing to give up a larger amount of income for an additional house of leisure. Workaholics have
flatter indifference curves and thus are willing to give up less income for an additional hour of leisure.
7
Magic would be a workaholic. To see why, go from right to left along indifference curves. Magic would
be willing to give up a large amount of leisure (play more) for a small increase in income. This is
consistent with flat indifference curves.
8
Lecture3
1/22/2007 7:18 PM
Appendix: Review of Tangent Lines / Slopes
Surely, you remember that the equation of the slope of a line from fifth grade:
slope =
rise y1 − y 0
=
run x1 − x0
This is super easy when the function is a straight line, as the slope of a straight line is constant. That is, it
does not change depending on where we are on the line.
In this class, we will be look at some relationships where the slope changes as we move along our function
or curve. To determine the slope of a function at a particular spot, we draw what is called a tangent line.
To draw a tangent line you simply find a line that just barely touches the function at that point. See the
picture below, where I have drawn four tangent lines – one each for points A, B, C and D. To determine
the slope of the function at each point, we would just figure out the slope of the tangent line. Pull out a
piece of paper and a straight edge, draw something like this function, and draw a couple tangent lines. It is
not hard.
D
C
B
A
What you will be able to need to recognize for this course is how the slope changes. At point A, the slope
of the function is relatively low. As we move from point A to point B, the slope of the function is
increasing. Notice at point B, the function is steeper than it was at point A. In addition, notice as we move
from B to C to D, the slope of the function is decreasing. The tangent lines are becoming flatter. Flat
tangent lines are associated with lower slopes while steep tangent lines indicate larger slopes.
This gets a bit trickier when it comes to a function that has a negative slope like the one pictured below
(which looks oddly like an indifference curve, eh?). It is still the same process to draw the tangent lines,
and we will still figure out the slope by looking at the slope of the tangent lines. What is trickier is how to
talk about comparing these slopes.
9
Lecture3
1/22/2007 7:18 PM
A
B
C
Perhaps some made up numbers are in order here. At point A, the slope might be something like -4, while
at point B the slope might be -3, and at point C -1.5. The confusion comes about when we talk about which
has the larger slope. Technically, point C has the largest slope because -1.5 is the largest of those three
numbers (it is the least negative). Now the confusion becomes that steep lines are associated with lower
slopes and flat lines are associated with larger slopes. Unfortunately, this is the exact opposite as we had
in the situation above. We are not going to like this confusion.
So instead of talking about where the slope is the “largest”, what we will do is talk about where the slope is
the “steepest”. I think everyone would agree that the function is the steepest at point A and become less
steep at we scoot down to point C. I think everyone would agree that the function becomes flatter as we
move from point A to B to C. If you look at the picture on the previous page, point B is the steepest.
If you like your math and are not scared away by absolute values, we could say that slopes that are large in
absolute value are steeper, while slopes that are small in absolute value are flatter. We could also say that
the absolute value of the slope falls as we move from point A to B to C. If you can handle this, this is the
way to go. If you cannot, just think in terms of "steeper" and "flatter" and you will be fine.
If you have read all of Lecture 3, you can think of the curve above as a convex indifference curve. Of the
three points labeled A, B, and C, at which point is the MRS the highest? The lowest?8
8
The MRS is highest at point A. Remember, the MRS is the absolute value of the slope. Here, the slope is
– 4, and thus the absolute value of the slope is 4. Alternatively, you could have just noted at point A the
curve was the steepest. The MRS is lowest at point C, as the MRS is 1.5, or the curve is the flattest.
10
Lecture 4
1/31/2006 2:10 PM
We have spent a bunch of time illustrating people’s preferences for work and leisure as reflected by
indifference curves. We noted that as we added more income and leisure, a person’s satisfaction level
increased (they ended up on a higher indifference curve). However, we cannot learn much looking at
preferences in a vacuum. I personally would like to consume 23 hours of leisure a day and earn $150,000 a
year, but this is not attainable for me. The next step of the process is to look at all of the combinations of
income and leisure that are attainable (affordable). Then, of those attainable combinations of leisure and
income, we will try to find that one that will result in the highest level of satisfaction.
We will start with budget constraints and then move on to optimization. We will next see how optimal
choices change when wages change – a big deal indeed.
Budget Constraints
To start with, we will make simplifying assumptions.
1.
People cannot save or borrow. This, while not very realistic, will simplify our problem quite
nicely. You can relax this with a bit of work. This means people will choose a point on the
budget constraint (more in a bit).
2.
People have no sources of non-labor income. Of course, this means all income will come from
labor. On the next page, you will see how to add non-labor income to the story.
3.
We will assume that the individual’s wage is given. Specifically, the wage that a worker receives
does not depend on how many hours the worker works. Overtime is an obvious exception and
there are others.
A budget constraint – shows all the various combinations of income (goods) and leisure that a worker
might realize or obtain, given the wage rate. Your textbook sometimes also calls these income-leisure
budget lines.
It is very simple. Suppose the wage rate is $1 per hour. If you work 0 hours (24 hours of leisure), you have
$0 income. If you work 4 hours (20 hours of leisure) you earn $4 a day. If you work 14 hours (10 hours of
leisure), you have $14 in income per day.
As far as drawing this picture, a nice trick is to look at the extremes (and connect the dots). As noted above
if we work 0 hours, we have zero income. If we work 24 hours a day, we earn $24 a day. Connect the
dots. You will find that the other points described above will fall right on the line you have just drawn.
See the picture below – we have just constructed the budget line shown in blue (the one in the middle).
Now increase the wage to $2 per hour. What happens to the budget line? You find that if you work 0
hours, you still have $0 in income. If you work 24 hours, you now have $48 in income per day. It looks
like the budget constraint is “fixed” in the lower right-hand corner. The result of increasing the wage is to
rotate the budget line clockwise. In the picture, it is shown in red (the one on top).
Go back to the original case and consider what happens if the wage falls to $0.50 per hour. You should
find the budget constraint rotates counterclockwise. It is shown in black (the one on the bottom).
Hours of Leisure
Hours of Work
24
23
22
21
…
0
0
1
2
3
…
24
Labor Income
(wage = $0.50)
$0
$0.50
$1
$1.50
…
$12
Labor Income
(wage = $1)
$0
$1
$2
$3
…
$24
Labor Income
(wage = $2)
$0
$2
$4
$6
…
$48
1
Lecture 4
1/31/2006 2:10 PM
If you are good at math, you will notice that as the wage increases, the absolute value of the slope of the
budget line increases. If you are not as good at math, you will notice that as the wage increases the budget
line become steeper.
Income (per day)
Wage is $2.00 / hour
$48
Wage is $1.00 / hour
Wage is $0.50 / hour
$24
$12
0
4
8
12
16
20
24
Leisure (per day)
24
20
16
12
8
4
0
Labor (per day)
Before we get too far, let us see how to add non-labor income to the picture. Go back to the case where
the wage is $1 per hour again. Suppose you have an additional source of income. Perhaps you live on top
of a pocket of natural gas and the gas company pays you $8 a day for the right to extract this gas.
Hours of Leisure
24
23
22
21
…
0
Hours of Work
0
1
2
3
…
24
Labor Income
$0
$1
$2
$3
…
$24
Non-Labor Income
$8
$8
$8
$8
…
$8
Total Income
$8
$9
$10
$11
…
$32
(Total) income has increased by $8 (the amount of the non-labor income) at all levels of labor. All you
have to do is shift up the budget constraint (vertically) by the amount of the non-labor income. Your
textbook’s notation on non-labor income is usually “N” – so you will see a “N” in the right hand corner.
2
Lecture 4
1/31/2006 2:10 PM
Income (per day)
No non-labor income (W=$1)
$32
Non-labor income is $8 (W=$1)
$24
$8
N
0
4
8
12
16
20
24
Leisure (per day)
24
20
16
12
8
4
0
Labor (per day)
See if you can figure out what the budget constraint would look like if you faced this situation. If you work
8 hours or fewer your wage is $2 per hour. If you work more than 8 hours you get paid “time and a half”,
or $3 per hour. Pull out a piece of graph paper and draw that budget constraint. You should find that your
budget constraint has a kink (at 8 hours of labor).
Even with these simple ideas, we can show the constraints people face when their wages change, when
non-labor income is available, when overtime is paid, and things that are even more exotic we have not
even thought of.
Utility Maximization
So far, we have preferences (indifference curves) and constraints (budget lines). Preferences indicate what
we like. Constraints indicate what is attainable. The last step is to choose the best (highest satisfaction)
combination of leisure and income that is attainable. Recollect that the further away from the origin an
indifference curve is, the higher the level of satisfaction it represents. Some indifference curves will be
unattainable, to the northeast of our budget constraint. We want to pick the one furthest from the origin
that we can afford.
3
Lecture 4
1/31/2006 2:10 PM
Income (per day)
I3
I2
Satisfaction Level Increases
I1
C
B
A
0
4
8
12
16
20
24
Leisure (per day)
24
20
16
12
8
4
0
Labor (per day)
First off, consider the indifference curve labeled I3. It is clearly the highest level of satisfaction of the three
indifference curves drawn, but not attainable.
Every point on the budget line is attainable so I know that both point A and point B are attainable.
However, can we do better than A or B?
The answer is yes, and it turns out to reach the highest possible indifference curve we will end up choosing
the indifference curve that is just tangent (barely touches) the budget line. This occurs at point C. If you
do not believe me, draw in some more indifference curves and see how they look. You will not do better
than C.
Your textbook goes through a whole page of telling you why point B and point A are not optimal. If you
are super interested, read it. If not, do not.
Back to the Big Picture
Let us not lose site of why we are doing all of this. We are after the supply curve of labor. We are
interested in what determines the amount of how many hours people wish to work. We noted long ago that
the wage is surely an important part of this decision. We also noted that non-labor income availability
might be a factor as well.
We have spent all this time developing some preferences and constraints, and we have assumed people try
to maximize satisfaction levels. When we do so, out popped a person’s optimal choice of labor and leisure.
For instance, the person picture above appears to work about 11 hours a day.
What is the end? What is the point? What we are going to do now is to see what happens to the amount of
hours people wish to work as things change. For instance, what happens to the optimal choice of labor if
the wage increases or decreases? What happens to the optimal choice of labor if someone’s non-labor
income increases or decreases?
Along the way, we will assume that people’s preferences do not change – but that their budget lines do. So
all we will have to do to figure out all this stuff is change something, the wage for instance. We will draw a
4
Lecture 4
1/31/2006 2:10 PM
new budget line that reflects the changes. Then will find the new optimal labor / leisure choice. We will
compare before and after and we are done.
We will spend what will seem like an inordinate time working on just what happens when wages change
because as well all know, the wage is important.
Finally, the Supply Curve of Labor
The idea of the supply curve of labor is to present workers with various wages and see how many hours of
they wish to work. We then plot the relationship between wages (vertical axis) and hours of labor
(horizontal axis). In Econ 211, all of your supply curves were upward sloping. What do we get here?
Simply draw a bunch of different budget constraints (that reflect different wages) and note the optimal
choices. Then flip around the horizontal axis.
Income (per day)
W5
I5
W4
I4
W3
I3
W2
I2
I1
W1
0
4
8
12
16
20
24
Leisure
24
20
16
12
8
4
0
Labor
Start with the budget line with the lowest wage (W1). Consider what happens as the wage increases. As
the wage increases from W1 to W2 and from W2 to W3, hours of labor increase (hours of leisure decrease).
However, when the wage increases from W3 to W4 and from W4 toW5, hours of labor decrease. This will
not be your garden-variety Econ 211 supply curve.
We now graph the wage rates and optimal choices of hours of labor in the picture above. But we flip over
the horizontal axis so that now as me move to the right we will be increasing hours of labor. Having done
all this, the result is the supply curve of labor. It will look like the thick black dotted line above flipped
over.
5
Lecture 4
1/31/2006 2:10 PM
Wage rate (per day)
SLABOR
Backward bending portion
W5
W4
W3
W2
W1
0
4
8
12
16
20
24
Hours of Work
It is called a “backward-bending” labor supply curve because eventually as wages rise to a high enough
level there is a reduction in the number of hours of labor supplied. Be sure to notice that we are measuring
hours of work along the horizontal axis.
Are you struggling with how it could be possible there is a backward bending portion of your labor supply
curve? How many hours a week would you work if you were paid $100 million dollars an hour?
Still do not believe it? Do you recollect those questionnaires I had you fill out? One of the questions I
asked went something like this: if you controlled your hours, and you suddenly got a 20% increase in your
wage, would you change the number of hours you work?
Some of you answered you would work more – you folks were on the lower portion of your supply curve.
Some of you answered you would work less – you folks were on the backward bending portion of your
supply curve. Not many of you, but at least one or two did.
Finally most of you answered you would not change your hours at all. Perhaps you were right in the
middle (imagine stretching out the supply curve vertically).
It should not be surprising that not very many of you are on the backward bending portion of your supply
curve, yet. Most of you are still early in you careers and have low wages (compared to where you might be
in ten years, say). You are obviously more likely to be on the backward bending portion the higher your
wage.
Income / Substitution Effects
One of the questions you might be asking is - why do we have this funny backward bending supply curve?
What is it that is unique about the supply of curve? We think it is instructive to show you something
called the substitution effect and the income effect of changes.
Income effect:
The income effect refers to a change in the desired hours of work resulting from a change in income,
holding the wage rate constant. When you think about an income effect, think about winning the lottery
or getting an inheritance. An increase in the wage means that roughly, that the worker is wealthier, has
more purchasing power, or has a larger potential income. Since the worker’s wealth has increased, they
will wish to purchase more goods and services in general. However, we also think that leisure itself is a
normal good. This means as people get wealthier, they will wish to consumer more leisure, and thus they
6
Lecture 4
1/31/2006 2:10 PM
work less. An increase in the wage provides an increase in potential income, which leads to an increase in
consumption of leisure, and therefore less labor.
Substitution effect:
The substitution effect indicates the change in the desired hours of work resulting from a change in the
wage rate, keeping income constant. Think back to the discussion of opportunity cost in Econ 211 (or see
Lecture 1). The opportunity cost of consuming an hour of leisure is an hour or labor. If you did not watch
cartoons this morning, you could have gone and worked for an hour instead. If you wage is $12 an hour,
the cost of an hour of leisure is $12. If your wage increases to $14 an hour, the cost of an hour of leisure is
$14. As your wage increases, the opportunity cost of consuming leisure increases. As with anything that
gets more expensive, you will want to do less of it. An increase in the wage increases the cost of
consuming leisure, reduces leisure time, and thus results in more labor.
Net Effect:
If you are following well, you should have noticed that the income effect and substitution effect are
pushing in opposite directions. The overall result of what happens to labor hours depends on the
magnitudes of these two effects. Economic theory cannot predict the outcome.
If the substitution effect dominates the income effect, the net result of an increase in the wage will be an
increase in hours of labor. This means the increase in labor associated with the substitution effect is larger
in magnitude than the reduction in labor associated with the income effect.
If the income effect dominates the substitution effect, the net result of an increase in the wage will be a
reduction in hours of labor. This means the reduction in labor associated with the income effect is larger in
magnitude than the increase in labor associated with the substitution effect.
Take a look at the backward bending labor supply curve. On which part is the substitution effect
dominating the income effect? On which part is the income effect dominating the substitution effect?
Result of wage ↑
Result of wage ↓
Supply Curve Shape
Substitution effect (only)
Hours ↑
Hours ↓
--------------------
Income effect (only)
Hours ↓
Hours ↑
--------------------
Net Effect
Uncertain
Uncertain
--------------------
If subs. effect dominates inc. effect
Hours ↑
Hours ↓
Upward sloping
If inc. effect dominates subs. effect
Hours ↓
Hours ↑
Backward bending
What do data in the real world (outside of Econ 325 questionnaires) say about which dominates?
Male labor supply is mildly backward bending, while female labor supply tends to be upward sloping.
Why?
Graphical Version of Income & Substitution Effect
Coming next set of lecture notes.
7
Income and Substitution Effects
I think when you are done with these lecture notes you’ll have a much better sense of what it is we are
talking about when we say “income effect” and “substitution effect”. The big thing here is that when the
wage changes there are simultaneously two things happening. While this is true for both an increase in the
wage rate or a decrease in the wage rate, let us first focus our attention on an increase in the wage rate.
When the wage increases, this means the consumer has a higher potential income (or wealth). As you
know, the budget line rotates and ultimately the person will be able to reach a higher level of satisfaction.
The person is wealthier. It is this increase in potential income that we are trying to capture when we
discuss the income effect. The income effect will be the part of the change that could be described by an
increase in income, holding wages constant.
At the same this is going on, an increase in the wage is causing the price of leisure to change. It is
fundamentally altering the rate at which an hour of leisure can be exchanged for income. The cost of
enjoying an hour of leisure is the wage rate. Increasing the wage rate changes the increases the cost of
consuming an hour of leisure. As with any price, increasing the price of leisure leads to a reduction in the
amount desired. The substitution effect will be the part of the change that could be described by an
increase in wages, holding income (or the level of satisfaction) constant.
Look at an example, and then come back to the words. Suppose we start with a wage and its associated
budget constraint. The consumer chooses the optimal amount of leisure and income, labeled point A and
ends up on the indifference curve labeled I1. Then the wage increases causing the budget constraint to
rotate clockwise. Suppose after the wage increases, the optimal amount of leisure and income are indicated
by point B. Point B lies on the (higher) indifference curve labeled I2.
Ultimately, the net effect of these changes is that we have gone from point to A to point B and that the
satisfaction level has increased. What we want to do next is to identify the size (and direction) of the
income and substitution effects. Here come the mechanics.
We will always find the income effect first1. Start with the original budget line. Keep in mind that the
slope of the budget line (really the absolute value of the slope) reflects the original wage. Imagine
increasing the person’s non-labor income slowly (holding the wage constant – so they will be parallel
shifts) until we end up just reaching the new indifference curve, I2. When you find this right level of
income, draw in this imagined budget line – I like to draw mine in with a dotted line. Finally, given this
new imagined budget line, indicate the optimal choice as point C. Since we purposely chose the amount of
income to add so that we would end up on I2 (the new indifference curve), the optimal choice given this
new imagined budget line will be on I2.
We will call the change that results as we move from point A to point C the income effect. What you can
see clearly from the graph is that a “pure income” effect leads to more leisure and less labor. We know a
wage increase increases wealth (and the satisfaction level). The income effect is figuring out the amount of
income that (we could have given to the person) that would yield the same increase in satisfaction (that the
original wage changed caused).
We find the substitution effect second. The idea here is to see what happens as a resulting of changing
the wage while holding income (the level of satisfaction) constant. What we would like to find is an
optimal choice given the original wage and another optimal choice given the new wage, but the whole time
ending up with the same level of satisfaction for both these choices. It turns out you have already done
1
There is not anything economically meaningful about finding the income effect first, then moving on to
the substitution effect. However, for the simplification it provides, I will require you to find the income
effect “first”. In your previous courses, you may have done just the opposite, but doing so will not change
the direction of the income or substitution effects. Instead of indicating the substitution effect along the
new indifference (as we will do), reversing the order would result in indicating the substitution effect on the
original indifference curve.
this. As you move from point C to point B, you are increasing the wage (rotating the budget constraint),
but still end up on the same indifference curve, I2. Thus, the movement from point C to point B is the
substitution effect. Not surprisingly, the substitution effect illustrates that an increase in wage leads to a
decrease in leisure and an increase in labor.
You will be asked about the net effect. This is easy. You already know the net effect is that you went
from A to B. Do not forget is not actually the case that person moves from point A to point C and then
moves from point C to point B – these changes happen all at once. The decomposition we make is to help
us understand. Nonetheless, of the advantages of the graphical treatment is that we can tell, given the shape
of indifference curves, whether the substitution effect or the income effect dominates.
I have put the pictures in the same order we discussed them in class. We did not get to the last case in
class, but you should definitely take a look.
In addition, for some practice, I have posted the pictures (without the answer) in case you would like to
give it a whirl. You could also draw your own and figure everything out yourselves. Whether the income
effect or substitution effect dominates will depend on exactly how you draw you indifference curves, but
you should always find the income effect (by itself) and the substitution effect (by itself) move in
predictable directions.
Income (per day)
W2
Wage Increase
Income:
Leisure ↑, Labor ↓ (A → C)
Substitution: Leisure ↓, Labor ↑ (C → B)
Net:
Leisure ↑, Labor ↓ (A → B)
Income effect dominates
Backward bending part of labor supply
W1
B
C
A
I2
I1
0
4
8
12
16
20
24
24
20
16
12
8
4
0
Income
Substitution
Net
Leisure (per day)
Labor (per day)
Income (per day)
W2
Wage Increase
Income:
Leisure ↑, Labor ↓ (A → C)
Substitution: Leisure ↓, Labor ↑ (C → B)
Net:
Leisure ↓, Labor ↑ (A → B)
Substitution effect dominates
Upward sloping part of labor supply
B
W1
C
I2
A
I1
0
4
8
12
16
20
24
20
16
12
8
4
24
0
Income
Substitution
Net
Leisure (per day)
Labor (per day)
Income (per day)
W1
Wage Decrease
Income:
Leisure ↓, Labor ↑ (A → C)
Substitution: Leisure ↑, Labor ↓ (C → B)
Net:
Leisure ↓, Labor ↑ (A → B)
Income effect dominates
Backward bending part of labor supply
W2
A
C
B
I2
I1
0
4
8
12
16
20
24
20
16
12
8
4
24
0
Income
Substitution
Net
Leisure (per day)
Labor (per day)
Income (per day)
W1
Wage Decrease
Income:
Leisure ↓, Labor ↑ (A → C)
Substitution: Leisure ↑, Labor ↓ (C → B)
Net:
Leisure ↑, Labor ↓ (A → B)
Substitution effect dominates
Upward sloping part of labor supply
W2
A
C
I2
B
I1
0
4
8
12
16
20
24
20
16
12
8
4
24
0
Income
Substitution
Net
Leisure (per day)
Labor (per day)
Income (per day)
B
A
I2
I1
0
4
8
12
16
20
24
24
20
16
12
8
4
0
Leisure (per day)
Labor (per day)
Income (per day)
A
B
I2
I1
0
4
8
12
16
20
24
24
20
16
12
8
4
0
Leisure (per day)
Labor (per day)
Income (per day)
B
I2
A
I1
0
4
8
12
16
20
24
24
20
16
12
8
4
0
Leisure (per day)
Labor (per day)
Income (per day)
A
I2
B
I1
0
4
8
12
16
20
24
24
20
16
12
8
4
0
Leisure (per day)
Labor (per day)
Lecture 6
2/26/2007 1:19 PM
Let us start with the same basic definitions of labor market measures. These will be statistics to monitor
the overall trends in the economy and in the labor market.
Labor Market Definitions
Our Uncle Sam goes through great pains to collect data on the labor market status of the population. Every
month, the Current Population Survey program surveys 60,600 age-eligible workers and ask them a series
of questions. Based on their answers, they classify workers into categories and tabulate a number of
measures. Your textbook does half of this in Chapter 3 and half in Chapter 18. You may want to look at
both chapters. First, the definitions:
•
POPULATION = the overall population of the US. Your book finds in interesting to note that
changes from population come from birth, deaths, or immigration. Deaths are predictable across
time, but birth rates (e.g. baby boom and baby bust) and immigration can be volatile.
•
CHILDREN = the number of children under age 16. The idea here is that these children, for the
most part, are not eligible to work, so we do not wish to include them in our labor market
statistics.
•
INSTITUTIONALIZED = the number of people who are “institutionalized”. This would include
persons in nursing homes, mental hospitals, and penal institutions. They are not available for
work.
•
POTENTIAL LABOR FORCE = POPULATION – CHILDREN – INSTIUTUTIONALIZED.
These are people eligible to be labor market participants.
Now focus on just those people in the POTENTIAL LABOR FORCE. Think of this as the group of ageeligible people. The potential labor force is the universe people that could participate, if they chose to, in
the labor market. We categorize these people into one of three mutually exclusive categories. Mutually
exclusive means that each person can belong to only one category.
•
EMPLOYED = people with any paying job, people that are self-employed, and people that have a
job but are not currently working right now because they are ill, on-strike, on vacation, or not
working due to weather. If you worked a single hour, you are considered employed.
•
UNEMPLOYED = people who have no job but are available and actively looking for work. To
be counted as actively looking for work you must be been looked for work in the past 4 weeks.
You would also be counted as unemployed if you are waiting to be called back from temporary
layoff, you are temporarily ill but otherwise would be looking for work, or you are waiting to start
a new job that will be in less then 30 days.1
•
NOT IN LABOR FORCE = people who have no job and are not looking for work, but are
available for work. The big groups here are people who are retired and students. 2
We define the labor force as those people who participating in the labor market:
•
LABOR FORCE = EMPLOYED + UNEMPLOYED
Finally, we calculate a few more items of interest:
1
CHILDREN and INSTITUTIONALIZED are not counted as UNEMPLOYED (they are not available for
work).
2
See footnote above.
1
Lecture 6
2/26/2007 1:19 PM
•
LABOR FORCE PARTICIPATION RATE = (LABOR FORCE / POTENTIAL LABOR
FORCE) * 100
•
EMPLOYMENT POPULATION RATIO = (EMPLOYED / POTENTIAL LABOR FORCE) *
100
•
UNEMPLOYMENT RATE = (UNEMPLOYED / LABOR FORCE) * 100
Below is a pie chart breaking down the 288.4 million people in the US in 2003 by their labor market status.
The figures given are in millions of people. Also notice that CHILDREN & INSTITUTIONALIZED have
already been combined.
Unemployed,
8.8
Not in Labor
Force, 74.7
Employed,
137.7
Children &
Institutionalized
, 67.2
Using the figures given above, we can calculate some items.
POTENTIAL LABOR FORCE
= POPULATION – CHILDREN – INSTITUNIONALIZED
= 288.4 million – 67.2 million = 221.2 million
LABOR FORCE
= EMPLOYED + UNEMPLOYED
= 137.7 million + 8.8 million = 146.5 million
LABOR FORCE PARTCIPATION RATE = (LABOR FORCE / POTENTIAL LABOR FORCE) * 100
= (146.5 million / 221.2 million) * 100 = 66.2%
EMPLOYMENT POPULATION RATIO
= (EMPLOYMENT / POTENTIAL LABOR FORCE) * 100
= (137.7 million / 221.2 million) * 100 = 62.3%
Shortcomings of Unemployment Statistics
There are some things to note when interpreting unemployment statistics
1.
2.
3.
Discouraged Worker Effect (Hidden Unemployment)
Added Worker Effect
Underemployed (Subemployed) Workers
2
Lecture 6
2/26/2007 1:19 PM
Discouraged Workers - Note in the classification system above, to be unemployed, one must have no job
and be actively looking for work. Particularly during economic downturns, some unemployed workers
become discouraged while trying to find a job with an acceptable wage rate and stop searching. We call
such a person a discouraged worker. As that worker is no longer searching for work, they are no longer
counted as an unemployed worker, and instead are reclassified as “not in the labor force”.
Take an example where 90 people are employed, 10 people are unemployed, and 50 people are not in the
labor force. Calculate all the metrics above (labor force, LFPR, unemployment rates, employmentpopulation ratio).
Now, let 5 of the people who were previously employed become discouraged workers. Recalculate all the
metrics above.
You will find that the unemployment rate has fallen. As workers are most likely to become discouraged
during periods of economic downturns, one should be caution when interpreting unemployment rates alone
during these time periods. An increase in the unemployment rate may be an indication that the economy in
general is picking up, or it may be an indication of discouraged workers. To help you distinguish, notice
what is happening in the example above to the employment-population ratio and the labor force.
Added Worker Effect - Often when one family member loses their job, other family member may enter
the labor force. Depending on whether or not this person is successful in find a job, this may either
increase or decrease the unemployment rate.
Subemployed Workers - Notice the definitions count a person as employed regardless of where the work
or how many hours they work. If a person is fired from a high-wage job and takes a job at McDonalds, the
unemployment statistics will not be changed. Yet this worker is working at a job “below” their normal job.
Another example would be sometime who was working (and preferred to be working) full time, and
suddenly is reduced to part-time employment. In both cases, the unemployment rate, labor force, and
LFPR would not change, but there is less employment. The statistics are misleading.
Types of Unemployment:
Frictional Unemployment
Frictional employment is called so because it is associated with the normal frictions of the labor market.
This type of unemployment is unavoidable (and perhaps even desirable), and would be expected to be
roughly constant across time, or at the least predictable, and short-term in nature. One type of frictional
unemployment is called search unemployment. Quite literally, it is the unemployment associated with
searching for a new job. Example of search employment would include:
1.
2.
3.
4.
5.
a person who quit their original job to shop around for a new job
a person who is looking for a new job after lose a pervious job
a person who is a new entrant into the labor force
a person who is reentering the labor force
a person who is waiting to start a new job within 30 days
A second type of frictional unemployment is called wait unemployment. Examples include:
1.
2.
3.
Seasonal workers (construction worker in winter)
Someone waiting to be called back after a temporary layoff
Someone waiting in line (queuing) for union jobs
Structural Unemployment
Structural Unemployment refers to a more long-lived unemployment problem. It refers to situations where
there is a mismatch between the skills of job seekers and the skills required by firms. A person whose
3
Lecture 6
2/26/2007 1:19 PM
skills have become obsolete would be said to be structural unemployed. Examples would include someone
who knows how to program in Pascal, a now obsolete computer programming language, or someone who
repairs 8-tracks. This worker may benefit from new training or re-training.
A second type of structural unemployment would be a situation where the location of the jobs and the
location of the people with the necessary skills are not in the same geographic area. Equilibrium may take
a while to reach here.
Some of these distinctions between structural and frictional are a bit arbitrary. For instance, in some books,
they will classify unemployment brought on by unions, minimum wage laws, and other government
regulations as structural, not frictional.
Stocks vs. Flows
The unemployment and labor force statistics we have looked at thus far as called stocks. They are
snapshots at a point of time. The simply tell you how many people are unemployed at one point in time.
There can be more learned by looking at the flows. Flows are rates of change. They are how many new
people are being hired in a given week, how many people are being fired during a week, etc.
The classic example of a stock vs. flow is your bathtub. The stock is the level of water in the bathtub. The
flow into the bathtub is the water coming out of the faucet. The flow out of the bathtub is the water going
down the drain. If the flow into the bathtub is larger than the flow out of the bathtub, then the water level
(stock) will rise. If the flow into the bathtub is smaller than the flow out of the bathtub, then the stock will
fall.
We can break down the flows between labor force categories quite simply and summarize them in one
diagram.
Flow view of unemployment statistics
NILF
8
Unemployed
4
3 2
1
7 6
5
Employed
(1) Discharges / Fires
(2) Layoffs
(3) Quits
(4) Retirement & Withdrawals from labor force
(5) New Entrants & Reentrants (depends on whether they become immediately employed or not)
(6) New Hires
(7) Recalls from pervious layoffs
4
Lecture 6
2/26/2007 1:19 PM
For example, flow (1) represents people who are fired. They were previously employed and become
unemployed. Likewise, flow (5) refers to new entrants and reentrants. They were previously not a part of
the labor force, and depending on whether or not the immediately find a job, they will be either classified as
employed or unemployed. The bathtub analogy still applies. If the flows from unemployment into
employment are larger from the flow employment to unemployment, than the unemployment rate will fall.
With just the stocks, all we know as that the unemployment rate has gone up over the last month. With the
flow methodology, we might know, for example, that layoffs have increased while new hires have reduced
substantially.
If you are following along well, you will notice that discouraged workers are missing from this diagram. I
have stuck them in the diagram as (8).
The natural rate of unemployment
When the economy is doing well, we are like to see unusually low unemployment rates. When the
economy is in a recession, we are likely to see unusually high unemployment rates. However, not even in
the tight labor markets during WW II did we observe unemployment rates at zero. In short, we still have
frictional and structural unemployment.
The idea of the natural rate of unemployment (some times called full employment) is the there is some
unemployment rate that would be observed when the economy is just average – neither good nor bad. You
can think of it as the unemployment rate when the labor market is in equilibrium. As mentioned above,
there will always be frictional unemployment, and structural unemployment is predictable over time. If we
add up these types of unemployment, we arrive at the natural rate of unemployment.
If you remember your Econ 212, you may recall something called cyclical unemployment. This is the
employment associated with the “ups and downs” of the economy.
What is the natural rate of unemployment in the US? Economists disagree on its precise value, but most
economists agree it is between 4.0% and 6.0%, with a consensus being near 5.0%. While we cannot be
exactly sure what is, we can predict the factors that might change the natural rate of unemployment.
Demographics are important. Young people (teenagers in particular) tend to have higher unemployment
rates than the general population. When the large cohort of baby boomers reached their teenage years, it
would be too surprising that the natural rate of unemployment rate went up. When these same progressed
to their prime earning years, the natural rate of unemployment fell.
Welfare benefits and unemployment assistance will be important as well. As we know, the amount and
availability of welfare benefits may cause people to be less likely to work, and more likely to be
unemployed. In fact, one of the boxes in your text compares long series of national unemployment rates
for a number of countries. You will see that France has the highest unemployment rates of the countries
pictured. It is no coincidence that they have one of the most generous unemployment compensation
schemes as well. If the US were to increase unemployment benefits significantly, we would expect the
natural rate of unemployment to rise.
5
Lecture 6
2/26/2007 1:19 PM
Some pictures
Unemployment – Teenagers vs. Adults
Compare the grey and yellow lines (teenagers) to all the other lines (adults) above. You can see clearly that
teenagers have higher unemployment rates than adults. This is not hard to explain. They have fewer skills
than adults. Often they are simply looking for spending money and are not seriously attached to the labor
force.
Unemployment – Black Teenagers vs. White Teenagers
Compare the grey line (black teenagers) to the yellow line (white teenagers) above. Clearly black teenagers
have higher unemployment rates than white teenagers. On average, black teenagers have fewer years of
schooling and lower quality education compared to white teenagers. Black teenagers are more likely to live
in the city while many low-wage jobs (part-time) jobs are located in the suburbs. Discrimination plays a
role.
6
Lecture 6
2/26/2007 1:19 PM
Unemployment – White Adult Males vs. White Adult Females
Very similar. Compare the black and red lines above.
Unemployment – Black Adult Males vs. Black Adult Females
Very similar. Compare the blue and pink lines above.
Unemployment – Black Adults vs. White Adults
Compare the red and black lines to the blue and pink lines. White adults have lower unemployment rates
than do black adults. Same as the story as with teenagers, except the suburb story is less important.
What should I read?
Chapter 18
7
Lecture 7
2/26/2007 1:12 PM
Becker’s Model of Time Allocation
We want to take a little more realistic look at the tradeoffs facing people. In the past, decisions were made
by individuals (we were always drawing one person’s indifference curve on person budget line). In
addition, we assumed there were only two uses of people’s time – work and leisure. By this definition,
washing the dishes, cooking meals, mowing the grass and changing diapers are all leisure. You try telling
someone washing the dishes that they are enjoying leisure.
Therefore, Becker’s model tries to tell the story a bit more realistically. The main reason we discuss
Becker’s model is because if would be very difficult to explain the broad change in the rate that women
participate in the labor force without this model. Traditionally, women have been responsible for those
types of leisure that are not really leisure (cooking, cleaning, etc). Becker’s insight will help us out
immensely in explaining women’s labor force trends.
Overall there are two basic changes. Ultimately, you will want to know about at income effect and a
substitution effect. Bust rest assured, two things will make your life easier. First, you will not have to
locate these income and substitution effects on a graph. Second, the answers will not change. However, it
will be a little more insightful way to take you to the same answer - the hope if you will have a richer
understanding.
There are two meaningful changes from previous simple model:
(1) Instead of viewing the decision-making unit as an individual, we will view the decision-making unit as
a household.
The idea is simple. If you are trying to figure out the labor market outcome of a married woman
(man), and you analyze this without any information about her husband (his wife), then you will
be missing something significant. For you folks who are already married, you know that decisions
are made jointly. Husbands and wives coordinate on their decisions. If you are not married, you
will learn this soon after you are married. Very soon after you are married.
(2) Instead of simply labor and leisure, there will be three uses of time
•
•
•
Labor market time
Household production time
Consumption time
You already know about labor market time. This is time you spend in the labor market. This is
what we used to call (and still will call) labor. The point of labor is to earn income with which
goods can be purchased. There is not much new going on here.
Household production time is new. No longer will washing the dishes be considered as leisure.
Now, all those things that are done at home that seem like production are treated as such.
Washing the dishes, doing the laundry, cooking meals will be examples of household production
time. If you notice that these activities can also be purchased (send out your laundry, buy a meal),
you see where we are going.
Consumption time is new as well. Enjoying goods takes time. When you go golfing, you spend
time golfing. When you watch TV, you spend time watching TV. The insight here is it takes
more than just goods (the TV and the golf clubs) to make you happy, it takes time and goods
together for you to enjoy. Consumption time is the time used in the actual consumption of goods
and services.
1
Lecture 7
2/26/2007 1:12 PM
Examples
Your textbook has an example of a meal cooked at home. There is labor time involved in
purchase of food, household production time used in preparing the food, and consumption time
used in eating the food. Imagine three different ways to cook a chicken and vegetable dish.
Household Production
Time
Market Time
Consumption Time
Grow your own
vegetables, raise your
own chickens, cook the
food at home
HIGH
Buy it in a box, stick it
in the microwave
Order it a restaurant
SOME
LITTLE
LOW
SOME
SOME
SOME
HIGH
SLIGHTLY MORE?
Check out the table below where I did my best to come up with examples of each permutation. I am sure
you can complain about a couple, but I think this will help you get the idea.
Market Time
HIGH
HIGH
HIGH
HIGH
LOW
LOW
LOW
LOW
Household
Production Time
HIGH
HIGH
LOW
LOW
HIGH
HIGH
LOW
LOW
Consumption Time
Activity
HIGH
LOW
HIGH
LOW
HIGH
LOW
HIGH
LOW
Refurbishing old houses
Cooking gourmet deserts
Sailing
Roller coaster ride
Boiled crabs (self-caught)
Baking sugar cookies
Reading novel
Buying sugar cookies
We will call consumption activities that involve a relatively large amount of time and a relatively
small amount of goods time-intensive activities. Examples would be reading a novel, sitting on
the beach, watching the sunset, bird watching, and chipping golf balls in your back yard.
We will call consumption activities that involve a relative large amount of good and relatively less
time goods-intensive activities. Examples would include a meal at a fast food restaurant, and a
roller coaster ride.
There will be some gray areas. It turns out the absolute categorization will not be necessary, only
a relative comparison. Suppose you live in Detroit. You can go to a regular season football game
in Detroit one week or a few weeks later, you can go to the Super bowl. It will not be important
for our purposes if you do not have a knee-jerk reaction to whether the regular season game is
time-intensive or goods-intensive. What will be important is that you can recognize which of
these two choices is more goods intensive (or more time-intensive). Because these games both
use up the same amount of consumption time, and because the Super bowl tickets are more
expensive (more goods), you certainly can conclude that Super bowl is more goods intensive than
the regular season game. You could also conclude that regular season game is more time intensive
than the Super bowl.
The household will make three basic choices.
1.
What goods do they want to consume?
2.
How do they want to “produce” these goods? Purchasing them (with proceeds from labor market
time) or producing them within the home. Basically, make at home or buy?
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Lecture 7
3.
2/26/2007 1:12 PM
How do we allocate household members time? Here, comparative advantage is the doctrine. If
someone is particularly good at labor market time, they should spend time working. If another
family member is particularly proficient at home production, they should spend time on home
production. Family members have different characteristics that may include different preferences,
age, sex, educational attainment, previous labor market experience, previous home production
experience, and likelihood they will be discriminated against. All of these will be factors. I am
not trying to be smartass here, but there is a biological aspect here that will push women toward
having a comparative advantage in childbearing.
After all that, remember this is labor econ class. When we see what shakes out of all these
decisions above, ultimately we will find that some people are working, some people are not.
Some people spend much time on home production, some people do not. Some families have one
person who specializes in market time and one who specializes in household production. Some
families have two workers and therefore purchase meals and laundry services from the market.
These are the types of outcomes we are interested.
Becker Income Effect
An increase in wages means there is an income effect. Just as Econ 211 class, people will want to consume
more of most goods (so long as we are considering normal goods), and thus the consumption of most good
will increase. Here is the twist. To consume more goods, we must also spend time consuming these goods.
Consuming more goods means that we require more consumption time. This leaves less market time
available, so people supply fewer hours of labor.
This is the same answer we had before with the plain old income effect. It is a little different story, and you
should remember it, say on a test. If this does not seem that exciting or different, I agree. The action is in
the substitution effect.
Becker Substitution Effect
A higher wage rate means your time is more valuable. There are simultaneously two changes the
household will make as a result:
•
A wage increases causes less household production time and more market time.
Because market time is more valuable, the household will substitute away from home production time and
toward market time. The way to think of this is that are two ways to “produce household goods”. You can
“produce” them by using market time or you can produce them by using household production time.
Instead of cooking meals from scratch (time-consuming), you will buy them in a box. Instead of doing the
ironing at home, you will send things to the cleaners. In your books language, you have produced
commodities in a less time-intensive way. The result of the wage increase, then, is to have more market
times and thus work more hours.
•
A wage increase will also cause the household to substitute away from time-intensive
commodities towards goods-intensive commodities, freeing up time for market time.
Again, time is more valuable. Instead of driving 2 hours to climb a real rock at no charge, you could drive
5 minutes to the local gym and climb a fake rock for $20. Instead of driving across the county to
Grandma’s house, you will fly. Because time is more valuable, time-intensive commodities are more
costly, so people switching to less time-intensive consumption activities. This switch frees up time to
spend on market time, and thus more hours are worked.
At the end of the day, according to the Becker Substitution effect, a wage increase still leads to an increase
in hours of labor (just as it did with the plain old substitution effect). However, it does so through a
different path.
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Using Becker’s Model to explain differing labor force participation rates – but first the trends
We next won to attempt to use this model to explain broad trends in labor force participation. First the
trends, then the explanations.
LFPR Trends - Men versus Women
You need to recollect the general shape of this picture. Men’s LFPRs have been decreasing steadily while
women’s LFPRs have been increasing. The overall LFPR is rising, indicating that the decrease in men is
being more than offset by the increase in women. The picture below is similar but goes back further in
time.
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LFPR Trends - Men versus older men
The big thing to see here is that the biggest decline comes from older men, and to a lesser extent from men
aged 45-64. While the LFPR of younger men has decreased, the decrease is rather slow.
Explanations for Men’s LFPR Trends
If we take the stereotypical view men typically are inclined to specialize in market time (as opposed to
household time), then there is not a whole bunch of value in worrying about Becker’s model here. So
below, when I write income effect in the notes below, you can think of this as a plain old income effect or a
Becker income effect – it will not change the story or the answers. I will focus on the Becker model when
we get to women’s labor force participation rates in just a second.
1. Rising real wages and income
Wages have risen significantly between 1940 and 2000. Rising wages result in an income effect
and a substitution effect. The income effect says work less, while the substitution effect says work
more. The income effect seems to dominate for men. Your text suggests that declining health of
older men may change preferences of me to make men more like “leisure lovers”. This strikes me
as a fluffy story, as this allegedly occurred during times of sizable increases in life expectancy. If
it were right, this would push men to spend more time on leisure and less on labor.
2. Social Security and Private Pensions
The existence of a private pension is a pure income effect and greatly reduces the labor force
participation rate by increasing the probability of retirement. An increasing number of men had
pension plans during this period. At the same time, social security benefits were increasing faster
than wages, another income effect. Both tend to reduce LFPR. In addition, social security benefit
reduction that increase in labor earnings (just like the welfare question on the test) are a
substitution effect that reduces the likelihood of men working. There is debate if these benefit
reductions were significant.
3. Disability Benefits
The existence of substantial disability benefits (no work allowed) looks just like the pension and
hence is an income effect leading to retirement and lower participation rates. Of course, this
decision is only relevant if the nature of the disability still allows work. (If the person cannot
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work, the reason they are no longer in the labor force is because of the disability, not because of
the existence of generous disability benefits).
We saw previously, higher wage workers would be less likely to accept a pension or disability
payment than entails an agreement they no longer. Because black men on average are more likely
to be low wage earners than white men, black men would be more likely to have accepted the
disability benefits. Therefore, the existence of these generous disability benefits may help to
explain why the decrease in the LFPR of black men over the period is larger than the decrease for
older white men.
4. Life Cycle Considerations
Men’s wages (women’s too) reach a peak before retirement, usually just after 50 year olds. The
reason could be due to diminished mental or physical capacity diminishing, or perhaps that their
skills are becoming obsolete. Whatever the case, after this peak, wages will be decreasing. This is
a substitution effect and could reduce labor.1
LFPR Trends - Women versus older women
Check out picture cross-country comparisons of LFPR of women in your textbook. My stereotypical view
of Italian families involves wonderful meatballs being cooked at home by mom and adult (male) children
still living at home with mom. Are the men living there because she is not working? Or is mom not
working because she has to take care of her adult children? It’s hard to say.
There is not much happening with older women (those aged 65+). Their LFPR increases, but not very
rapidly. It seems to me that most of the LFPR increases are coming from younger and especially middle
aged women (45-64). The picture also suggests that most of increase in the LFPR of younger women
comes after 1960. Not pictured, but 2/3 of the increase in LFPR is from married women.
1
If you have been following closely, it seems as though the book (or me) is talking out of both sides of our
mouth. Earlier we claimed that income effects dominated for men, and by saying here that labor would
decrease as a result of the wage decrease, we are claiming the substitution effect dominates. I think we are.
I think this story here is swamped by the pensions and other more subtle pension effects going on.
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Explanations for Women’s LFPR Trends
Here is where worrying about Becker’s model pays some dividends.
1. Rising real wage rates for women
The Becker income effect of an increase in the wage results in fewer hours work, while the Becker
substitution effect results in more hours of labor. Looking at the data suggests the substitution
effect is dominating. Becker’s model tells us that women will spend more market time and less
time on household production. Why the increase in wage rates? One important reason we will
return to later is that women now have more education.
2. Changing preferences and attitudes
We could write a book here, and many have. Attitudes have changed since WWII. You can think
of women’s preferences toward work as changing. Think back to “leisure-lovers” and
“workaholics”. If women’s preferences toward work change to look more like the workaholics,
they will end up spending more time in the labor market. Your book also mentions antidiscrimination legislation (essentially raising wage - see above). There is a complex interaction
between education and work. It could be that women with better educations find they can get jobs
that are more desirable, or that women who desire to work go and get more education. Check out
the WWII propaganda below – the Hitler thing is just amusing to me.
3. Rising Productivity in the Household
Better technology and more capital lead to increased productivity and increased wages in the “for
pay” sector, but also increase productivity in household production. Becker’s model says in
increase in household productivity will free up time for the labor market (think of it as taking less
time to produce the same quantity of household goods). Freezers, microwaves, washers, dryers,
fast food, and supermarkets are just a few examples. Some people disagree about which caused
which. Did women want to work, and thus need appliances? Or did appliances show up enabling
women to have time to work? Freezers are a big deal.
4. Declining birth rates
Your text reports some data in births per childbearing age woman. In 1957 peak of the baby
boom, 3.8 births per women. Over the last 10 years, less than 2 births per women. Raising
children takes up time (household production time) and leaves less time for labor. Fewer children
means less home production time, meaning more market time. More recently, the presence of
young children has a smaller negative effect on women’s labor force participation rate than it did
40 years ago. This is due to the increasing availability and acceptance of daycare and perhaps
more flexibility from dad’s employer. Cheap effective birth control is mentioned here it is
important, giving some women additional control over how many children to have and when to
have them. Is this related to (5)?
The opportunity cost of having children increases as women’s wages rise. On average, higher
wage women have fewer children. So perhaps this really refers back to higher wages, changing
preferences, etc. But again, we are dealing with a complex relationship.
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I will give you one story to illustrate one of the many complications. Say there is a high wage job
available to women, but there is no flexibility in hours whatsoever and this job demands long
hours. Taking 12 months maternity leave or leaving 3 hours early on Friday because the child has
a doctor’s visit are not viable options. Say there is another job available, with much greater
flexibility, but this job pays a lower wage. If a woman were planning to have children, might she
be inclined to choose the second type of job? That is, might there be a wage / flexibility tradeoff
in occupations? And take it further, suppose the second occupation requires the woman to obtain
less schooling. Could women that are planning to end up in this second occupation rationally
choose to have less schooling from the get go? This is getting into something we will call human
capital theory, but more later.
On this topic, here’s an article a friend of mine sent me pointed out (in a bit more unusual
circumstance) that tradeoffs between work time and child raising time in an occupation near and
dear to my heart. When you read about, try to generalize to a broader household view and how the
choices might be different. I do not think it is the case that men do not have to choose as she
suggests.
http://chronicle.com/jobs/news/2006/02/2006021401c/careers.html
5. Rising Divorce Rates
Divorce rates increased substantially in the late 1970s and 1980s. It is claimed that with a higher
likelihood of divorce, women (or better still the family member that specializes in home
production) may participate in the labor market as insurance – so if they are divorced that have
labor market experience and labor market skills. From the view of one individual, their spouse’s
income is a source of non-labor income. If they are divorced and do not receive a toasty alimony
payment, there is a big reduction in their non-labor income. We of course predict that they are
more likely to work as result of this income effect. The specialization we get within a household
(stereotypically man working, woman household production) is no longer possible if the
household dissolves. The market time specialist will find themselves needing to devote more time
to household production (or purchase it), but it may be a bit tougher on the household production
specialist. Again, this is very complex.
6. Expanding Job Accessibility
So called “women’s occupations” such as nursing, administrative work, and teaching have
expanded over time. The places women work are more likely to be suburban than inner city, and
there has been a move to the suburbs. In addition, women are more likely to work part-time and
there has been an expansion of the number of part-time jobs over time.
7. Attempts to Maintain Living Standards
Male wage growth has been slow if not zero for many. If the family is attempting to maintain
some (self-determined) standard of living and the husband’s wage growth is slow, the story would
be that the women would work to pick up the slack and maintain the standard. This then would
explain the increase in women’s labor force participation rate. Think of this slow or zero wage
growth of the husband as a negative income effect (they are working to maintain a certain level of
income). Women work more.
Fuchs on relative importance of these causes – see text for more
Not so important:
•
•
•
Cause (2) - Anti-discrimination legislation – predated by increase in women’s LFPR
Cause (2) - Feminism movement – predated by increase in women’s LFPR. While you can argue
about the “feminism movement” per se, it is impossible not to agree that preferences have not
changed meaningfully, whether it be before, during, or after the “feminism movement”
proper.
Cause (7) - Stagnant wage growth – predated by increase in women’s LFPR
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Lecture 7
•
2/26/2007 1:12 PM
Cause (3) - Which came first – women’s participation, or the washer?
Important:
•
•
•
Cause (1) – Wages key.
Cause (6) – Availability of the job also of major importance.
Cause (4) – But again, complicated
There seems to be general agreement that wages, preferences, and job opportunities are important. I think
education has been important, birth control, and divorce also contributes, but it is difficult to disentangle.
LFPR Trends – White adult women vs. black adult women
Unfortunately, this picture does not go as far back for black women’s labor force participation rates. Black
women’s labor force participation rates used to exceed white women’s by a wide margin. This is not the
case now. Stare at the red line versus the pink line.
LFPR Trends – Black adult men vs. white adult men
See the data in the picture above. The blue and the black are the lines to focus on. Since the 1950s, there is
an increasing gap of LFPR between white men and black men. Why? Some of the explanations put
forward:
•
Lower wages – on average, black men have lower wages, and thus the substitution effects says
they will be less likely to work. (Substitution effect dominating)
•
Lower educational outcomes – on average, black men receive less schooling and lower quality
schooling.
•
Discrimination – for now, think of it as a tax, or just as a lowering of the wage.
•
Public income programs - blacks are disproportionately low income, therefore are
disproportionately represented on public assistance, and thus as a result of non-labor income
source, less like to work.
•
Health – black are disproportionately represented in physically demanding occupations and be
more likely to be disabled when they reach older ages. This is said to be an explanation of the
lower LFPR of black men above 55 (relative to white men).
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Lecture 7
•
2/26/2007 1:12 PM
High LFPR of black women – text suggests this, perhaps due to the fact that black women face(d)
less discrimination and thus have(had) better labor opportunities.
Other Trends – Hours of Work
More questions than answer. If you look at the picture (see your text), the hours per work steadily decline
from 1900 - WWII, but have remained steady since. The decline in hours makes sense with rising wages
and the income effect dominating. But why steady since then? The stories here are not very appealing.
The best story your text has is that people have increased their education levels quite a bit. As a result, the
jobs they can receive are no longer physically demanding unpleasant job, but rather are more desirable,
changing people’s preferences toward “workaholics”. The story would be changing preferences that
counteract the income effect that we expect with rising wages. They may even stick in that slow wage
growth rates for men story. It sounds a bit fluffy to me. In addition, the claim is that getting a bunch of
education in and of itself may change your preferences.
What should I read?
Chapter 3
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Physical Capital Analogy
In your previous classes, you may have been exposed to the decision making process of a firm considering
investing in a machine or project. The noteworthy characteristics were that the bulk (if not all) of the costs
of the investment project were incurred up front (now), while the stream of benefits (higher profits) came in
the future, by way of higher future sales or higher future profits.
Along the way, you no doubt talked about the time value of money (MATH 106). You learned that a dollar
today is more valuable than a dollar tomorrow. The other side of that same coin is that a dollar received in
the future is worth less than a dollar received now. As a result, to make accurate comparisons about the
feasibility or profitability of a potential investment project, there had to be “discounting” – a process by
which future dollars are turned into their current or present value. Only then can the costs (already in
current dollars) be compared to the benefits (now appropriately discounted into their current dollar
equivalent). This is where discounted present value and net present value came in.
The economic term for the machines, projects, tools, etc that are being invested in above scenario is
physical capital (or some times just plain out capital). Of course, this is labor economics class – why are
we talking about investing in machines?
Human Capital Theory - Introduction
The big insight of human capital theory is that any activity that increases the “quality of labor” may be
considered an investment in human capital. The one that leaps to mind is schooling. The costs are upfront, while the benefits (higher wages?) happen in the future. Human capital theory will treat expenditures
on education as an investment in human capital. The richness and beauty of this theory is that we do not
stop there. Formal education, on-the-job education, health, migration, job search, and even pre-school
nurturing of children can be viewed as investments in human capital.
More than usual, I encourage you to read over Chapter 4, again and again. Your text points out that $745
billion were spent in 2002 on elementary, secondary, and higher education. Investments in human capital
are huge, and we have not even mentioned the other categories, which admittedly ore more difficult to
calculate.
Some trends in Educational Attainment
The two lines are always the US as a whole, and just for fun, Louisiana. If you look at the picture above on
the left, you can see that that fraction of people who have been exposed to (some) elementary education has
risen drastically over time. While it seems as though there is less schooling at the end of the period, in fact
this is really because an increasing faction of the labor force has been exposed to (some) secondary
education (high school). This is illustrated on the right. This too begins to fall off after 1980, but in fact
what is happening is an increase as the fraction of the labor force that has been exposed to (some) higher
education (see below left). Finally, the average number of years of schooling is shown bottom (right).
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0
Average years of schooling
5
10
15
There is no denying that trend. There is also no denying the fact that Louisiana is less educated that the
average American. Interesting, LA has been catching up, particularly after 1960.
1850
1900
1950
2000
year
Average years of schooling - US
Average years of schooling - LA
Why should you be glad you are investing in human capital right now?
This picture is clipped out of your textbook and called an age-earnings profile, simply because it looks at
average wages for workers of different ages. Of course, the picture is divided into various education
categories. What you can see clearly is those people with a college education (on average) make much
more than those people with only a high school education. It turns out that things are a little more
complicated than simply “go to college earn more money”, but this picture sure is suggestive. Keep in
mind this is “on average”. As a 30 year old with 20+ years of education, this picture suggests I would be
putting more away bank than I do, but being a college professor has its perks. Think of my old friend from
grad school, Karim. My best guess is 28 years and no earnings. Something is happening though. We will
hold off on gender and racial differences.
Investment in Schooling – The Math
Say you are trying to decide to spend some money on a college education. What we will be interested are
the incremental costs of you decision and the incremental benefits of the decision. We will ignore things
that you have to pay whether or not you go to college or not. Take for instance room and board. You have
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to eat and live somewhere if you go to college, you have to eat and live somewhere if you go to college, so
we will not worry about room and board when we do the calculations.1
Costs:
(1) Direct or out of pocket costs – tuition, fees, books, supplies, parking permits
(2) Indirect or opportunity costs – foregone earnings you give up by not entering the labor force
Benefits:
(1) Higher future earnings
earnings
incremental earnings
indirect costs
0
18
22
direct costs
65
age
Complications – Time Value of Money
As mentioned above, a dollar of higher earnings in the future is not worth a dollar today. Think of this way
- would you give some $20,000 today if they promised to give you back $20,000 in 5 years? Of course
not.2 Likewise, you would spend $20,000 on your college education if you were going to receive an extra
$1000 in earnings every year for the next 20 years.
The point, as alluded to above, is that we have to “discount” those future earnings.
If you do not like doing math, take it on faith that the formula for converting benefits (or costs) that you
receive (or pay) in the future is given by
Vp =
Vn
(1 + i ) n
where
Vn
is some amount of money you receive (n years into the future)
1
If your room or board is more expensive in college than you would have otherwise experienced if you
hadn’t go to college, it would be correct to include “excess” room and board in your costs of going to
college. This is only strictly true if the room and board is of the same quality (a dubious assumption given
cafeteria found I have experienced).
2
If you think this a good deal, please bring me $20,000 and 10 of your friends who also think this is a good
deal. I am sure we can work things out. I am FDIC insured.
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Lecture 8
n
i
Vp
3/10/2006 8:34 PM
is the number of years into the future you receive this payment
is the interest rate
is the present dollar equivalent (present value) of the future benefits
For example, the present value of $100 you receive three years into the future when the interest rate is 10%
is:
Vp =
Vn
100
100
100
=
=
=
= $75.13
n
3
3
1.331
(1 + i )
(1 + 0.10)
(1.10)
For example, the present value of $2500 you receive seven years into the future when the interest rate is
11% is:
Vp =
Vn
2500
2500
2500
=
=
=
= $1204.15
n
7
7
2.076
(1 + i )
(1 + 0.11)
(1.11)
It also turns out that you can add up present values. If you wanted to know the present value of a bundle of
two payments, you simply add up the present value of each individual payment.
Book Example
(1) Earnings W/O class
(2) Earnings W/ class
(3) Direct cots of schooling
Year 0
$5000
$0
$1000
Year 1
$5000
$7500
$0
Year 2
$5000
$8000
$0
Year 3
$5000
$8500
$0
(4) Indirect cost of schooling
$5000
$0
$0
$0
(5) All Incremental Costs
$6000
$0
$0
$0
(6) All Incremental Benefits
$0
$2500
$3000
$3500
All Incremental Earnings
-$6000 $2500
$3000
$3500
Start with the story. Carl is going to take a class. The direct cost of the class (tuition) is $1000. The course
will take one year to complete, in which Carl will have no time to work. Carl could have earned $5000
during the year he took the class (you can see that from his earnings if he did not take the class). If he goes
takes the class, his wages will increase in year 1 (by $2500), year 2 (by $3000), and year 3 ($by 3500).
Carl will retire after three years. Suppose the interest rate is 0.10 (10%).
Start with direct costs, add on indirect costs to arrive at total costs. You arrive at $6000. Next, ask how
much of these costs are incremental costs. In this case, all $6000 are incremental costs, because they would
have been incurred if Carl had not taken the class.
Here’s where the book is a bit unclear, I fear. Since wages in year 1 would have been $5000 without the
class, and since they will be $7500 after the class, the incremental benefits are $2500 in year 1. Likewise,
$3000 in year 2 and $3500 in year 3. These are the additional benefits that would be enjoyed if Carl takes
the class.
Stick a negative sign on the costs, and we arrive at the last row.3
3
Sometimes the distinctions become a bit blurred. Some people like the mechanics, others like to cut to the
chase. What is important is arriving at the last row. If you skipped some steps or made up your own steps
and get to -$6000, $2500, $3000, $3500, you are fine. Also, see the homework solutions or you class notes
for an alternative way to make the comparison.
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Now we are ready to discount the future benefits and see how it comes out. If the current costs (already in
current dollars because they are paid today) exceed the discounted future benefits, it will not pay to go to
school. If the future benefits outweigh the currents costs, then it does pay to make the investment. In fact,
the rule for deciding if the investment is profitable will be to make the investment if the sum of
(discounted) incremental earnings is greater than zero.
You book changes notation on you just a bit, but letting En represent incremental earnings in year n.
E3
E2
E1
+
+
2
(1 + i ) (1 + i) (1 + i) 3
$2500 $3000 $3500
= −6000 +
+
+
=
(1.10) (1.10)2 (1.10)3
= −6000 +$2273 +$2479 + $2630 = $1382
V p = E0 +
This is a profitable investment. Holding everything else constant, Carl will be $1382 (current dollars)
better off if he takes the class.
Internal Rate of Return
Some people prefer to solve this problem with an alternative route. The idea is that is the discounted
present value of incremental earnings was exactly zero, you would be right on the razor’s edge between
investing and not investing. The idea is to find the interest rate where the discounted present value is in
fact zero, and to call this interest rate the internal rate of return (r). Then to decide if an investment is
profitable, you compare the actual interest rate (i) to the calculated internal rate of return (r).
Say the internal rate of return was 7.34% (r = 7.34%). This means the investment in human capital would
be profitable so long as the actual interest rate was less 7.34% (i < 7.34%). If was say 7%, you invest. If in
fact you did the present value calculation when i = 7%, you would find it the discounted present value of
incremental earnings is greater than 0. If i is more than 7.34%, you wouldn’t find it profitable.
There are some disadvantages to the internal rate of return compared to the discounted present value
approach. Finance majors know what I am talking about – net flow reversals, multiple roots. It is tricky to
calculate. But it has a nice interpretation and we’ll see a bit later.
If you pull out your calculator, or if you like to play on Excel, you should be able to find the IRR for Carl’s
problem above. Not so adventurous? It turns out the internal rate of return for Carl’s schooling investment
is 21.92%. At any i < 21.92 (say 10%) for example, the project is profitable. Do the calculation when i =
21.92, it will come out very near zero. Do it with a higher interest rate, it will be less than zero and hence
not profitable.
Extensions of Human Capital Investment Math
1.
Length of Income Stream – Ceteris paribus, the longer the stream of post investment incremental
earnings, the more likely the net present value of an investment in human capital will be positive.
If you are not sure why this is true, push back Carl’s retirement a year and give him $4000 in
incremental earnings in year 4, then have him retire. What happens to the present value of
incremental earnings? You should not have to do the math to answer this question, but you surely
can. Costs stay the same, while benefits increase. (I did the math – the answer is now $4113).
•
Why might men’s investment in human capital be associated with a longer income stream than
women’s investments in human capital? Based on this information alone, who would rationally
invest more in human capital – men or women? If more human capital is associated with higher
5
Lecture 8
3/10/2006 8:34 PM
earnings, who will have higher earnings as a result – men or women? Can you be sure that higher
earnings for men (compared to women) is discrimination?
•
Might young people’s investments in human capital be associated with a longer income stream
than older persons’ investments in human capital? What does this suggest about the age
distribution of college students?
•
Think of migration (moving) as an investment in human capital. It has costs up front (truck, gas,
realtors) and benefits in the future (higher earnings at the new job and location). What does
human capital theory say about who will be more mobile – young people or old people?
2.
Costs – Ceteris paribus, the lower the cost of a human capital investment, the larger the number of
people who will find that investment to be profitable.
If you are not sure why this is true, make Carl’s tuition $500 and recalculate. Or go the other way
and make Carl’s tuition of $5000 and recalculate it. You should not have to do the math to this
question either.
•
Subsidies for college loans – what happens to higher educational enrollment?
•
Increases in tuition – what happens to higher educational enrollment?
•
College enrollments are said to be countercyclical. Enrollments climb when the economy is doing
poorly, while they fall when the economy is doing well. How would human capital theory explain
that?
•
Might older people have higher opportunity costs of attending college (than say 18 years olds with
no work experience)? What does that imply about the age distribution of those people attending
college?
•
Who is more likely to take a college class? Someone who is paying out of their own pocket, or
someone who has their parent paying the bills? How about someone who is paying out of their
own pocket vs. their employer paying the bills? Expalin, using the framework of the human
capital model.
3.
Earnings Differentials - Ceteris paribus, the larger the college-high school earnings differential,
the larger the number of people who will find it profitable to invest in a college education.
•
My brother goes to college primarily to play baseball. He is a political science major. I went to
school primary to chase after money. I was an economics major. I would guess (I think he would
agree) that my incremental earnings are larger than his? Based on earnings differentials alone,
who is more likely to find school a profitable investment?
•
But wait, my brother really enjoy playing college baseball. For him, could the ability to play
college baseball be treated as an incremental earning?
•
Is it possible that someone would invest in college just to get a job that paid the same amount of
money (than the job they were working at previously), but had much more desirable working
conditions? How would you treat desirable working conditions in the context of the human capital
model?
•
How would you incorporate draft dodging in a human capital model?
6
Lecture 8
3/10/2006 8:34 PM
About these high school vs. college earnings differential – how much?
Caution: Again, these are averages.
Caution: If you take someone who cannot read and stick them in college calculus class, do you think their
earnings will increase by 57%? Along the same lines, frequently labor market studies show that married
men earn more than single men. Does this mean that if you run off to Vegas this weekend and get married
your earnings will increase? Hold off on booking those tickets.
What is next?
I had previously indicated I would update these notes. In fact, they are continued in Lecture 9.
What should I read?
Chapter 4.
7
Lecture 9
3/14/2007 11:09 PM
Internal Rate of Return, revisited
Last time, we did the math for Carl’s investment.
E3
E1
E2
+
+
2
(1 + i ) (1 + i) (1 + i) 3
$2500 $3000 $3500
= −6000 +
+
+
=
(1.10) (1.10)2 (1.10)3
V p = E0 +
= −6000 +$2273 +$2479 + $2630 = $1382
We claimed that in investment was profitable, as present value of incremental earning was larger than zero.
Carl comes out $1382 ahead (in terms of current dollars) by making the investment.
As mentioned earlier, we can calculate the internal rate of return. Recall the internal rate of return on an
investment is defined at the rate interest at which Carl would be indifferent between making the investment
and not making the investment. In Carl’s case, the internal rate on return from class is 21.92%. You can
interpret the internal rate of return as the maximum rate of interest that one could pay on borrowed funds
(to go to college) and still break even.
If i = 12%, Carl would find the investment profitable.
If i = 16%, Carl would find the investment profitable.
If i = 20%, Carl would find the investment profitable.
If i = 24%, Carl would find the investment not profitable.
It turns out economist are very much interested in the rate of return on schooling. Different studies and
different economists come up with different answers, but most find that rate of return on a year of college
as being between 10% and 15%.
It turns out those same three things that were important in determining the present value of incremental
earnings are important in determining the rate of return. It really just two sides of the same coin.
1.
2.
3.
As the length of the income stream increases, the internal rate of return increases.
As the costs of making the investment decrease, the internal rate of return increases.
As the college-high school wage gap increases, the internal rate of return increases.
How might the rate of return change as we go to more school?
We think the rate of return decreases as more and more schooling is attended.
Your textbook tells you two stories:
(1) Diminishing returns
(2) Falling Benefits, Rising Cost
I am not sure I like the way the textbook explains the first. Let me give you an example of a story that
would be about diminishing returns. Imagine college was only about learning languages. Suppose you
could master a language in one year. If you went to school for four years you would learn Spanish,
German, French, and Chinese. You would be a more marketable employee because of the knowledge of
these languages. In year 5, you would learn Portuguese. In year 12, you would learn some archaic Latvian
dialogue. In year 17 you would be spending your time at ye olde pub studying ye olde English, while in
year 18, you would be trying to figure out the difference between slang terms spoken in Bayou Blue vs.
Houma. The point is that the additional earnings associated with the knowledge and skills you are
acquiring would decrease.
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Lecture 9
3/14/2007 11:09 PM
The second part is just a rehash of what we have already discussed. If you got to school at age 18, done at
age 22, and will retire at 65, you have 43 years to recoup your investment. If you got to school for 8 years,
you are note done until 26, and thus will have only 39 years to recoup your investment. Each extra year of
schooling gives you more skills and increases your opportunity cost of not working and at the same time
reduces the number of years where you get the benefits from your increasing schooling. The net benefit of
another year of schooling is decreasing.
They both contribute, and it turns out the rate of return decreases as we attend more and more schooling.1
This does not mean that no person will want to go to school for 10 years, just that it must be the case that
even for these people, the return on the 11th year of schooling will be lower than the return on the 10th.
If we buy this, to keep things simple, we will draw a nice smooth downward sloping relationship between
the rate of return on an additional year of schooling and years of schooling.
rate of return (r%)
years of schooling
The demand curve for human capital
Now, as we noted before, we make investments in human capital if the rate of return on the investment is
larger than the interest rate.
We will assume that someone can borrow as much money as they want at a fixed interest rate to go to
school.2 This results in the supply curve of human capital being a horizontal line at this interest rate.
Consider initially the interest rate labeled i1. The first year of schooling has a rate of return that far exceeds
the interest rate, so the person will go to the first year of schooling. So is the second. This continues until
the point where the supply and demand curves intersect. We can conclude the person will invest in e1 years
of schooling. Any further investments in human capital will not be profitable, as the rate of return will be
smaller than the interest rate.
1
There is one important exception. The data suggests people who complete only 3 years of schooling earn
far less than people who complete 4 years of schooling. It would seem that rate of return on the 4th year of
schooling is larger than the rate of return on the 3rd year. The reason for this is related to something we will
call “signaling” or “screening” and will be discussed later. It will be ignored here for simplicity.
2
Even if you have the “cash” on hand before going to school, this interest rate is still pertinent. If you did
not use the money on school, you could have stuck the cash in the bank and earned interest on it. If you
knew college would only return 8% a year, and the interest rate was 10%, it would be wiser to forgo
college and earn the interest. In short, whether borrow or lending, there is still an opportunity cost of using
the funds.
2
Lecture 9
3/14/2007 11:09 PM
rate of return (r%)
S3
S2
S1
DHC
e3
e1
e2
years of schooling
We can follow similar logic if the interest rate was i2 or if the interest rate was i3.
•
What does the picture suggest will happen to college enrollment rates if interest rates go up?
•
What does this picture suggest will happen to college enrollment rates if Uncle Sam subsidizes the
interest rate on our college loans (reduces the rates)?
Ability Differences
When I refer here to ability, I mean ability defined broadly. Ability could be IQ, motivation, discipline,
etc. Stealing the example from the book, suppose there are two people named Adams and Bowen. It turns
out that Bowen is more able. It stands to reason that Bowen’s rate of return of schooling will be higher
than Adams rate of return for any given year of schooling. In the picture below, I have tried to illustrate
this point by comparing each person’s rate of return on an arbitrarily selected 6th year of schooling. You
should confirm that Bowen’s rate of return on year 6 is higher than Adams’, and this is true not only for the
6th year of schooling, but also for every year of schooling.
Given this, now see who invests in more schooling. We find, we find, not so unexpectedly I suppose, that
the more able worker (Bowen) invests in more human capital.
rate of return (r%)
S
DA
6
eA
DB
eB
years of schooling
Next, consider the impact that ability difference will have on earnings differences. We would expect just
based on their ability alone that high ability workers would have higher earnings than lower ability
workers. In addition, we have just seen that higher ability workers will invest in more human capital than
lower ability workers, which will increase their earnings further. Stated differently, the fact that higher
ability individuals will invest in more schooling than low ability workers will further widen the earnings
gap between high ability workers and low ability workers.
3
Lecture 9
3/14/2007 11:09 PM
Discrimination, a preview of coming attractions
Suppose the two people are of equal ability, but Adams faces discrimination, while Bowen does not. As a
result of the discrimination faced by Adams, his return to schooling will be lower, perhaps because he
receives lower wages than he would have absent discrimination.
Again, what we find is a double whammy. First, Adams will have lower earning directly as a result of the
discrimination. Second, since he rationally invests in less human capital than Bowen does, the earnings gap
will widen. Stated differently, that fact that the person who is discriminated against invests in less human
capital (than the person who is not discriminated against) further widens the earnings gap between the two.
Access to Funds
•
Suppose Bowen, due to financial connections, is able to borrow money at a low interest rate,
perhaps because his family can plunk down some collateral. Suppose Adams family has no such
connections and must borrow at a higher interest rate. Who invests in more schooling? Consult
the picture below.
rate of return (r%)
SA
SB
DHC
eA
eB
years of schooling
•
What might happen in the next generation? Since Adams did not invest in as much schooling, his
earnings will be lower, and he might be less able to provide financial resources to his children.
Could this turn into a viscous cycle? Might his children have to borrow at a higher interest rate?
•
Does this explain why Uncle Sam might attempt to provide low interest rates for everyone? Or
provide need-based scholarships?
•
Suppose that both Bowen and Adams have the same financial connections, but as a result of
discrimination in the lending market, Adams must pay a higher interest rate. What happens?
A word on capital market imperfections
Most loans of large amounts involve collateral. If you borrow $150,000 for a house, and you do not pay
back the money the lender can confiscate your house. If you borrow $25,000 for a car, and you do not pay
back the loan the lender can confiscate your car. If you do not pay back the money for your student loan,
can the lender confiscate you? Nope. This presents a bit of a problem for the lender.
A further problem is that when assessing the risk of lending money to anyone, lenders will want to know
about your credit history. But at age 18, the age where most people first go to college, lenders know very
little about you. It would be a risky loan from their point of view. Your lender does not know how you
will turn out. As a result, there is a chance that lenders would not want to loan you money at all, or if they
did, would want to charge a high interest rate to compensate them for the risk. Think of it this way – how
many credit card offers did you get when you were 18 with a $100,000 credit limit?
Of course, with high interest rates, few people would find it profitable to invest in schooling.
4
Lecture 9
3/14/2007 11:09 PM
My guess if you were accepted to Harvard, some lender might rightfully think you are a low-risk loan. My
guess would be absent government intervention (more in a bit), Harvard student might not have too much
trouble borrowing. But what about LSU? Nicholls? Delgado? Further, the parents of student who get into
Harvard tend to much more affluent, on average, that the parents of students who get into NSU. Harvard
students would be much more likely to get support from family than LSU and Nicholls students.
This above is an argument for why Uncle Sam subsidizes and guarantees student loans. The argument is
that the capital market (the market for lending and borrowing money) cannot really solve this problem and
lend money to student unless Uncle Sam comes in. The people who benefit the most, in some sense, are
the people who would be least likely to get the loans.
Another reason why Uncle Sam may subsidize student loans is that the social returns to schooling might be
larger than the private returns to schooling. There might be benefits that accrue to people other than the
person deciding on whether or not to go to school.
(1)
(2)
(3)
(4)
People who go to college are less likely to collect unemployment benefits in the future
People who go to college might be more informed participants in the democratic process
People who go to college might find cures for cancer or other things that would benefit society
People who go to college might have more resources to provide for their children
When people decide to go to college, they would only look at their private return to schooling. But from a
societal level, we would want to consider the social return. We would include the private return on and
these items listed above. Subsidizing college education would lower the private costs of investing in
schooling and induce more schooling investment.
At the end of the day, as someone who has benefited substantially from government subsidies on higher
education, I say “Yeah for subsidies”.
On – the – Job Training
General training refers to the creation of skills or characteristics that are equally usable in all firms and
industries. Example would include learning to drive a truck, general accounting and bookkeeping
knowledge, math skills, computer skills.
Specific training refers to the creation of skills or characteristics that can be used in only the particular
firm that provides the training. Examples would include specific information about the pharmaceutical
trials for Viagra for someone who is a sales rep for Viagra. If you go to some other company and start
selling Paxil, this knowledge is no longer valuable. Detailed knowledge of a proprietary computer system
that is only used by one firm, or working on lecture notes for a class that is only offered by one college.
To discuss the economics of training, we have to introduce some terminology that we be further expanded
in lecture 10. We call the firm’s marginal revenue product (MRP) the increase in firm’s total revenue
associated with employment of a given worker. The idea is that firms hire workers to make stuff. The firm
then sells that stuff. The value to the firm of hiring the worker is dollar amount of the stuff that worker
produces. Think of it as the value of the workers productivity.
General Training
First, consider the productivity path of a worker with no training. If they receive no training, their
productivity will never change (MPRU). The firm will have to offer them a wage that is commensurate
with their productivity; else the worker will go to another firm that does (WU). As a result, both the wage
of the work and the time path of their MRP will be flat.
Next, consider the productivity path of a worker who undergoes training (MPRT). During the training
period, the workers productivity will fall because the worker will be using time that previously was for
5
Lecture 9
3/14/2007 11:09 PM
“producing” on learning new skills. The worker will have their nose in a book or be in a classroom instead
of being on the line or producing. After the training period, the worker will have more skills and thus be
more productive. See the picture below. MRP is first lower than a worker who underwent no training, but
after the training period exceeds the MPR of a worker that underwent no training.
Next, consider what happens to wages of a worker who undergoes training (wT). Since the training the
worker receives in general, it is valuable to all employers. Can the firm get away with paying the worker a
wage that is less than their MRP after the training? The answer is no, because the worker would be able to
go to another firm that will. As a result, the firm will find it has to pay the worker commensurate with their
skill level after the training.
But, surely, the firm is not in the business of handing out free training for employees. The firm knows that
the workers productivity will be lower during the training period. So the firm will only pay workers that
level of their (lower) productivity during the training period. The firm does not pay for training it all.
Think of this reduction in wages as equivalent to taking the workers “off the clock” when they are learning
general skills at work.
The worker “pays” for training by having to accept a lower wage during the training period.
From the employee’s perspective, the tradeoff is lower wages during the training period in exchange for
higher wages in the post-training period. Looks just like the investment in schooling picture, doesn’t it?
wage, MRP
WT = MRPT
wU = MRPU
Training period
Post - training period
Time
Specific Training
Start again with someone who does not undergo training. Their productivity (MRPU) and their wage (wU)
will both be flat, just as before.
Next, consider the productivity path of a worker who undergoes training (MRPT). Just as before, during the
training period, the workers productivity will fall. Just as before, after the training period, the worker will
have more skills and thus be more productive. See the picture below. MRP is first lower than a worker
who underwent no training, but after the training period exceeds the MRP of a worker that underwent no
training.
Next, consider what happens to wages of a worker who undergoes training (wT). Since the training the
worker receives in specific, it is valuable to only the present employer. Can the firm get away with paying
the worker a wage that is less than their MRP after the training? The answer is yes, because if the worker
6
Lecture 9
3/14/2007 11:09 PM
tried to go to another firm, they would be treated as an untrained worker at the new firm (the training they
have is not valuable to this new firm). The current firm (the one doing the training) can pay them the same
wage that it would pay an untrained worker after the training.
But if the worker will not receive a higher wage in the future, will they agree to accept a lower wage during
the training period? Certainly not. They will have to be paid just as much as they would have earned if
they were an untrained worker. The wage the trained worker will receive will follow the same path of the
wages that untrained worker receives.
So with specific training, it is the firm that “pays” for the training. Think of it as being as if workers
are “on the clock” while they are learning the specific skills.
Now, the investment decision is being made from the firm’s point of view. Should the firm “spend” the
money up front on training in exchange for the benefits of more productive workers?
wage, MRP
MRPT
wU = MRPU = wT
Training period
Post - training period
Time
One more twist on specific training
Consider the incentives of the firm providing the specific training above. It pays the cost of training up
from and gets the benefits (gap between MRP and wages) down the road. As we know, if the length of the
future income stream is longer, it is more likely the investment will be profitable. If firms are constantly
training new workers who leave immediately, it would be all costs and no benefits. The firm may want to
do something to improve retention and reduce turnover.
One thing it could do is offer a slight wage increase after the training period. Now the worker would have
an additional incentive to say, as they would be earning a slightly better wage at the current firm than they
could earn at another firm. This is called an efficiency wage. It would reduce the MRP wage gap, but may
increase the average amount of time an employee would stay (make the box longer).
7
Lecture 9
3/14/2007 11:09 PM
wage, MRP
MRPT
wT
wU = MRPU
Training period
Post - training period
Time
Criticism of Human Capital Theory
1.
Investment or Consumption?
Some critics suggest that not all expenditures on college are purely for investment purposes. Think of that
class you took on the history of baseball, English literature, or astronomy. Are these really going to
provide you with skills that will increase your wage?
If this is the case, and some of what was classified previous as investment is really consumption, then only
a fraction of the expenditures on college should be included in the math when we determine if the
investment if profitable.
By doing so, the true rate of return on college is actually higher than economist would estimate. We get the
same increase in earning with a smaller “true” cost of going to college making college investments more
profitable. The rate of return that economist estimate for schooling is understated.
2.
Ability
It is clear that higher ability people are more likely to go to college. Critics here claim that the increased
earnings we see of college graduates not only reflect the increase in earnings that are caused by college
proper, but also are because we are looking at a more able group of people in general. They suggest that
rate of return that is estimated by economist wrongly attributes all of the increased earning to college,
where in fact a portion is really ability. As a result, the rate of return that economists measure is overstated.
On this note, there is an interesting box in your text about identical twins.
3.
Screening
As previously mentioned in a footnote is these notes, people who completed four years of college earn
quite a bit more than people who completed three years of schooling. You could claim that you learn a lot
during your senior year with all those upper level classes. And yet when I think back to my senior year of
college and the skills I acquired, many of them seem to revolve around learning to drink (more responsibly)
and how to bounce ping pong balls into cups. The story with the screening criticism is that college is not so
much about learning and knowledge and skills per se, but is a cheap way for prospective employers to
screen applicant workers. By seeing that Sally has a college degree, they see Sally as a smart and hard
working dedicated person. Gong to college is sending a signal that you are a productive smart worker. I
think there is something to this criticism.
8
Lecture 9
3/14/2007 11:09 PM
From a personal perspective, this is not going to change the rate of return on schooling. Whether you got a
15% rate of return from going to college because you were screened or because you are more
knowledgeable, it is still a 15% rate of return. It is not the reason why you got the return that is important,
it is that you got the return.
But from a social perspective, it is a bit different. Is it wise to spend all this time and effort on “college” if
all it is doing is screening? Would there be a less wasteful way to do the screening? Should Uncle Sam be
in the business of subsidizing college education if this is all that is going on?
It is clear that it is not the only thing going on with college, but there is something here.
What should I read?
Chapter 4
9
Lecture 10
3/21/2007 7:11 PM
Demand for Labor
So far, we have been focusing exclusively on the supply for labor. We want to turn out attention to the
demand for labor. The demand for labor is a bit peculiar compared to many of the demand curves you have
learned about previously. The demand for labor is called a derived demand, because it is derived from the
product or service that it is helping make.
If you are an autoworker, it is good news for you if the demand for autos increases. This in turn will
increase the demand for autoworkers. However, if you are a textile producer and the demand for textiles
decreases, this will result in a reduction in the demand for textile workers. Looked at differently, if the
only skill you have it to repair 8-tracks, and no one needs repair services for their 8-tracks, you will be out
of luck. The demand for your labor services depends on the demand for the product you help produce.
Two important factors determine the demand for labor. The first is the productivity of labor in producing
the product. The second is the market value of the item being produced. Of course, along the way we will
have to introduce some terminology. You will also have to learn a bit about production functions.
Short Run Production Function
A production function is a mapping between amounts of input and amount of outputs. Your book calls it
a relationship between the quantity of resources and the corresponding production outcomes.
We will assume that there are two types of inputs: labor and capital. Labor of course is the human effort.
Capital is the machines, tools, buildings, factories, vehicles, and other man-made aids to production.
We will focus for a while on the short run production function. The short run is defined as the period in
which at least one resource is fixed. In the short run, we assume the amount of capital is fixed. Why? It is
not easy to increase the size of a factory overnight, or to double the size of a restaurant, or stick in a new
grill. These changes take time.
On the other hand, it would be much easier to increase the amount of labor quickly. More hours, overtime,
call up a few more workers. We call labor the variable input.
Notation
When you book begins talking about production functions, you will see the following notation:
TPSR = f ( L, K )
TP stands for total production (the amount of stuff produced), while the SR stands for short run. L stands
for labor, while K stands for capital. The bar above the K serves to remind us that we are assuming the
amount of capital is fixed in the short run. The f stands for “is a function of”. The idea here is just that the
amount of stuff a firm will be able to produce is a function of (or depends on) the amount of labor and
capital the firm has at its disposal. More labor, more stuff. More capital, more stuff.
Example, Production Function
Consider the first two columns of the table below. They would represent a production function. For a
given the quantity of labor, it tells us the amount of total output that can be produced. I have stolen the
numbers out of the textbook with only a slight modification. The patterns are typical of what would be
expected of a firm. I have also drawn a picture of the production function.
1
Lecture 10
Total
Product (TP)
0
1
3
7
15
27
36
42
45
46
50
Total Product
Units of
Labor (L)
0
1
2
3
4
5
6
7
8
9
3/21/2007 7:11 PM
40
30
20
10
0
0
2
4
6
8
10
Labor
Marginal Revenue Product
The next step is to calculate the marginal product. The marginal product is the increase in total
production associated with each one-unit increase in labor. For example, because we can produce 7 things
with 3 units of labor, and because we can produce 15 things with 4 units of labor, it must be the case that
the marginal product of the 4th unit of labor in 8 things. Likewise, the marginal product of the 9th unit of
labor is only one unit of production.
Units of
Labor (L)
Total
Product (TP)
0
1
2
3
4
5
6
7
8
9
0
1
3
7
15
27
36
42
45
46
Marginal
Product
(MP)
-1
2
4
8
12
9
6
3
1
Next, we need to know the price of the good that is being produced. For now, let us assume this firm is a
perfectly competitive seller of its good. It takes the price as given and outside of its control. Under these
conditions, the firm may sell as much as it wants at the market price. In this case, suppose the price is
given as $2, regardless of how much output is produced.
Using this new information we can we calculate the total revenue of the firm. Total revenue is simply
equal to output * price.
2
Lecture 10
3/21/2007 7:11 PM
Units of
Labor (L)
Total
Product (TP)
0
1
2
3
4
5
6
7
8
9
0
1
3
7
15
27
36
42
45
46
Marginal
Product
(MP)
-1
2
4
8
12
9
6
3
1
Price (of
output good)
-$2
$2
$2
$2
$2
$2
$2
$2
$2
Total
Revenue
(TR)
$0
$2
$6
$14
$30
$54
$72
$84
$90
$92
Next, we calculate marginal revenue product (MRP). This is the same thing we alluding to when we
discussed on the job training. MRP is literally the change in total revenue associated with a one-unit
increase in labor. For example, when we hire 2 units of labor, we get $6 of total revenue. When we hire 3
units of labor, we get $14 of total revenue. Therefore, the MRP of the 3rd unit of labor is $8.1
Units of
Labor (L)
Total
Product (TP)
Marginal
Product
(MP)
Price (of
output good)
Total
Revenue
(TR)
0
1
2
3
4
5
6
7
8
9
0
1
3
7
15
27
36
42
45
46
-1
2
4
8
12
9
6
3
1
-$2
$2
$2
$2
$2
$2
$2
$2
$2
$0
$2
$6
$14
$30
$54
$72
$84
$90
$92
Marginal
Revenue
Product
(MRP)
-$2
$4
$8
$16
$24
$18
$12
$6
$2
It is a good time to take a break and develop some intuition on MRP. Think about what saying the MRP of
the 4th unit of labor is $16 means. We know the 4th unit of labor resulted in 8 extra things being produced.
We now know that those 8 extra things could be sold for $2 a unit, thus the 4th unit of labor resulted in $16
extra revenue to the firm. The idea is to translate the workers productivity into dollars.
How does the firm decide how much labor to hire?
Like any economic decision, we compare the costs and the benefits. When benefits are higher than costs,
we expand the activity. We continue until this is no longer the case.
The benefit to the firm of hiring another worker is that the worker produces stuff, which is then sold,
generating revenue for the firm. We just learned that the amount each worker adds to the firm’s total
revenue is called the marginal revenue product.
1
In class, we skipped this step, and to be honestly, I was being a bit sloppy. The algorithm that will never
go wrong is to calculate total revenue, and then calculate marginal revenue product, as is illustrated in the
notes above. It turns out for a perfectly competitive firm, there is a bit of a shortcut, as MRP = P * MPL.
So we could have (and did in class) calculated MRP this way. For a firm that is not perfectly competitive,
this short cut will not work. Again, the safe way is to calculate TR and then calculate MRP.
3
Lecture 10
3/21/2007 7:11 PM
The cost to the firm of hiring another worker is that the firm must pay the worker a wage. The amount a
worker adds to total costs is called marginal wage cost and is defined as the change in total cost associated
with a one-unit increase in labor. For today, we are going to make the simplifying assumption that our firm
is what is called a “wage-taker”. This means the firm takes the market wage as given. It can hire as much
labor it wants at this wage (W).
In general, the firm will hire labor as long as the MRP ≥ MWC. Since our firm is “wage-taker”, our
firm will hire labor until the MRP ≥ W.
One more complication
It turns out that the firm would never willingly operate on the part of its production function where the MP
is increasing. As a result, when considering the firms decision, we will only have to worry about the part of
the production function where the MP is decreasing.2 See the footnote below for the details.
Units of
Labor (L)
Total
Product (TP)
Marginal
Product
(MP)
Price (of
output good)
Total
Revenue
(TR)
0
1
2
3
4
5
6
7
8
9
0
1
3
7
15
27
36
42
45
46
-1
2
4
8
12
9
6
3
1
-$2
$2
$2
$2
$2
$2
$2
$2
$2
$0
$2
$6
$14
$30
$54
$72
$84
$90
$92
Marginal
Revenue
Product
(MRP)
-$2
$4
$8
$16
$24
$18
$12
$6
$2
How much labor will the firm hire?
At least, we have all of the information we need.
Suppose the market wage is $11. How many units of labor will the firm hire?
First, compare the MRP to the wage for the 5th unit of labor. Hiring an additional unit of labor
will result in $24 extra revenue for the firm and will only cost the firm $11 in wages. Should the
firm hire the 5th unit of labor? The answer is yes.
Repeat for the 6th unit of labor, which is also profitable, for the MRP of the 6th unit is $18, again
the wage is only $11.
2
Suppose the firm were to find it profitable to hire the 1st unit of labor (because MRP > W). If the firm
were on the upward sloping portion of the MP curve, we know that MP, and hence the MRP of the 2nd unit
of labor will be larger than the MRP of the 1st unit. What this means is that hiring the 2nd unit of labor will
provide more additional revenue that hiring the 1st unit of labor did. Because we pay the 2nd unit of labor
the same wage the 1st unit of labor is paid, the 2nd unit of labor is more profitable for the firm that the 1st.
So long as we are still on the upward sloping portion of the MP curve, the firm will find each additional
unit of labor more profitable that the last, and will want to continue hiring labor. Eventually, we will find
that MP will begin to fall, and each additional unit of labor will be less profitable, and only then will the
firm stop hiring labor. Since the firm will never “stop” on the upward sloping portion of the MP curve, we
can ignore this portion, and focus on the downward sloping portion of the MP curve.
4
Lecture 10
3/21/2007 7:11 PM
Repeating once again for the 7th unit of labor, it is also profitable, as the MRP ($12) exceeds the
wage ($11).
However, the 8th unit of labor is not profitable. Hiring the 8th unit of labor will enable only three
additional units of output to be produced, resulting in an additional $6 worth of revenue (MRP =
$6). This worker will have to be paid $11. The firm would be losing money if it hired the 8th unit
of labor.
Suppose the market wage is exactly $6.
In this case, the 5th, 6th, and 7th units of labor are profitable. While technically, the firm would be
indifferent about producing the 8th unit of labor (because MRP and W are both $6), let us go ahead
and produce this last one. We know the firm will not produce the 9th as MRP is $2 and the wage is
$6. So when W = 6, the quantity of labor hired is 8.
Confirm these:
If the market wage is $24, you will find the firm will hire 5 units of labor.
If the market wage is $12, you will find that the firm hires 7 units of labor.
What should I read?
Chapter 5.
5
Lecture 11
3/21/2007 7:11 PM
The demand curve for labor is the MRP curve
Units of
Labor (L)
Total
Product (TP)
Marginal
Product
(MP)
Price (of
output good)
Total
Revenue
(TR)
5
6
7
8
9
27
36
42
45
46
12
9
6
3
1
$2
$2
$2
$2
$2
$54
$72
$84
$90
$92
Marginal
Revenue
Product
(MRP)
$24
$18
$12
$6
$2
First, draw a picture of the MRP curve (and ignore the first few units where MRP is increasing). We will
plot MRP on the vertical axis and the quantity of labor on the horizontal axis. See the picture below on the
left. Try not to look at the picture on the right for a moment.
Now, go back, pick some wages, and see how much labor the firm will hire.
Suppose the wage is $24, how much labor will the firm hire?
Suppose the wage is $18, how much labor will the firm hire?
Suppose the wage is $12, how much labor will the firm hire?
Suppose the wage is $6, how much labor will the firm hire?
Suppose the wage is $2, how much labor will the firm hire?
5 units
6 units
7 units
8 units
9 units
$30
$30
$25
$25
$20
$20
wage
MRP
Finally, plot the wages we just selected above and the quantity of labor hired. See the picture below and to
the right.
$15
$15
$10
$10
$5
$5
$0
$0
4
6
8
Quanity of Labor
10
4
6
8
10
Quanity of Labor
Of course, the point is that the MRP curve is the same information as the demand curve for labor.
Why is this important? Things that affect the marginal revenue product will also then affect the demand
curve for labor. We know the two things that affect the MRP are the productivity of labor and the price of
the good being produced. Therefore, we know two things that affect the demand curve for labor.
Determinants of Demand for Labor
1.
Product Demand – A change in the demand for the product that a particular type of labor is
producing, ceteris paribus, will shift the labor demand curve in the same direction.
Say we consider an increase in product demand. This will cause the price of the good to rise. While the
productivity of workers has not changed (MP is unchanged), the value of the good they are producing has
increased, and thus the MRP of the worker has increased. As we now know, an increase in the MRP means
1
Lecture 11
3/21/2007 7:11 PM
there has been an increase in the demand for labor. Thus we conclude that an increase in product demand
leads to an increase in the demand for the labor (that produces that product).
We can see this from doing the math. Go back to our original example, but now increase the price of the
good to say $3, recalculate TR and MRP, and then redraw the graph.
Labor
5
6
7
8
9
TP
27
36
42
45
46
MP
12
9
6
3
1
P
$2
$2
$2
$2
$2
TR
$54
$72
$84
$90
$92
MRP
$24
$18
$12
$6
$2
TP
(no change)
27
36
42
45
46
MP
(no change)
12
9
6
3
1
P'
$3
$3
$3
$3
$3
TR'
$81
$108
$126
$135
$138
MRP'
$36
$27
$18
$9
$3
$60
$50
DLABOR
wage
$40
$30
DLABOR'
$20
$10
$0
4
6
8
10
Quanity of Labor
Likewise, a decrease in product demand will lead to a decrease in the demand for labor. If you get very
bored, change the output price to $1, update the chart above, and draw the demand curve for labor. You
will see it has shifted to the left.
2.
Productivity – Assuming that it does not cause a fully offsetting change in product price, a
change in the marginal product of labor (MP) will shift the labor demand curve in the same direction.
Start again with the original example. Suppose we consider an increase in productivity. To be more
specific, suppose each amount of labor is now able to increase twice as much output. Continuing with the
math, this will result in a doubling of the marginal product of labor. Finally, MRP also increases by a
factor of two. See the picture below. The result of an increase in productivity is an increase in the demand
for labor.
Labor
5
6
7
8
9
TP
27
36
42
45
46
MP
12
9
6
3
1
P
$2
$2
$2
$2
$2
TR
$54
$72
$84
$90
$92
MRP
$24
$18
$12
$6
$2
TP'
54
72
84
90
92
MP'
24
18
12
6
2
TR'
$108
$144
$168
$180
$184
MRP'
$48
$36
$24
$12
$4
2
Lecture 11
3/21/2007 7:11 PM
$60
$50
DLABOR
wage
$40
$30
DLABOR'
$20
$10
$0
4
6
8
10
Quanity of Labor
Likewise, a decrease in productivity will result in a decrease in MRP and a decrease in the demand for
labor.
3.
Number of Employers – Assuming no change in employment by other firms, a change in number
of firms employing a particular type of labor will change the demand for labor in the same direction.
An increase in the number of firms will increase the demand for labor, while a decrease in the number of
firms will decrease the demand for labor.
4.
Changes in the prices of other resources – We will come back to this in a bit. For now, make a
couple of notes (explanation to follow). The other resource we will concentrate on is the price of capital.
If capital and labor are gross substitutes, then a change in the price of labor will cause the demand for
labor to change in the same direction.
A decrease in the price of capital will cause a decrease in the demand for labor.
An increase in the price of capital will cause an increase in the demand for labor.
If capital and labor are gross complements, then a change in the price of labor will cause the demand for
labor to change in the opposite direction.
A decrease in the price of capital will cause an increase in the demand for labor.
An increase in the price of capital will cause a decrease in the demand for labor.
Short Run vs. Long run demand for labor
Recall that thus far, we have considered only a short run production function and the short run demand
curve for labor. Recall that we have assumed that in the short run, the amount of labor hired is variable
while the amount of capital is assumed to be fixed.
This means in the short run, the firm has only one option to produce more or less – that is to hire additional
labor of hire less labor.
In the long run, the firm can increase or decrease the amount of capital. The notation in the book is as
follows:
TPLR = f ( L, K )
3
Lecture 11
3/21/2007 7:11 PM
Keep in mind that firms will be able to produce output with various combinations of capital and labor.
Consider that the output being produced is “digging holes”. There are various ways we could dig holes.
Suppose there are only three options, listed below:
Option 1 – give 1000 people each a tablespoon
Option 2 – give 10 people each a shovel
Option 3 – given 1 person a backhoe
large amount labor, low amount capital
medium amount labor, medium amount capital
low amount of labor, high amount of capital
Surely, the prices of labor and capital will influence the choice of the firm. If labor is cheap relative to
capital, the firm might choose option 1, while if labor is expensive relative to capital, the firm may choose
option 3. We will return to this in a just a second.
To aid our thinking about what is happening in both the short run and in the long run, we will find it useful
to think about the output effect and the substitution effect.
As it relates to labor demand, the output effect is the change in employment (units of labor) resulting
solely from the effect of a wage change on the employers’ cost of production.
Consider a wage decrease. We know from Econ 211 then when the firm’s costs of production decrease, the
firm will expand output. Since wages are portion of production costs, a wage decrease will cause the firm
to expand output. To expand output, the firm will want to hire more units of labor (and capital) to produce
this extra output. Thus, according to the output effect, a decrease in wages will lead to additional units of
labor hired.
Following a similar logic, a wage increase will increase the costs of production, lead to less output and less
labor hired.
As it relates to long-run labor demand, the substitution effect is the change in employment resulting solely
from a change in the relative price of labor, output being held constant. Keep in mind this type of
substitution can only occur in the long run (as the amount of capital is assumed to be fixed in the short run).
If the wage decreases, the firm will substitute toward using more labor, as labor is relatively cheaper. Thus
according to the substitution effect, a wage decrease will result in more labor being hired.
If the wage increases, the firm will substitute toward using more capital and will use less labor as labor has
become relatively more expensive. Thus, according to the substitution effect, a wage decrease will result in
less labor being hired.
Finally, we want to compare the long run labor demand curve to the short-run labor demand curve.
Consider for each, a decrease in the wage.
In the short run, the output effect suggests that there will be an increase in labor. In the picture below, the
output effect is illustrated by the move from a to b.
In the long run, there will be an additional substitution effect, shown below as the move from b to c. The
change in the quantity of labor hired will be larger in the long run that it was in the short run.
4
Lecture 11
3/21/2007 7:11 PM
wage rate
a
w1
c
b
w2
DSR
Q
Q1 Q2
DLR
Quantity of Labor
If you remember your elasticities from Econ 211, this means the long run demand curve for labor is more
elastic than the short run demand curve. If you do not, it is ok to think of the long run demand for labor as
being more sensitive to a given wage change or at the very least, note that long run demand curves are
flatter than short run demand curves.
The price of capital revisited
Suppose the price of capital decreases. Because there is a decrease in the costs of production for the firm,
there will be an output effect. The firm will wish to produce more output. As a result, the firm will hire
more labor. But, there is also a substitution effect associated with a decrease in the price of capital. Since
capital is relatively less expensive, the firm will substitute away from labor towards capital, and hence the
firm will less labor. Which wins?
If the substitution effect is larger than the output effect, we say that capital and labor are gross substitutes.
This means the substitution effect dominates the output effect.
If the substitution effect is smaller than the output effect, we say that capital and labor are gross
complements. This means the output effect dominates the output effect.
If capital and labor are gross substitutes:
Price of capital
Increase
Decrease
Output Effect
Labor decreases
Labor increases
Substitution Effect
Labor increases
Labor decreases
Overall Effect
Labor increases
Labor decreases
Substitution Effect
Labor increases
Labor decreases
Overall Effect
Labor decreases
Labor increases
If capital and labor are gross complements:
Price of capital
Increase
Decrease
Output Effect
Labor decreases
Labor increases
Go back up to the top of page 3 and check out that section again. Don’t forget that the end we are trying to
achieve here is what happens to the demand for labor. For instance a test question might be:
Suppose capital and labor are gross complements. Suppose the price of capital increases. What happens to
the demand for labor?
You would reason that an increase in price of capital leads to an output effect. An increase in the
price of capital will increase the costs of production and result in less output. Less labor will be
hired.
5
Lecture 11
3/21/2007 7:11 PM
You would also reason that an increase in the price of capital leads to a substitution effect. An
increase in the price of capital will lead to substitution away from capital and towards labor. More
labor will be hired.
Finally, you would reason that because you were told that capital and labor are gross
complements, the output effect dominates the substitution effect. The net results will be that less
labor will he hired. That is, there is a decrease in the demand for labor.
What types of labor and capital might be gross substitutes and what types might be gross complements?
Consider a crane as the capital and a crane operator as the labor. In this case, there is a natural
complementarity of the capital and the labor. One crane needs one crane operator. There still needs to be
someone pulling the levers. We would expect cranes and crane operators to be gross complements. As a
result, a decrease in the price of cranes will lead to an increase in the demand for crane operator labor.
Another example here would be x-ray machines and x-ray readers.
Consider an elevator as the capital and an elevator attendant as the labor. Here, it would seem that capital
and labor would be quite substitutable. We can either run elevators with a computer and some shiny
buttons or an actual person. Here, a decrease in the price of “elevators” will result in a decrease in the
demand for elevator attendants. Another example here would robots and some types of car assemblers.
What should I read?
Chapter 5.
You will find I have skipped over a few items. Do not worry about
•
•
•
The stages of production
The short run demand for labor for an imperfectly competitive seller
Elasticity of Labor demand
Do check out the real world examples at the end of the chapter
6
Lecture 12
3/26/2007 1:17 PM
Perfectly Competitive Labor Market
We start by considering the perfectly competitive labor market. The assumptions are:
•
•
•
•
Large number of firms with identical jobs
Large number of qualified people with identical skills
Wage taking behavior – both firms and workers
Perfect information and costless mobility
Because there are a large number of buyers and sellers of labor acting independently, no single firm and no
single worker can exert any influence on the market wage. The last assumption concerning information
and mobility suggests that the adjustment process to a new equilibrium will be rapid.
The goal of this lecture is to do these four things:
1.
2.
3.
4.
Learn to combine individual supply curves into the market supply curve for labor
Learn to combine individual demand curves into the market demand curve for labor
Review the things that affect labor supply and labor demand.
Comparative statics in the labor market
Market Supply of Labor
Recollect from back in chapter 3 that each person’s individual labor supply curve has a backward bending
portion. We learned before that associated with a wage increase is a substitution effect that induces the
individual to work more and an income effect that induces the individual to work less. At low wages, the
substitution effect dominates while at high wages the income effect dominates.
We first need how to combine individual labor supply curves into the market supply curve. Then, given
that each individual supply curve is backward bending, we must figure out whether or not the market
supply curve for labor also has a backward bending portion.
While hopefully you recall from Econ 211 or Econ 255, the process to combine individual supply curves
into market supply curves is called horizontal summation. The general idea is to a pick a certain wage,
and then see how much labor each individual would choose to supply at that wage. We add up each
individual’s quantity of labor supplied at that wage and call the result the market quantity supplied. Simply
repeat for all other wages until the market supply curve is traced out.
For example, at a wage of $1, only person A and B participate in the labor market. Person A supplies 4
units of labor, while person B supplies 6 units of labor, and thus the total number of units of labor supplied
to the market is 10 units. That is, if the wage is $1, the market quantity supplied of labor is 10 units.
Likewise, at a wage of $2, persons A, B, and C all participate and a total of 20 units of labor are supplied (5
+ 5 + 10). While perhaps belaboring the point, both person A and person B increase their quantity supplied
of labor, increasing the market quantity supplied. The addition of person C also serves to increase the
market quantity supplied.
Finally, at a wage of $3, all five persons participate in the labor market and a total of 30 units of labor are
supplied (2 + 7 + 6 + 7 + 8). Notice as the wage increases from $2 to $3, A and B are both on the
backward bending portion of their labor supply curves and are reducing the quantity of labor supplied – this
will reduce the market quantity supplied. However, person C is still on the upward sloping portion of their
labor supply curve and person D and person E are new entrants into the labor market, both increasing the
market quantity supplied.
1
Lecture 12
3/26/2007 1:17 PM
4
Wage
3
2
1
0
0
5
10
15
20
25
30
Quantity of Labor
Sa
Sb
Sc
Sd
Se
Sm
The point is this - as the wage increases, it is true that some individuals will be on the backward bending
portion of their labor supply curves. However, as the wage increases, some people will become new
entrants into the labor market. Overall, for most markets and most realistic wage rates, labor economists
find that the market supply curve for labor is indeed upward sloping. The new entrants and the people on
the upward portion of their labor supply curves overwhelm those that are on the backward portions.
Market Demand of Labor
To find the market demand for labor we follow the same general process of horizontally summing each
firm’s individual demand curve. However, there is one additional complication.
As you recollect from Chapter 5 that each firm’s marginal revenue product (MRP) curve is that firm’s
demand curve for labor. Surely you would be tempted just to add these up (using the horizontal summation
process) as was done above for market supply and be done. This is not quite correct.
There are two important things to keep in mind. First, the firm’s demand curve for labor (MRP) changes
when either marginal productivity or the price of the good being produced changes. Second, each firm
takes the output price as given – they assume they can sell as many units as they want at the given market
price.
Suppose we imagine adding up many identical firms each with the labor demand curve labeled DL1 below.
If you prefer a concrete numerical example, suppose we are adding up 20 firms, and at W1, each of these 20
firms is producing 50 units of output (Q1 = 50). Therefore, ∑Q1 = 1000 units of output.
Now, suppose the wage falls to W2. Each individual firm will want to expand output to Q1’, say 70 units of
output (Q1’ = 70). Therefore, ∑Q1 = 1400 units of output. However, this decision was based on the
assumption that the market price would not change. However, if the industry is now producing 1400 units
instead of 1000, surely the price of the output good will fall. See the picture below.
2
Lecture 12
3/26/2007 1:17 PM
whole market
one firm
∑Q2
W1
c
C
e’
E’
W2
∑D
DL1
Q1
Q1’
Quantity of Labor
∑Q1
∑Q1’ Quantity of Labor
Simply summing the individual demand curves suggests the increase in market quantity demanded of labor
will be 400 units, or the distance between ∑Q1 and ∑Q1’. But this increase in output will decrease the price
of the good and therefore will cause a decrease in each firm’s labor demand. As a result, the expansion in
market quantity demanded will not be as large as we expected (not all the way to ∑Q1’), but instead will be
a slightly smaller quantity, perhaps the one represented by the circle in the graph above.
On the graph below we show each individual firm’s decrease in demand caused be the output price
reduction and connect the dots on the market demand for labor.
After all this, the punch line is that after we account for the change in the price of the output good, the
market demand curve is steeper than the horizontal summation of the individual demand curves.
3
Lecture 12
3/26/2007 1:17 PM
whole market
one firm
∑Q2
c
W1
C
E
e’
e
W2
DLM
DL1
Q1
Quantity of Labor
Q1’
∑Q1
E’
∑D
∑Q1’ Quantity of Labor
Your textbook calls this “price adjusting” the market demand curve.
Labor Market Equilibrium
Finally, we are ready to put the market supply curve and the market demand curve of labor together and
look at equilibrium.
S0
Wes
W0
Wed
D0
Q1
Q0
Q2
If you need a refresher on equilibrium, first consider the wage labeled Wes. This wage is not an equilibrium
wage because at this wage, the quantity of labor supplied would exceed the quantity of labor demanded
(called an excess quantity supplied or a surplus). In this case, as there are more people willing to work at
this wage than there are firms willing to hire them, and there will be pressure for the wage to fall.
Likewise, consider the wage labeled Wed. This too is not an equilibrium wage because at this wage, the
quantity of labor demanded would exceed the quantity of labor supplied (called an excess quantity
demanded or shortage). Here, are there are more firms willing to hire workers than there are workers
willing to work at that wage, and thus there will be pressure on the wage to rise.
4
Lecture 12
3/26/2007 1:17 PM
Of course, the equilibrium wage is the wage labeled W0. At this wage and this wage alone, the quantity
supplied and quantity demanded of labor are equal. W0 and Q0 are the equilibrium wage and quantity of
labor hired (employment).
Review of the Determinants of Labor Supply and Labor Demand
Throughout the last couple of weeks, we have been through all of the items that can shift labor supply and
labor demand curves. Here’s a list:
Labor Supply
1.
Other wage rates
•
2.
•
An increase in the wages paid in other occupations for which workers in a particular labor market
are qualified will decrease labor supply
A decrease in the wages paid in other occupations for which workers in a particular labor market
are qualified will increase in labor supply.
•
•
Nonwage income
An increase in the income other than from employment will decrease labor supply.
A decrease in the income other than from employment will increase labor supply.
3.
Preferences for work versus leisure
•
•
4.
An increase in people’s preferences for work relative to leisure will increase labor supply.
A decrease in people’s preferences for work relative to leisure will decrease labor supply.
Nonwage aspects of the job
•
•
5.
An improvement of the nonwage aspects of the job will increase labor supply
A worsening of the nonwage aspects of the job will decrease labor supply
Number of qualified suppliers
•
•
An increase in the number of qualified suppliers of a specific grade of labor will increase labor
supply.
A decrease in the number of qualified suppliers of a specific grade of labor will decrease labor
supply.
Labor Demand
1.
Product demand
•
•
2.
Change in product demand that increase the product price will raise the MRP of labor and
therefore increase the demand for labor.
Changes in product demand that decrease the product price will reduce the MRP of labor and
therefore decrease the demand for labor.
Productivity
•
•
Assuming that it does not cause an offsetting decline in product price, an increase in productivity
will increase the demand for labor.
Assuming that it does not cause an offsetting decline in product price, a decrease in productivity
will decrease the demand for labor.
5
Lecture 12
3.
3/26/2007 1:17 PM
Prices of other resources
•
•
•
•
4.
When resources are gross complements, an increase in the price of the other resource will decrease
the demand for labor.
When resources are gross complements, a decrease in the price of the other resource will increase
the demand for labor.
When resources are gross substitutes, an increase in the price of the other resource will increase
the demand for labor.
When resources are gross substitutes, a decrease in the price of the other resource will decrease the
demand for labor.
Number of employers
•
•
Assuming no change in employment by other firms hiring a specific grade of labor, an increase in
the number of employers will increase the demand for labor.
Assuming no change in employment by other firms hiring a specific grade of labor, a decrease in
the number of employers will decrease the demand for labor.
Examples
Textile Industry – increased foreign competition
Over the last 20 years, the textile industry has faced increased competition from foreign producers. As a
result, the demand for domestically produced textiles has decreased. What has happened to the equilibrium
wage and number of workers hired in the textile market?
This is a simple decrease in product demand. In the previous lecture, we noted that a decrease in product
demand would lower product price, lower MRP, and therefore lower the demand for textile workers. The
last step would be to draw a picture of the labor market for textile workers. You would conclude that wage
and employment (number of workers fall).
S0
W0
W1
D1
Q1 Q0
D0
Textile Workers
Textile Industry – decrease in price of capital
Suppose you were told the price of the capital used in producing textiles has decreased substantially over
the last 20 years. Suppose you were also told that labor and capital are gross substitutes in the textile
industry. What effect has the decrease in the price of capital had on wages and employment in the textile
industry?
6
Lecture 12
3/26/2007 1:17 PM
Here we have the “price of other resources” changing. When the price of capital changes, two things
happen. First, the output effect says that because capital is cheaper, the cost of production decreases, firms
want to produce more output, and thus hire more labor to do so. This tends to increase the demand for
labor. However, the substitution effects says that because capital is cheaper, firms will substitute away
from using labor in production and toward using capital in production. This tends to decrease the demand
for labor. Since you were told that capital and labor are gross substitutes, this means the substitution effect
dominates. This means overall, the change in the price of capital has decreased the demand for labor.
Finally, you would draw a picture of the labor market, but you will find it is identical to the one you have
drawn above. You would conclude the wages and employment in the textile industry would fall.
American Medical Association – medical school seat caps
The AMA controls the number of students admitted into medical school. Suppose that the AMA reduces
the number of students allowed to go to medical school. (Because you must have a medical degree to
practice medicine in the United States, this will eventually reduce the number of qualified doctors). What
happens to the equilibrium wage and number of doctors?
This is a simple case of a decrease in the number of qualified suppliers. As a result, there will be a
decrease in the supply of labor in the labor market for doctors. Wages will increase and employment will
fall. This is nice for existing doctors. See the picture below.
S1
S0
W1
W0
D0
Q1 Q0
Doctors
United Auto Workers – minimum wages
Even though there are no UAW members who earn minimum wages, the UAW consistently supports
minimum wage increases. Why?
Think of union members as “skilled laborers” and think of minimum wage workers as “unskilled laborers”.
The first question will be whether “skilled labor and unskilled labor would tend to be substitutes or
complements. I would guess substitutes.
An increase in the minimum wage would be just like an increase in the “price of other resources”. The
output effect suggests that an increase in the price of other resources will raise costs of production, result in
less output, and therefore a decrease in the demand for skilled labor.
The substitution effect will result in automakers switching from using unskilled labor to using skilled labor,
resulting in an increase in the demand for skilled labor.
7
Lecture 12
3/26/2007 1:17 PM
As we suspect that unskilled labor and skilled labor are gross substitutes, the substitution effect dominates
and the result is an increase in the demand for skilled labor. The wages and employment of the UAW
members will increase. Draw the market for “skilled worker” increase demand, and note that wage and
employment increase.
What should I read?
We are skipping around Chapter 6. Find the parts we talked about here, don’t worry about the parts we
haven’t talked about just yet.
How about some practice questions?
Ultimately, you will be asked to determine what some change will have on wages and the quantity of labor
hired in some labor market. Here are a couple of sample questions.
1.
Suppose we are considering the labor market for dump truck operators. Suppose you are told that
dump trucks (capital) and dump truck drivers (labor) are gross complements. Suppose there is an
increase in the price of dump trucks. What happens to the wages of dump truck operators?
a.
What happens to the demand for the labor of dump truck operators according to the
output effect?
b.
What happens to the demand for the labor of dump truck operators according to the
substitution effect?
c.
What happens to the wages of dump truck operators?
d.
What happens to the number of dump truck operators employed?
2.
Suppose that some elite professional athletes are qualified to play professional basketball and
professional baseball. Suppose we are considering the labor market for professional baseball
players. What will happen to the wages of professional baseball players if the wages paid to
professional basketball players increase? Sketch a picture to support your answer.
3.
Suppose a government reports reveals that working in coalmines is not as dangerous as was
previously reported. At the same time this report comes out, the price of coal increases. Sketch a
picture illustrating what happens in the labor market for coal miners.
4.
Suppose we consider the labor market for high school teachers. If you get stuck, it will help if you
check out the picture on page 5 of lecture 11.
a.
b.
Draw a long run demand curve and a short run demand curve of labor so that they
intersect somewhere in the middle. Label the point they intersect point A.
Draw in a supply curve of labor that also goes through point A. (What you have just
down is started in initial equilibrium in both the short run and in the long run.)
Now, suppose there is a news report that shows an alarming increase in the number of teachers
injured by violent students.
c.
d.
e.
Illustrate this change on the graph you have just drawn.
Compared to the initial equilibrium (point A), what happens to wages and employment of
teachers in the short run?
As we move from this new short run equilibrium to the new long run equilibrium, what
will be happening to wages and employment of teachers?
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Lecture 12
3/26/2007 1:17 PM
Answers:
1.
Output effect says cost of production increases, thus less output and therefore labor demand
decreases. Substitution effect says firms substitute away from capital and toward labor,
therefore labor demand increases. Because capital and labor are gross complements, output
effect dominates. Thus, overall, the demand for labor decreases. Wages fall and employment
falls. Draw the standard decrease in the demand for labor.
2.
If the wages of basketball players increase (an “other wage rate”), the supply of baseball
players will decrease. Wages in baseball will increase, while employment will decrease. (If
you know the institutional details about rosters in major league baseball, ignore this for the
purposes of this question). Draw the standard decrease in the supply of labor.
3.
News on the (lack of) danger is an improvement in nonwage aspects of the job and therefore
increases the supply of labor. The price of coal is an increase in product price, therefore an
increase in MRP, and therefore an increase in the demand for coalminers’ labor. Depending
on the sizes of your demand and supply shifts, wages may increase or decrease, but the
quantity of coalminers employed will certainly increase. Sketch an increase in supply and an
increase in demand.
4.
See picture below. The news on injured teachers is a worsening of nonwage aspects of the
job and will reduce the supply of labor. In the short run, wages rise and employment falls.
As time goes on, the wage begins to fall and employment continues to fall.
wage rate
S’
W1
S
c
b
W2
a
W0
DSR
Q2 Q1 Q
DLR
Quantity of Labor
9
Lecture 13
4/18/2007 6:54 PM
Introduction to Unions - What do Unions Do?
More than any set of lecture notes this semester, the portion of these notes on unions is very similar to what
you will find in the textbook. Rather than give you all the details here, I have given you a quick outline and
will refer you back to Chapter 6.
What is it that unions do?
1.
2.
3.
Increase the demand for labor
Decrease the supply of labor
Bargain for above equilibrium wages
How does the union increase the demand for labor?
You already know the items that determine the demand for labor. Unions attempt to increase the demand
by using each of these determinants.
1.
Increase product demand
The big item here is that unions will attempt to use the political process to increase the demand for their
labor. Construction workers will do their best to convince politicians that levies need to be rebuilt, that
construction projects in general are necessary, that new infrastructure needs to be invested in, etc. If they
can convince the population or the politicians to undergo these projects, the result will be an increase in the
demand for (union) labor.
Teacher unions will suggest that more money is needed for children’s education (But what about the
children?), while airplane manufacturers will advocate subsidies for foreign purchasers of planes, etc.
Unions will also attempt to utilize the political process to increase the price of substitutes to the product
they produce and to decrease the price of complements to the product they produce. For steel customers,
domestic steel and imported steel are substitutes. Domestic steel producers will lobby for tariffs to raise the
price of imported steel, therefore increasing the demand for domestic steel labor. Hotel workers unions
will support a reduction in hotel taxes, as this will increase the demand for the labor of hotel workers.
2.
Enhancing Productivity
Some people think it is the case that unions enhance productivity, others do not. Read your text on this one
if you like. It talks about quality circles and co-determination, stressing the roll of communication between
rank and file workers and management. Personally, I am rather skeptical, and I think it is very firm
specific.
3.
Influencing Prices of Related Inputs (Resources)
Labor unions are in favor of increases in the minimum wages as skilled labor and unskilled labor are likely
to be gross substitutes.
The Davis-Bacon act is a neat law that requires that projects being paid for using federal government funds
pay “prevailing wages”. Often, the prevailing wages observed in the labor market are the wages paid to
unions. As a result, no firm can pay wages below the union wages if they wish to bid on federal projects.
This reduces the competitive disadvantage of unions, as firms can no longer compete on the basis of wages.
Whoever came up with that one was very clever.
4.
Increasing the number of Employers
Your textbook gives you an example of legislation that the United Auto Workers were advocating. It
would have required cars sold in the United States to have a minimum fraction of the actual assembly done
1
Lecture 13
4/18/2007 6:54 PM
within the borders of the United States. This “domestic content” regulation clearly would increase the
number of employers, increasing the demand for autoworkers. It did not pass. If you find yourself thinking
that increasing product demand and increasing the number of employers are basically the same, so do I.
How does the union decrease the Supply for Labor?
Your textbook feels that is important to point out that rather than directly decreasing the supply curve for
labor, a union may act to simply slow labor supply growth. While the overall result is the same, the latter is
perhaps a bit more politically viable.
On the left is a direct reduction in the supply of labor from SL to SL’. The result is an increase in wages and
a reduction in the quantity of labor.
On the right, we look at supply and demand in a more dynamic setting. We start at SL and DL. Say that if
the union took no action, the demand curve would increase to DL’ while the supply curve would increase to
SL2’. We would see no change in wages, but an increase in employment.
However, if the union were somehow to slow the increase in the supply of labor to SL1’ (instead of to SL2’),
the result would be a higher wage and lower employment (than if the union had not slowed labor supply
growth).
Basically, it is a bit sneakier to slow labor growth than to reduce the supply of labor outright. Fewer new
jobs is easier to sell than a reduction in the number of jobs.
Wage
SL’
Wages
SL
SL
SL1’
SL2’
DL’
DL
DL
Labor
Labor
How else can labor unions slow or decrease the supply of labor?
1.
Reducing the number of qualified sellers (these are all things unions support)
•
•
•
•
•
2.
Immigration restrictions
Child labor laws
Compulsory retirement
Shorter work weeks
Occupational licensure – AMA, Massage Therapists
Influencing non wage income
I really dislike the textbook here. Skip it.
2
Lecture 13
4/18/2007 6:54 PM
How does the union bargain for above equilibrium wages?
A large part of this bargaining is based on the threat to strike. First, if the labor market were competitive,
we would see WC and QC. Say, the union is successful in raising the wage to WU.
Notice at WU, there will be an excess quantity supplied. Stated differently, there will be more people
willing to work at that wage then there are jobs. In fact, the size of the gap will be the distance between
point b and point e. Part of this increase comes about because there are fewer jobs (the distance between
point b and point c), while the other part of this increase comes about due additional workers attracted by
the union wages (the distance between point c and point e).
Because of this overall gap, union jobs are typically associated with a queue, or waiting list. Often workers
must wait along time before landing a union job that pays above equilibrium wages.
Wage
SL
WU
b
c
e
WC
DL
QU QC
Labor
Monopsony
Most of you are familiar with the situation called monopoly. In monopoly, there is only one seller of a
good. Since the seller faces no competition from other sellers, intuitively we think this firm will be able to
sell the good at a more favorable price than if it faced a great deal of competition
When you learned about monopolistic firms, you might have called this type a firm a “price searcher”. The
idea is that a monopoly firm could choose different prices for the good they were selling - they could
choose any spot along the demand curve. This firm could choose a high price and sell a relatively low
quantity of their good. Alternatively, the firm could sell more but it would have to lower the price it
charges.
This lecture, however, is a situation called monopsony. In monopsony, there is only buyer of a good. As
this is labor economics class, we will consider when one firm is the only demander of labor. Since the
(firm) buyer faces no competition from other (firms) buyers, you might not be surprised to see in a few
pages that a monopsonistic will be able to hire labor at favorable (wages) prices.
A monopsonistic firm can choose any spot along the supply curve of labor. They could choose a lower
wage, but will not attract as much labor. To attract a larger amount of employees, they will have to offers a
high wage.
The assumptions we will make for monopsony are:
(1) there are a large number of qualified homogeneous workers
(2) perfect information and costless mobility
(3) there is only one demander of labor
3
Lecture 13
4/18/2007 6:54 PM
The wage-taking firm, revisited
Before we learn about monopsony, we need to go back and be a bit more detailed about a wage-taking firm.
Suppose we reconsider a wage-taking firm. While we weren’t very explicit about it when we were
discussing the supply and especially demand for labor previously, we were talking about a wage-taking
firm. The idea that was floating around in the background was that there were many firms, all hiring the
same type of worker, resulting in healthy competition for workers amongst firms. Each firm was small
relative to the overall labor market. This resulted in each firm taking the market wage as given. If a firm
were to try to pay a wage lower than the market wage, the firm could not attract any laborers. Nor was
there any reason to pay a wage higher than the market wage, as the firm could attract enough labor by
paying the market wage.
As a result, the wage-taking firm assumed that it could hire as much labor as it wanted at the market wage.
If it wanted another unit of labor, the firm simply hired another unit of labor at the market wage.
To understand what is going on, we need to draw a picture with two panels. On the left, we draw the entire
labor market. On the right, we examine what is occurring from the perspective of one individual firm.
First, focus on the picture on the left. Market supply and market demand determine the equilibrium wage
and the quantity of labor hired. We use Q to denote the total quantity of labor hired in the market.
From the perspective of the wage-taking firm, they literally take the market wage as given. They act as if
they can hire as many workers as they want at the market wage. From the individual firm’s perspective,
then, the supply curve of labor is horizontal at the market wage. The firm then compares this market wage
to the MRP values and decides how much labor to hire just like we did before the last exam. We use q to
denote the quantity of labor hired by one firm.
Entire Labor Market
One Firm
Wage
Wage
SL
SL
W0
W0
DL = MRP
Q0
QLABOR
DL = MRP
qo
qLABOR
Now, suppose the market supply curve of labor decreases. What happens? We decrease the market supply
curve on the graph on the left. This causes the market wage to increase. The individual firm takes this new
higher market wage as given, and then responds be hiring less labor. See the picture on the next page.
4
Lecture 13
4/18/2007 6:54 PM
Entire Labor Market
One Firm
SL’
Wage
Wage
SL
SL’
W1
W1
SL
W0
W0
DL = MRP
Q1 Q0
QLABOR
DL = MRP
q1 q0
qLABOR
So what? Still more on the wage-taking firm
I know, I know, we haven’t learned anything new just yet. But this will help with understanding
monopsony. We are working toward added the marginal wage cost to the story. To do so, it makes sense
to say with the wage-taking firm, but to look at a numerical answer.
Suppose, for example, the market wage is $2. See the chart below. The first two columns are standard –
they represent the supply curve of labor as the individual firm conceives it.
The third column is a new one, total wage cost. Total wage cost is just what it sounds like. It is the total
amount spent on wages. It is found by simply multiplying the number of units of labor times the wage
(TWC = W * L). The next column is labeled average wage cost. It is calculated by taking total wage
costs and dividing by the number of units of labor (AWC = ATC / L).1
Marginal wage cost is the change in total wage costs associated with a one unit increase in labor.
Literally, it is the extra wage cost associated with hiring that last unit of labor (MWC = ∆TWC / ∆L).
What you should course notice here, is that for a wage-taking firm, the marginal wage cost is equal to
the market wage.
How much labor will the wage-taking firm hire? Before, we stated the rule was to hire labor until MRP =
W. While this is true for the wage-taking firm, it was a special case of the more general rule (and won’t be
true for a monopsonist). The general rule is that all firms want to hire labor until MRP = MWC.2
This rule should make sense if you do not forget what it is that MRP and MWC actually mean. MRP is
literally the additional revenue associated with hiring one more unit of labor. MWC is literally the
additional wage costs associated with hiring one more unit of labor. It will be profitable to hire additional
units of labor as long as MRP > MWC. We stop when MRP = MWC.
1
If this steps seems like a waste of time it might be. The point here will eventually be that the supply curve
for labor is the AWC. You should know how to find it, but as you’ll see, the “action” will be the MWC
curve.
2
Both wage-taking firms and monopsonistic firms will hire labor until MWC = MRP. For a wage taking
firm only, since MWC = W, the rule can be restated hires labor until W = MRP. Keep reading.
5
Lecture 13
4/18/2007 6:54 PM
Labor
Wage
(SLABOR)
Total Wage
Cost
Average Wage
Cost
Marginal
Wage Cost
1
2
3
4
5
6
$2
$2
$2
$2
$2
$2
$2
$4
$6
$8
$10
$12
$2
$2
$2
$2
$2
$2
$2
$2
$2
$2
$2
$2
Marginal
Revenue
Product
$7
$6
$5
$4
$3
$2
This wage-taking firm will hire 6 units of labor.
Also, if you co back to the pictures above, you could note that for the individual firm, the supply curve for
labor, the average wage cost curve, and the marginal wage costs curve are all the same – the horizontal line
at the market wage.
Finally on to Monopsony
The monopsonistic firm can choose any point on the market supply curve of labor. It may choose a low
wage, but will only be able to hire a small amount of labor. If the firm wishes to attract more labor, it will
have to increase the wage. See the numerical example below. The first two columns are the market supply
curve of labor. If the firm wants to hire 2 units of labor, it must pay a wage of $2. If it wishes to hire 3
units of labor, it must pay a wage of $3.
We will also assume that the monopsonistic firm is not able to “wage discriminate”. It will have to pay the
same wage to all of the employees. Stated a bit differently, the firm will not be able to offer a higher wage
to only the last worker hired.3
Let’s proceed by calculating the Total Wage Cost (TWC) in the same fashion we did for the wage-taking
firm. This is still done by multiplying the wage by the number of units of labor. And again, we calculate
the Average Wage Cost (AWC) by taking the total wage cost and dividing by the number of units of labor.
(This again may be a waste of time). Lastly, we calculate the Marginal Wage Cost (MWC) by calculating
the change in total wage costs when each additional unit of labor is hired.
The fundamental difference between a monopsonistic firm and a wage-taking firm is that for a
monopsonistic firm, MWC > W, while for a wage-taking firm, MWC = W.
If a monopsonistic firm wishes to hire more labor, not only does it have to pay a higher wage to attract the
last worker, it will have to increase the wages to all workers (all the previous workers). Consider the 4th
unit of labor. Suppose previously the firm was hiring 3 workers at a wage of $3 for a total wage cost of $9.
To hire the 4th unit, it must offer the 4th unit of labor $4 (increasing total wage costs $4), but it must also
increase the wage from $3 to $4 for the 3 previous units of labor (increasing total wage costs $3). Thus,
hiring the 4th unit of labor results in a $7 increase in total wage costs, which is precisely what the MWC of
the 4th unit of the labor measures. You could simply have noted that TWC increased from $9 to $16, as
well.
3
For example, suppose the firm has already hired 3 units of labor at a wage of $3. By saying the firm
cannot wage discriminate, we are stating it is not possible to hire those first three units of labor at a wage of
$3 and pay only the 4th worker $4. In order to hire four workers, the firm must pay all four workers a wage
of $4.
6
Lecture 13
4/18/2007 6:54 PM
Labor
Wage
(SLABOR)
Total Wage
Cost
Average Wage
Cost
Marginal
Wage Cost
1
2
3
4
5
6
$1
$2
$3
$4
$5
$6
$1
$4
$9
$16
$25
$36
$1
$2
$3
$4
$5
$6
$1
$3
$5
$7
$9
$11
Marginal
Revenue
Product
$7
$6
$5
$4
$3
$2
Finally, the firm compares MWC to MRP. Again, MWC is literally the extra cost associated with hiring
another unit of labor, while MRP is literally the extra revenue associated with hiring an additional unit of
labor. On the first and second units of labor, the MRP > MWC, thus the firm will find it profitable to hire
these units. The third unit of labor has a MRP = MWC, so technically the firm is indifferent between hiring
the third unit or not, but we will have the firm hire this unit. The firm will not hire the 4th unit of labor, as
the MWC > MRP. Wage costs increase more ($7) when the 4th unit of labor is hired that revenues increase
($4).
In short, hire until MWC = MRP. In this case, the monopsonist will hire 3 units of labor.
What does the picture look like for a monopsonist?
First, draw in the market supply curve for labor. Then draw the demand for labor (MRP). Stop for a
second and note if the labor market was comprised of a bunch of competitive wage-taking firms, we would
simply get the intersection of the supply and demand curve for labor (labeled WC and QC).
Next, notice that the MWC is always above the supply curve for labor (the MWC > W). See the picture.
Draw in the MWC curve.
Finally, choose the amount of labor hired by finding the intersection of the MWC (SL) and MRP (DL)
curves (labeled Q1). Be careful here. This intersection determines the quantity of labor, but the wage is
found by noting the location of the supply curve at this quantity of labor (labeled W1).4 In the example
above, the firm hires 3 units of labor because at 3 units, MWC = MRP = $5. But the firm pays workers a
wage of $3 (not $5).
Notice that compared to the wage-taking firms:
• the monopsonistic firm pays a lower wage
• the monopsonistic firm hires less labor.
Also, notice that the last unit of labor hired has MRP > W.
4
Find the quantity from the intersection of MWC and MRP, then “scoot down” at that quantity to the
supply curve of labor to find the wage.
7
Lecture 13
4/18/2007 6:54 PM
Wages
MWC
SL = AWC
WC
W1
DL = MRP
Q1
QC
Labor
Why don’t we see much monopsony in the real world?
1.
There are a large number of potential employers.
2.
Workers today have a great deal of geographic mobility
3.
Often, if workers were to find themselves in a monopsonistic situation, they will organize and
form a union. In this case, there will be one buyer of labor (the monopsonistic firm) and one seller
of labor (effectively the union). We call this situation bilateral monopoly - it is discussed in your
text if you would like to read about, but this is not required. Bargaining under conditions of
bilateral monopoly becomes complicated.
Are there real world examples of monopsony?
Not many.
If you are elite professional baseball player, there is really only one place you can work, well maybe 30,
because there are 30 professional baseball teams. Now, I know what you are thinking, to be exactly a
monopsony, there would need to be only one baseball team.
However, for many players early in their careers, the player can only negotiate with one firm, effectively
resulting in a monopsony situation. Almost all professional baseball players become a professional
baseball player after being drafted. After being drafted, the player may only play for the one team that
owns that player’s draft rights. They are not allowed to negotiate with other teams.
Roughly, baseball players earn “free agent status”, the right to negotiate and sell their services to all 30
teams, only after playing for 6 years after they are drafted. A player operates in a monopsonistic labor
market in the first 6 years of their professional career.
Look up Ryan Howard’s salary on ESPN. He won the Most Valuable Player award in the National League
last year. How much did he get paid?
If this arrangement that baseball has sounds stinky, there was a time (up until the early 1970s) where a
player never earned free agency. A player could only negotiate with one team throughout their entire
career. The contractual provision was called the “reserve clause” and was not seriously challenged until a
player named Curt Flood refused to play for the team that had his rights, walking away from a $100,000
contract offer in 1970.
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Lecture 13
4/18/2007 6:54 PM
Incidentally, much of his inspiration was that Curt Flood really didn’t want to play for the Phillies,
apparently in part because he felt that fans in Philadelphia were racist (Curt Flood was an African
American). Curt Flood’s case went all the way the Supreme Court, but he lost. However, after some
further negotiations surely spurned on by Flood’s case, the rules were substantively changed beginning in
1976 leading us toward the basic system we see today.
As you might suspect, when players become free agents, and no longer face a monopsonistic situation, the
salaries they receive increase substantially. It is quite clear that players are being paid below their MRP
until reaching free agency in professional baseball, basketball, and football.
Search Curt Flood on Google. By the way, are professional baseball players unionized?
What should I read?
Again, the discussion of what unions do in these notes is very similar to that found in Chapter 6 of your
textbook.
Monopsony is also discussed in Chapter 6. Check out the box on p. 186 for more on baseball.
For a one-page summary of Curt Flood, try the link below:
http://www.baseballreliquary.org/flood.htm
9
Lecture 14
3/29/2006 9:22 PM
Fringe Benefits Facts
Some copyright infringement. These next two pictures come from p. 209 – 210 of your text.
Legally required benefits include social security, unemployment insurance, workers compensation, and
temporary disability insurance. Insurance includes life, health, and accident. Supplemental Pay includes
overtime & holiday premium pay, shift differentials, and non-production based bonuses. Other benefits
include severance pay and merchandise discounts.
Fringe benefits are a larger fraction of total compensation in:
• High paying industries (vs. lower paying industries)
• Good producing industries (vs. service producing industries)
• Transportation and public utilities (vs. retail trade)
• Blue collar workers (vs. white color workers)
1
Lecture 14
3/29/2006 9:22 PM
Questions this lecture should answer
What don’t companies just pay us cash and let us purchase these items on are own?
What explains the broad upward trend in the fraction of compensation paid as fringe benefits?
How do we model fringe benefit determination?
We will have the joy to revisit our old friend the indifference curve and the budget line (or at least its first
cousin).
What do the indifference curves look like?
We first want to draw an indifference curve between wages and fringe benefits. The first question to ask is
if people are willing to trade wages for fringe benefits. Wouldn’t you prefer a $1 in wages to a $1 in dental
benefits? Or a $1 in wages to a $1 in child care benefits? Do the answers change if you have no teeth? Or
no kids?
Even so, from the employee’s perspective, there is a tax advantage on fringe benefits. For instance on
qualified pension plans, you do not pay tax on interest until you receive the payments. Your benefits grow
at a pre-tax rate rather than a post-tax rate – through the wonders of compounding you come out ahead. In
addition, when you retire and draw on these benefits, you are likely to be in a lower marginal tax bracket
than when you earned the income. In short, the after-tax value of receiving $1 pension contribution is
larger than the after-tax value of receiving $1 in wage income. As a result, people are going to be willing
to trade wages for fringe benefits.
Your book gives you a second reason, which I find unappealing. It states that people are willing to
substitute fringe benefits for some of their wages to “guard against their tendency to purchase goods that
provide immediate gratification”. I think there are many ways to do this these days with automatic
2
Lecture 14
3/29/2006 9:22 PM
checking deductions etc, but this may have been more important 20 years ago. We can talk about people
who like big tax refunds in class.
Once we buy this, we know the indifference curve between wages and fringe benefits is downward
sloping. Employees will be willing to give up wages in exchange for fringe benefits.
The indifference curves are convex
When you have no fringe benefits, you may give up a good deal in wages to obtain one more unit of fringe
benefits. When you have tons of fringe benefits, you will be willing to give up a smaller amount of wages
for an additional unit of fringe benefit. It is the same story we told before when discussing indifference
curves between leisure and income. The indifference curves are convex. Enough said. Check out the
picture below. It should look familiar – it is a cut and paste job from lecture 3, only I have changed the
labels to “wages” and “fringe benefits”.
Wages
I2
I1
I3
Satisfaction Level Increases
Fringe Benefits
Can people have different preferences for wages vs. fringe benefits? Say you have crappy teeth or 10 kids.
Might you be willing to give up a large amount of wages for some additional fringe benefits (if these
benefits were childcare, dental care, or even perhaps health care)?
Say you have great teeth, no kids, and no you will die at 47. I would claim it is a different story and you
would be willing to give up very little in wages for additional units of fringe benefits. Which set of
indifference belongs to which group?
Wages
Wages
I1
I2
I3
I3
I2
I1
Fringe Benefits
Fringe Benefits
For now, we will just look at an average or representative worker’s indifference curves.
3
Lecture 14
3/29/2006 9:22 PM
Employer’s Isoprofit Curve
As you might guess, the next step is to draw something like the budget line or budget constraint. With
budget lines, the idea was to show us how much of each good was attainable with a given level of income.
What we do here is draw the analogous concept, but here we call it an isoprofit curve. An isoprofit curve
indicates the various combinations of wages and fringe benefits providing a given profit level. Firms
are assumed to earn a normal profit. Importantly, competition in the wage market forces the firms to pay
the total compensation given.1
Obviously, if the firm is to increase fringe benefits while keeping its profit level the same, it will have to
reduce wages. For simplicity, we assume the firm faces a constant trade of “price” for a unit of fringe
benefits. The result is that our isoprofit curve is a straight line.
Wages
Fringe Benefits
Optimal Fringe Benefit Determination
As you might have guessed, combine the isoprofit line and the indifference curves and find the tangency.
Wages
I2
I1
I3
a
b
c
Fringe Benefits
Of course, point a is not an optimal choice. If the firm were to lower wages and increase fringe benefits, it
would improve the satisfaction level of its employees while not altering the firm’s profits. The firm would
find it easier to find and retain employees. Likewise, c is not an optimal choice either. The firm will tailor
its fringe benefit plan to correspond to point b.
1
Firms won’t get to pick which isoprofit line they are on. Competitive forces will drive down their level of
profits to the “normal level”. If there were to try to increase profits by reducing wages and/or fringe
benefits, they will find it impossible to attract labor to their firm. Workers will work elsewhere.
4
Lecture 14
3/29/2006 9:22 PM
What happens if there is a lower “price” of fringe benefits?
The isoprofit line rotates out. If the firm was paying all wages (no fringe benefits) as in done as point d,
there will be no change. However, if the firm was paying out all compensation in the form of fringe
benefits as is done at point e, the firm will be able to provide more fringe benefits without reducing its
profits (point f). The isoprofit line will rotate counterclockwise. In fact, a competitive labor market will
require the firm offer these additional fringe benefits or employees will move to firms that do offer these
benefits.
Wages
d
e
f
Fringe Benefits
Finally, combing the isoprofit line with the indifference curve, workers will receive lower wages but more
fringe benefits after a reduction in the “price” of fringe benefits. The original optimal choice is given by
point b, while the optimal choice after the lowering of the “price” of fringe benefits will be given by point
d.
Wages
I1
W0
W1
I2
I3
b
F0
d
F1
Fringe Benefits
What could cause the “price” of fringe benefits to change?
Increasing taxes, and hence the tax advantages of fringe benefits, can reduce the “price” that the firm pays
for fringe benefits.
Firms are responsible for “paying” half of the 15.3% Social Security pay roll tax on worker earnings up to
$87,900. Their firm’s share is 7.65%.
First, consider a world with no payroll taxes and consider the tradeoff between paying workers wages or
fringe benefits.
5
Lecture 14
Option A1
Income = $30,000
Fringe Benefits = 0
Firm’s share of SS payroll tax (7.65%) = $0
3/29/2006 9:22 PM
Option B1
Income = $20,000
Fringe Benefits = $10,000
Firm’s share of SS payroll tax (7.65) = $0
The firm would be entirely indifferent. Now add payroll taxes to the mix.
Option A2
Income = $30,000
Fringe Benefits = 0
Firm’s share of SS payroll tax (7.65%) = $2295
Option B1
Income = $20,000
Fringe Benefits = $10,000
Firm’s share of SS payroll tax (7.65) = $1530
Clearly, the payroll tax tilts the firm toward providing fringe benefits. With no payroll taxes, it was the
case the firm could reduce wages by $1 and offer $1 in fringe benefits without changing the profit level.
Now the firm can reduce wages by $1 and offer more than $1 in fringe benefits without changing the profit
level (because of the tax savings). The price of providing fringe benefits has decreased.
Over the last 70 years, the base has increased (the amount of income that has to be reached before income
is exempt from SS tax has increased), as has the actual payroll tax rate. As the base and tax rate has
increased, the “price” of providing fringe benefits has continually decreased, and as a result, the fraction of
total compensation that comes in the form of fringe benefits has increased. This is the prime explanation of
the upward trend in the fraction of total benefits paid as fringe benefits.
Your textbook offers some additional explanations.
Economies of scale – basically, group discounts. An individual wishing to purchase health insurance may
not get as good a rate as 1000 people wishing to purchase insurance. This can come about purely from a
bulk discount negotiation, or because the adverse selection problem often seen in insurance markets could
be reduced. I think this is a better explanation of why larger firms offer more fringe benefits rather than the
overall trend. However, if average firm size has increased over time, then this would also explain the
overall increase in fringe benefits.
For another example of economies of scale, think of the cost of providing childcare in a small firm that has
only one worker with a child, versus the cost of providing childcare at a firm with 1000 employees, many
of whom have children. The cost per employee of providing the benefits will be much smaller for the
larger firm (one childcare worker could watch many children).
Unions – are said to bargain for more fringe benefits. Note that transportation, goods producing industries,
and blue collar workers are all more likely to be unionized and have a larger fraction of compensation
coming form fringe benefits.
Pensions – pension rules can help to increase retention and reduce job turnover.
What should I read?
The first half of Chapter 7
6
Lecture 15
3/30/2007 1:58 PM
Wage Structure, Big Picture
The main idea of this lecture is to explain the differences in wages observed across occupations and
industries. Thus far, we have always assumed (either implicitly or explicitly) that both workers and
occupations (jobs) are identical. These are“textbook” assumptions. They allow us to consider a single labor
market and a single market wage. Of course, these assumptions are not true. We will try to relax these
assumptions and see what we can learn and explain.
It turns out there are four main things that can cause wages to be different across occupations
1.
2.
3.
4.
Compensating Wage Differentials
Differing Skill Requirements
Differences Based on Efficiency Wage Payments
Other Job or Employer Heterogeneities
We will try to tackle the first two items (compensating wage differentials and differing skills requirements)
will this set of notes. We will be trying to understand what happens when we realize that jobs and
occupations are different. Even with identical workers, we will be able to explain much of the different
wages across occupations based on different characteristics in the occupations where these workers will
work.
Non-equilibrium Wage Differentials
First, we need to make sure we know the difference between a non-equilibrium wage differential and an
equilibrium wage differential.
Assumptions (for now)
1.
2.
3.
4.
Homogeneous workers (identical preference and qualifications)
Homogeneous jobs (identical working conditions, nonwage amenities)
Information is perfect
Mobility is costless
Imagine two submarkets within the overall labor market. The occupations are identical. Imagine, for
whatever reason, the wage in submarket A is larger than submarket B. The question is–is this an
equilibrium situation? Will this wage gap persist?
The answer is no. Since information is perfect, worker will quickly realize wages are higher in submarket
A than in submarket B. Since mobility is costless, people will be willing to move from submarket B to
submarket A. Doing so will increase the supply to submarket A (driving down wages) and decrease the
supply to submarket B (driving up wages). This process will occur until the wages are equal in the
submarkets (w1).
1
Lecture 15
3/30/2007 1:58 PM
Submarket A
Submarket B
wage rate
wage rate
SA
SB’
SA’
SB
w0
w1
w0
DA
QLABOR
DB
QLABOR
The wage difference we see initially is what is called a non-equilibrium wage differential or a
transitional wage differential. The point is that it is temporary in nature. It will not persist. This wage
difference will be a signal to workers that will promote mobility– this mobility will ultimately eliminate
these differences.
In the end, if the assumptions are as outlined above, everyone would receive the same wage, as workers
will move around until wages are equal in all submarkets.
Heterogeneous Jobs – Compensating Wage Differentials
Now we alter the second assumption. We no longer assume that jobs are identical, but allow jobs to have
different characteristics. Importantly, we are still assuming that workers are homogeneous (identical).
1.
2.
3.
4.
Homogeneous workers
Heterogeneous jobs (jobs have different characteristics)
Information is perfect
Mobility is costless
Of course, jobs are different. This will induce what we call compensating wage differentials. According
to your textbook, a compensating wage differential consists of the extra pay that an employer must provide
to compensate a worker from some undesirable job characteristic that does not exist in an alternative
employment.
Consider two people who have identical qualifications and preferences. Consider two occupations.
Suppose occupation A takes place outdoors in unpleasant weather while work in B takes place inside in
pleasant surroundings. In textbook jargon, there are differences in nonwage amenities between the two
occupations. Suppose that wage was identical in both occupations. The question is– is this an equilibrium
situation? Can it be the case that jobs with different nonwage amenities pay the same wage rate?
Since workers are identical, and because wages were the same in both occupations, everyone would wish to
work indoors (better non-wage amenities) and no workers would wish to work in the unpleasant weather.
To induce workers to work outside, employers will have to offer a wage premium in this occupation.
Perhaps the workers who work inside will receive a wage of $5, while those workers who work outside will
earn $10. We would call this $5 disparity a compensating wage differential.
As opposed to the non-equilibrium wage differential discussed above (Submarket A and B), this wage
differential (observed between indoor and outdoor workers) is an equilibrium wage difference. That is, it
will tend to persist. It is not temporary in nature.
2
Lecture 15
3/30/2007 1:58 PM
Do not forget that people who are working outside are not better off (more utility) than the people who are
working inside. In fact, workers would be indifferent between receiving $5 and working inside or
receiving $10 and working outside.
Workers who work inside earn $5, and suffer no disutility or unhappiness from working outside. Workers
who work outside earn $10. They do receive the wage premium, but they also suffer the adverse working
conditions. The extra $5 in compensation is just enough to compensate for the bad conditions, leaving
them with a “net” wage of $5.
That is the whole basic story. Next, we make a laundry list of the characteristics of occupations that lead to
compensating wage differentials.
1.
2.
3.
4.
5.
6.
Risk of Injury of Death
Fringe Benefits
Job Status
Job Location
Job Security– Regularity of Earnings
Prospect of Wage Advancement
Source of Compensating Wage Differentials
You will find these will seem pretty simple and repetitious. If the occupation has characteristics that are
undesirable, employers will have to compensate employees for this characteristic.
1.
Risk of Injury of Death
Jobs with a higher risk of accidents (relative to other jobs requiring the same skill level) will require a
compensating wage differential. Examples–coal miners, skyscraper window washers, Alaskan fishermen.
2.
Fringe Benefits
Jobs that offer fewer fringe benefits will have to offer higher wages. Not much more to say here.
3.
Job Status
Jobs that are associated with low status or prestige will have to pay a compensating wage differential. A
high status job (these days) might be a fire truck driver, a policeman, or a test-tube cleaner in a lab where
cancer research was occurring. A low status job might be a plain old truck driver, or a test-tube cleaner in a
sewage treatment plant.
4.
Job Locations
There are two different angles here and combining them can be confusing. Some big cities are known for
their amenities. For example, if you are a professional baseball fan, you may require a compensating wage
differential to work in Rockford, Illinois (a dump of a city with no professional baseball team) than to work
in Chicago, Illinois (a city with one professional baseball team and the Cubs). It would the same story if
you like fancy art museums or the opera.
On the other hand, the cost of living in cities is typically higher than the cost of living outside the city. So
to attract workers, firms might have to be a compensating wage differential (cost of living adjustment) to
work in the city.
Do you think people in Thibodaux receive compensating wage differentials? I am fairly confident that
there is a compensating wage differential that has to be paid now to attract workers to New Orleans.
5.
Job Security
3
Lecture 15
3/30/2007 1:58 PM
People like job security and regular earnings. If workers earnings are variable (uncertain), they will require
a compensating wage differential for this uncertainty. Construction, sales, and anything else that is
sensitive to the business cycle (ups and downs of the economy) or jobs where people are periodically laid
off are examples.
6.
Prospect of Wage Advancement
If there is no prospect of wage advancement, workers will need to be paid a compensating wage differential
when entering the occupation (entry-level pay will be higher in occupations with little wage advancement
potential).
Differing Skill Requirements
This really does not need to be its own category, because you could view differing skill requirements in the
context of the compensating wage differentials we have been discussing.
Of course, if there are two otherwise identical occupations, but one required a college education and the
other did not, it would not be an equilibrium situation if the wages in the occupations were identical. No
person will willingly invest in a college education if there is no return. As a result, the skill premium we
were discussing previously (back in our discussion of human capital) can be though as a compensating
wage differential paid to people that go to college.
In fact, we know that the differential that is required is the amount that is just enough so that the internal
rate of return on a year of schooling is just equal to the market interest rate. If the market rate of interest is
10%, and the wage gap is such that the math suggests that the internal rate of return on schooling is 10%,
than the wage gap will provide just enough compensation to compensate workers for going to college.
If the differential is not that large, people will not go to school, increasing the supply to the lower skill
occupations and decreasing its wage. At the same time, fewer people going to school will reduce the
supply to the high skill occupation, increasing its wage. In equilibrium, the wage gap will be just enough to
induce people to go to school.
Your book feels it necessary to point out that this premium is independent of all of the premiums above.
It is possible to have an occupation that requires a college education and is risky. In this case, both facets
of the jobs are tending to increasing wages.
However, it is possible to have an occupation that requires little education and is risky. In this case, the
wage differentials are operating in opposite directions. Risky increases wages, but the low skill level
reduces wages.
What should I read?
Chapter 8– You will find these notes are pretty similar to the textbook’s treatment of the material. We will
get to efficiency wage payments, differing preferences, soon.
4
Lecture 16
3/30/2007 2:51 PM
A word of caution about labor market discrimination – it is tricky
I’ve duplicated some pictures in your textbook. While all of these pictures are suggestive of discrimination,
none of them is sufficiently convincing evidence that discrimination exists.
Figure 14.1
Figure 14.2
90%
Black-White Earnings Ratio
Female-Male Earnings Ratio
80%
70%
60%
50%
40%
30%
20%
10%
0%
1973
1978
1983
1988
1993
1998
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
1973 1978 1983 1988 1993 1998 2003
2003
Based on Table 14.1
P h y sic ia n s
W a ite r s a n d W a itr e s se s
R e g is te r e d N u r se s
E lem /M id d le S c h o o l T e a c h e r s
C a s h ie r s
T y p is ts
J a n ito r s a n d C le a n e r s
T a xic a b D r iv e r s
N u r s in g A id e s
0
5
10
15
20
25
30
35
P e r c e n t B la c k
Crane Operators
Taxicab Drivers
Physicians
Janitors and Cleaners
Laundry Workers
Waiters and Waitressess
Cashiers
Elem/Middle School Teachers
Registered Nurses
Secretaries
0
20
40
60
80
100
Percent Female
1
Lecture 16
3/30/2007 2:51 PM
Female-Male Earnings Ratio
Figure 14.3
Figure 14.4
25%
High School or More
20%
College or More
90%
15%
80%
10%
70%
5%
60%
50%
0%
40%
1972 1977 1982 1987 1992 1997 2002
White Male
White Female
Black Male
Black Female
30%
20%
10%
0%
White
Male
Black
Male
Do not get me wrong. I certainly am not so foolish to suggest there is no discrimination against AfricanAmerican or women. However, from what we have learned thus far, there are several reasons that men
might earn higher wages then women, or white men might earn more than African-American men that are
not because of discrimination.
Women might be more inclined to invest less in schooling due to the possibility of having their time in the
labor force interrupted by caring for children. As a result, we would expect lower pay (on average) for
women then men. This again, would explain some, but not all, of the entire gap. I know what you might
be thinking. If we compared the wages of men and women who had the same educational level, that would
take care of this problem. Below I have duplicated Table 14.2.
No high school degree
High School
Associate
Bachelor’s
Master’s
Doctorate
Professional Degree
Total
White
Male
$29,302
$40,668
$50,747
$73,300
$81,478
$114,518
$153,827
$56,470
White
Female
$20,238
$28,337
$34,996
$49,831
$56,375
$74,024
$68,825
$37,780
African-American
Male
$25,838
$31,389
$43,325
$52,636
$67,093
Not avail
Not avail
$40,342
African American
Female
$19,702
$26,766
$32,084
$44,509
$52,789
Not avail
Not avail
32,573
Is that then airtight evidence of discrimination?
Not so fast. There are other explanations. We have learned that there are compensating wage differentials
associated with dangerous occupations. It is the case that men are more likely to be employed in dangerous
occupations. This alone would be a story that could explain why men earn wages that are on average
higher than women’s wages. Is this enough to explain the entire gap? Certainly not. However, it would be
wrong to suggest that the entire wage gap is because of discrimination.
Another story for men versus women is union pay gaps (men are more likely to be employed in an
occupation that is unionized). Women may prefer shorter hours, or jobs located in suburban areas, which
in both cases, have lower wages.
A story for whites versus African-Americans would be that on average, whites have attended more years of
schooling and have had higher quality schooling (the table above would not adjust for the quality of
schooling attended by African-Americans).
2
Lecture 16
3/30/2007 2:51 PM
Economists that have done research have attempted to disentangle all of the stories and find out how much
of the remaining wage gap is due to discrimination. The answers vary and these studies are difficult. Some
think that 15% of the wage gap is because of discrimination. Some say more.
On last note, and really it is really just a repeat of where we started. Discrimination is complicated. What
if the reason women invest in less schooling is not that they are planning to take care of children, but
because they know they will be discriminated against in the future (the return to schooling is lower)? What
if the reason African-American workers have less schooling is because of the fact they are discriminated
against in college admissions? For more, I strongly encourage you to read the section in the textbook (p.
445– 450).
Textbook Definitions
Economic discrimination exists when female or minority workers– who have the same abilities, education,
training, and experience as white male workers– are accorded inferior treatment with respect to hiring,
occupational access, promotion, wage rate, or working conditions.
Discrimination may also take the form of unequal access to activities that increase the workers amount of
human capital (formal education, apprenticeships, on-the-job training).
1.
Wage discrimination means that female (African-American) workers are paid less than male
(white) workers for doing the same work. More technically, wage discrimination exists when
wage differentials are not based on considerations other than productivity differentials. See
figures 14.1 and 14.2.
2.
Employment discrimination occurs when, ceteris paribus, African-Americans and women bear a
disproportionate share of the burden of unemployment (last hired, first hired). See figure 14.3.
Historically, African-American workers are said to have suffered extensively from this type of
discrimination.
3.
Occupation or job discrimination means that females (African-Americans) have been arbitrarily
restricted or prohibited from entering certain occupations, even though they are as capable as
white (male) workers of performing those jobs, and are conversely“crowded” into other occupations
for which they are frequently overqualified. See figure 14.4. Historically, women are said to have
suffered extensively from this type of discrimination.
4.
Human capital discrimination occurs when females (African-Americans) have less access to
productivity-increasing opportunities such as formal schooling or on-the-job training. This type of
discrimination is sometimes called pre-market discrimination.
Theories of Labor Market Discrimination
1.
2.
3.
Becker’s model (taste-for-discrimination)
Statistical Discrimination
Crowding Model
These notes will discuss the first two models listed above, with an emphasis on the Becker model.
Becker’s Taste-for-Discrimination model
People are assumed to have a taste for discrimination.
Take for example, nepotism, say perhaps people the hire their nephews, despite the fact that their nephews
are complete screw-ups. Despite the fact that hiring their nephew is not a profit-maximizing move, an
employer may do this because they have a taste for hiring their nephew. The employer must pay the “price”
3
Lecture 16
3/30/2007 2:51 PM
of hiring their nephew– that is the lower productivity and hence lower profits. There is an economic cost of
hiring the nephew.
Of course, we will want to apply this model to economic discrimination against women and AfricanAmerican employees, but one of the nice things is that the theory can be applied to any number of
situations. It not only applies to situation when employers discriminate against African-American
employees or women employees, but can also pertain to situations when customers discriminate against a
minority group.
We will concentrate on situation where the employer expresses a taste-for-discrimination. We will assume
the employer is white. In a moment, we will assume the white employer will discriminate against AfricanAmerican employees.
Before we get too far, you should note that while the labels would change, the theory would not change if it
were a male employer discriminating against female employees, or even an African-American employer
discriminating against white employees. Nonetheless, the rest of these notes will assume we have a white
employer that has a taste for discriminating against African-American employees.
Non-discriminatory Employer (Becker)
First, we will assume that African-American employees and white employees are equally productive. In
this case, our non-discriminatory employer will regard the African-American and white employees as
perfect substitutes.
While it seems no doubt silly to think of this way (it will make more sense in a bit), we will consider the
costs to the employer of hiring each class of worker.
Let wW stand for wage of white workers and wAA represent the wage of African-American workers.
Employer’s cost of hiring a white worker: wW
Employer’s cost of hiring an African-American worker: wAA
Discriminatory Employer (Becker)
Suppose we run into a discriminatory employer. Becker’s model would suggest that the white employer has
a taste-for-discrimination against African-American employees. Becker suggests as though the white
employer will act as though hiring African-American employees imposes a psychic or subjective cost on
the employer. The strength of this psychic cost is reflected in the discrimination coefficient, d, which
conveniently we will measure in dollars.
The employer will view the cost of hiring an African-American employee as the wage they must pay the
worker + d, the psychic cost host of hiring the African-American employee.
Employer’s cost of hiring a white worker: wW
Employer’s cost of hiring an African-American worker: wAA + d
Keep in mind that we have assumed that white workers and African-American workers are equally
productive.
Case #1:
wW = $10, wAA = $10, d = $2
In this case, the cost of hiring a white employee is $10, while the employer views the cost of hiring an
African-American employee as $12. The firm will hire only white workers.
Case #2:
wW = $10, wAA = $9, d = $2
4
Lecture 16
3/30/2007 2:51 PM
In this case, the cost of hiring a white employee is $10, while the employer views the cost of hiring an
African-American employee is $11. The employer will hire only white workers. Here, the employer is
paying a “price”for the taste for discrimination. The employer could have hired an equally productive
employee for $9, but instead paid $10 to hire only white workers.
Case #3:
wW = $10, wAA = $8, d = $2
In this case, the cost of hiring a white employee is $10, while the employer views the cost of hiring an
African-American employee is $10. The employer will be indifferent between hiring white and AfricanAmerican workers.
The thing to note here is that the discriminatory employer will only be willing to hire African-American
workers if their wage is lower than white employee’s wages by the amount of the employer’s taste for
discrimination.
If all employers were discriminatory, we would observe a 20% wage gap between African-American and
white employees.
Case #4:
wW = $10, wAA = $7, d = $2
In this case, the cost of hiring a white employee is $10, while the employer views the cost of hiring an
African-American employee is $9. The employer will hire all African-American workers.
The lesson here is that even a discriminatory employer will hire African-American employees, should their
wages be far enough below the wages of white employees. When the discrimination coefficient is $2, the
employer is willing to pay the white employees a wage premium of $2. In this case, the $3.00 wage
premium is too costly for the employer.
How does changing the value of the discrimination coefficient change the story? (Becker)
The value of the discrimination coefficient tells us how strong the employer’s taste-for-discrimination is.
A good exercise for you would be to change the value of d, say to $3, and see what happens in each of
these cases. Then change the value of d, say to $1, and see what happens in each of these cases.
You may also find it useful to note that a non-discriminatory employer has a discrimination coefficient of
$0.
Supply and Demand (Becker)
Be careful! This picture is a bit different from the regular supply and demand story.
On the vertical axis, we will measure the wage of African-American employees relative to that of the white
workers.
For example,
wW = $10 and wAA = $10, then wAA / wW = $10 / $10 = 1
wW = $10 and wAA = $9, then wAA / wW = $9 / $10 = 0.9
wW = $10 and wAA = $8, then wAA / wW = $8 / $10 = 0.8
On the horizontal axis, we will measure the number of African-American employees hired.
Assume that the wage and number of white workers is known and given at some level ($10 in the cases
above).
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Lecture 16
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Demand:
Now, imagine sorting employers from least discriminatory to most discriminatory (from lowest
discrimination coefficient to highest discrimination coefficient). We will put the least discriminatory
employers on the left and the most discriminatory employers on the right.
Since some employers are non-discriminatory. They will be willing to hire African-American workers at
the same wage white workers earn (where wAA / wW = 1). There will be a number of non-discriminatory
employers. Therefore, the demand curve for African-American workers will have a horizontal section at
relative wage equal to 1.
However, after we “run out” of non-discriminatory employers, as we noted above, the wage of AfricanAmerican workers will have to fall before discriminatory employers will be willing to hire AfricanAmerican workers.
If the wage ratio falls to 0.95, employers whose discrimination coefficient is less than 5% of the white
wage will be willing to hire African-American workers (Because wW is assumed to be $10 in this example,
an employer with a value of d of less $0.50 would be willing to hire African-American workers).
If the wages falls to 0.80, employers who discrimination coefficient is less than 20% of the white wage will
be willing to hire African-American workers. (Because wW is assumed to be $10 in this example, an
employer with a value of d of less than $2.00 would be willing to hire African-American workers.
The point is, the lower the wage of African-American wages relative to white wages, the larger will be the
number of employers who will be willing to hire African-American workers.
Supply:
Clearly, more African-American will be willing to work the higher the relative wage. The supply curve
will be upward sloping.
Equilibrium:
Simply find the intersection of supply and demand. The result is the wage of African-American relative to
white wages. See the picture below.
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Lecture 16
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wAA / wW
Non-discriminatory employers (d=0)
SAA
1
0.8
DAA
More discriminatory (larger d)
Quantity of African-American workers
So what? What can be learned from this picture?
What is nice here is that we are being a bit more realistic about the likelihood that employers will have
different discriminatory tastes and hence different values of d. There are two things this graph can tell us.
1.
The larger the supply of the group of discriminated workers, the larger will be the discriminatory
wage gap.
To see this, stick in supply curve in different locations. Intuitively, if there are some nondiscriminatory employers, and only a few African-American employees, they will have little
trouble finding employment at with a non-discriminatory employer. Holding the number of nondiscriminatory employers constant, a larger number of African-American employees will mean
more difficulty finding a non-discriminatory employer.
wAA / wW
SAA1
SAA2
SAA3
SAA4
SAA5
1
0.8
DAA
Quantity of African-American workers
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Lecture 16
2.
3/30/2007 2:51 PM
A change the demand curve will affect the wage ratio.
If attitudes change, or an effective anti-discrimination law is passed, there will be more employers
who are non-discriminatory (a longer flat section of the demand curve) and perhaps even a flatter
slope of the downward sloping portion. The result would be to increase the relative wage of
African American workers.
wAA / wW
SAA
1
0.8
DAA’
DAA
Quantity of African-American workers
Winners, Losers, and Long Term Dynamics (Becker)
The groups of people who are being discriminated against are obviously worse off, while the preferred
group is better off (as they face less competition from the minority group).
What is interesting is that the employers that discriminated are worse off. Assume that these firms sell
goods in a perfectly competitive market. The employers that have a taste for discrimination that hire white
workers could have hired African-American workers at a lower wage. To take a concrete example, if the
wages of white workers are $10, d = $3, and the wages of African-American workers are $8, the employer
will hire only white workers (and the firm’s workers will earn $10). A firm that hires African-American
workers will pay their workers only $8. Clearly, the discriminatory firm will hive higher costs of
production. (Recall that we have assumed African-American and white workers are equally productive).
This provides an interesting implication for the long-term future of discrimination. In a perfectly
competitive market, a firm with a cost disadvantage will lose market share and eventually go out of
business. A discriminatory firm will have a cost disadvantage. Therefore, the market will drive out the
discriminating firms out of the market. No government intervention is required.
Looked at another way, if discrimination was widespread, an entrepreneur would have the incentive to start
a firm with only African-American workers. Existing firms will be faced with the choice of going out of
business, or becoming non-discriminatory employers. Remember what Larry Summers said about women
in colleges? If women were being systematically discriminated against as professors, some school could do
very well hiring a bunch of women professors.
One of economists beefs with the Becker model is that discrimination has not been eliminated as suggested
by the Becker model (though there is evidence that is has been reduced substantially over the last 40 years).
An important caveat is that firms producing goods in a non-perfect competition situation will have more
latitude to discriminate.
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Statistical Discrimination (Statistical Discrimination will not be on Exam #3)
According to the textbook, statistical Discrimination occurs whenever an individual is judged on the basis
of the average characteristics of the groups, or groups, to which he or she belongs rather than upon his or
her own personal characteristics. The judgments are correct, factual, and objective in the sense that the
group actually has the characteristics that are ascribed to it, but the judgements are incorrect with respect to
many individuals within the group.
Your textbook gives you the example of auto insurance rates. Young male drivers, on average, are riskier
drivers than young female drivers. Surely it is the case that you can find a young male driver that is a safer
driver than some young female driver. The person being discriminated against in this case is the male
driver that is a safer driver than the average male. The insurance company is treating this driver as if he has
the characteristics of the average male driver, while in fact he is a safer driver then average male driver.
If this sounds like racial profiling, you are on the right track. I find it somewhat interesting that some
people are very opposed to racial or ethnic profiling, while other find it less disagreeable. I don’t hear much
complaining about statistical discrimination as it pertains to insurance.
In labor econ world, full perfect information about potential employees is not available to the employer.
Information is expensive to gather. The employer is not displaying a taste-for-discrimination, but instead is
using race (or age or sex) as a proxy for productivity related aspects of the employee that are hard to
observer. Basically, the employer is using the average characteristic of the employee’s group to proxy for
their productivity or ability.
On average, African-American workers have had lower quality education than white workers. If two
otherwise equally qualified workers applied (one white, one African-America), the firm may hire the white
employee because the employer would assume that the white worker has had better quality schooling than
the African-American workers (perhaps they both only have a high school education and the employer has
no information about the quality of their high school education). Of course, it is quite possible that the
African-American worker has a higher quality education than the average African-American worker and
possibly a higher quality education than the average white employee. The firm will fail to hire some
productive African-American employees and will hire some less productive white employees.
Another example in the book would be to fail to hire young married women, as the employer knows that on
average, young married women are more likely to leave the labor force to care for children. The women
who is not planning to have children will be discriminated against is she is treated as the“average” women.
The winners and losers are fairly straightforward. Minorities that are more productive than the average
member of their group are made worse off. Firms are not made worse off, and may in fact be better off.
The firms will be right“on average”. It is very expensive to acquire the information about which employees
will be well suited for each occupation, while is cheap to acquire information on the average characteristics
of the group. It should also be stated that statistical discrimination isn’t mean spirited. It is simply a cheap
way to screen potential employees.
Take the insurance example. While some male drivers will be safer than the average male driver, it is
necessarily the case that some drivers will be more risky the average male driver. Perhaps the insurance
company could hire someone to follow around drivers and determine if they are safe drivers, but this is
very costly. If the insurance company has many male drivers and charges them the average rate, the result
will be that the insurance company will get some riskier drivers and some safer drivers (this is the
definition of "average"). The average risk level of the males with insurance will be equal to that of the
average male driver. On average, the insurance company is correct.
There is little reason for statistical discrimination to be alleviated over time.
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What should I read?
Chapter 14. You will find the textbook is very similar to what was discussed in class and appears in these
notes. I referred in class to some textbook“Boxes” you should read. These include:
It Pays to Be Good Lucking (p.430) - Some papers written by Hammermesh and Biddle concerning
discrimination in favor of attractive people.
Competition and Discrimination (p. 435) - Some evidence consistent with the Becker model regarding how
competitive pressures result in less discrimination against women.
Discrimination in Professional Sports (p. 449) - Some results from the economic literature concerning
discrimination in sports. What I think is interesting here is that discrimination cam from the customers.
For the record, apparently there were two white people on the 1984-85 Lakers– Kurt Rambis and Mitch
Kupchak. My apologies to Mitch Kupchak.
Orchestrating Impartiality (p. 453) - An example of occupational discrimination. I think the carpet story is
funny.
----------------If you are interested, I encourage you to read about Occupational Segregation (The Crowding Model) in
Chapter 14. If you are interested in a brief history and the current state of anti-discrimination legislation,
the textbook’s discussion begins on page 450.
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Lecture17
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The Principal / Agent Problem
This lecture is really about alternative pay schemes. Throughout our class, we have assumed, either
implicitly or explicitly, that workers are paid hourly. However, as you know, many workers are not paid
hourly wages. The first thing that comes to mind is workers that are paid salaries, but there are other pay
schemes that are observed out there in the "real world". Before we get into the details of the alternative pay
schemes, and when we might see them, we should go back and talk about the generalities of princpals and
agents.
Principals are parties who hire others to help them achieve their objectives. Agents are parties who are
hired (by principals) to advance the interests of others.
Obviously, real estate agents and sports agents come to mind. If you are selling your house, you are the
principal and hire the real estate agent (agent) to help you sell your house. If you are a professional athlete,
you are the principal and you hire a sports agent to negotiate your contract or land you an endorsement
deal.
The Principal / Agent relationship only becomes a Principal / Agent problem when the goals or interests of
each party are not perfectly aligned. The owners of a firm (principals) want employees to maximize
profits. The employees want to maximize their utility. Employees are willing to help the firms to
maximize profits in exchange for wages – so the goals of the owners and employees are not entirely
inconsistent. However, a worker who earns a salary may not work very hard all day. They may play
solitaire during the day, increasing their utility, but not helping to maximize profits. Thus, the goals of the
principal and agent are not perfectly aligned.
When goals / interests of firms and workers diverge, a principal agent problem exists. Again, the
principal agent problem occurs when agents (workers) pursue some of their own objectives in conflict with
achieving the goals of the principal. Profit maximizing output requires that employees work all agreed
upon hours at agreed up effort. If not, output is reduced, and thus the costs of production increased.
The activity we will focus on is shirking – taking unauthorized work breaks or giving less than agreed
upon effort during work hours. Firms will have an incentive to find ways to reduce or eliminate principalagent problems.
What we will look at next, then, are ways the firm can structure compensation in order to reduce the
shirking problem. In general, these schemes are called incentive pay, or pay-for-performance.
Possibilities include:
•
•
•
•
•
•
Piece Rates
Commissions and Royalties
Raises and Promotions
Bonuses
Profit and Equity Sharing
Tournament Pay
Piece Rates
A piece rate is compensation paid in proportion to the number of units of personal output.
Found where workers control the pace of work and firms find it expensive to monitor effort. Not stated in
your textbook, but also important, you must be able to observe and measure (count) personal output.
While this seems obvious, if team production is involved, it is more difficult to determine who has
produced what. See below.
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Examples – apple pickers, apparel workers, typists, table makers, tax prepares, lawyers
Take, for instance, the apple pickers. Apple pickers determine how quickly the pick apples. It is difficult
to tell if apple pickers are exerting effort (you would have to be in the field with them). At the end of the
day, it is easy to determine how many apples each person has picked. One person picks his or her own
apples – not team production is involved.
Contrast this situation to someone working on an assembly line in Detroit. It would not be necessary to pay
the assembly line worker a piece rate. The assembly line would control the pace of output and the
supervisor can likely easily monitor effort.
Worker who are paid piece rats earn 10-15% more than hourly workers in same industry.
Advantages of Piece Rates:
•
Increased Effort
Drawback of Piece Rates:
•
•
•
•
•
Difficult to find appropriate piece rate “price” in rapidly changing industries.
Increased likelihood of income variability – workers dislike income variability and may demand a
compensating wage differential for this uncertainty. This will be particularly so if the “ups” and
“downs” are beyond the workers control (e.g. bad apple crop).
Likely to be ineffective with complex production or team production. It may be difficult to assign
output to individuals.
May not promote team activity or cooperation. Would you stop to help a co-worker who sprained
an ankle? (John Hackett is bad Samaritan.)
May result in reduced quality. Might I pick up apples off the ground? Quality control / inspection
efforts can mitigate this problem, but are costly.
Commissions and Royalties
Commissions and Royalties link pay to the value of sales.
Found where work effort and hours are difficult to observe. In these cases, time rates (hourly or salary)
would involve a lot of shirking.
If someone tells you they will pay you $50 an hour to write a book, it would likely take many hours for you
to write the book (hours are difficult to observe).
If you were paid $1000 a month to sell insurance, regardless of how many policies you sell, you would
likely not exert much effort (effort difficult to observe).
Examples:
Commissions – Realtors, Insurance, Stockbrokers, Sales
Royalties - Authors, Films, Recording Artists
Advantages of Commissions / Royalties
•
Increased Effort
Drawbacks of Commissions / Royalties
•
Reduces, but does not eliminate the problem. If you paid your real estate agent no commission (a
flat fee), they might urge you to take the first offer you get. If you paid your real estate agent
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Lecture17
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10%, every $1000 increase in the sales prices puts $100 in their pocket. This will provide more
effort, but not as much effort as they would exert if you gave them a 100% commission.
However, if you gave the real estate agent a 100% commission, you just gave away your house.
There is a tradeoff between the effort induced and compensation.
Raises and Promotions
Raises and promotions are just that – raises and promotions.
They are found where people are engaged in team production. It is difficult to monitor effort and measure
output of individuals in the team. If you have ever been involved a group project and have been required to
“divvy” up points among the members of your groups, you know this can be difficult. Two people moving
a piano?
Your textbook goes into this big deal about quasi-fixed resources, but I am not sure you need this story to
understand what is going on.
First, think of someone who is being paid hourly. Given a standard budget line and indifference curve, the
worker will wish to choose a certain number of hours.
Now, consider paying someone that same amount of compensation only paid as a salary. If the worker
could, the optimal choice would be to collect the salary and not work at all. In this story, it is difficult to
determine how much effort if being put forth, so employees might be likely to shirk. While they will not be
able to get away with putting forth zero effort, they will be likely to shirk. The question becomes – how
can we reduce shirking in this case? One answer - by offering raises and promotions.
Advantages of Raises / Promotions:
•
Increased Effort
The tradeoff between leisure and income is not based only on this year’s salary; there is also a
component of future compensation involved. Shirking today involves a reduced likelihood of a
raise or a promotion. On the other hand, working hard today involves the increased likelihood of a
raise or promotion. Salaried workers typically work more hours than hourly employees do. In
short, shirkers do not get raises or promotions
Drawbacks of Raises / Promotions
•
Raises and Promotions are sometimes difficult to undo (see below on bonuses)
Bonuses
Bonuses are extra payments – they can bed paid on personal or firm performance.
Consider bonuses as extension of Raises / Promotions. They will be seen where team performance is
involved and effort is difficult to observe.
Advantages of Bonuses
•
Increased effort. See above Raises / Promotions above
•
Bonuses are not permanent. A raise will permanently increase the salary base. It is unusual to see
someone receive a raise from $100K to $120K one year, then take a pay cut the following year.
A raise is permanent. However, with bonuses, the “extra pay” is not permanent. You can pay
$100K, give the employee a $20K bonus the first year, and if the second year the employee shirks,
you can give no bonus (back to $100K).
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Drawbacks of Bonuses (Personal)
•
Increased incentive for sucking up. If bonuses are paid based on something measurable (sales,
number of apples picked), this is not a problem. However, if the bonus is paid on something less
clearly measurable, that is determined by a supervisor, this provides the incentive for the employee
to curry favor with the supervisor. To be fair, this is also true of raises and promotions
•
Induces activity that is counterproductive to the firm. If Alan Iverson is paid a bonus based on the
number of points he scores a game, this will give him the incentive to shoot in situations where it
would be better for the team if he were passing. If NSU gives professors additional compensation
based on student evaluations, might this provide the incentive for professors to give good grades
and cancel classes?
Additional Disadvantages of Bonuses (Team)
•
Free Riding. In a team setting, the larger the group, the less each individual’s effort ultimately
affects the profit level of the firm. As a result, individuals may “free-ride” – shirk and hope the
other members of the group work hard. (On the other hand, the presence of group bonuses may
cause co-workers to pressure free riders to work harder). If free riding is present, this of course
reduces the effect that incentive pay has. The smaller the group, and the more likely each
individual’s job performance is to affect the “bottom line”, the more effective will be the incentive
scheme. This is why it makes more sense to give the CEO of Ford a bonus based on Ford’s
profitability that someone who attaches tires to the cars. The CEO has more impact on
profitability.
Profit Sharing / Equity Compensation
The dividing lines between bonuses, profit sharing, and equity compensation are fuzzy. While
operationally a bit different (bonus, percentage of profits to employees, stock options), they have the same
advantages and disadvantages of team bonuses. See Chapter 7 if you are interested in more details.
Tournament Pay
Tournament pay is a compensation scheme that is based on relative performance. They are usually seen
where extreme effort is desirable, and of course effort is difficult to monitor.
Typically, first prize is very large, and then prizes drop of significantly. The chance at winning the extreme
first prize is to encourage effort. At the Master’s golf tournament, first prize is $1.2 million, while second
is $530K.
Examples are professional golf tournaments, poker tournaments, NASCAR, and importantly, CEO pay.
Consider what having “really high” CEO pay might cause to happen. People just below the CEO level will
work really hard to try to become the CEO. People at junior management levels will also work really hart
to try to become the CEO some day. People in the mailroom might try really hard to become junior
management, and so on. The big prize at the top of the pyramid is said to promote effort throughout the
organization.
Other features – 2nd and 3rd prize. If the tournament is winner take all, people would get discouraged and
would be unlikely to participate. In the CEO realm, we need to have highly paid Vice-Presidents.
A nice thing is that because performance is relative, there is no problem with external factors. In the case
of a piece-rate apple picking, a bad apple harvest could reduce income. With an apple-picking tournament
based on relative apple picking, this problem is reduced. Participants are not “penalized” for circumstances
beyond their control, nor are they award for thing that are beyond their control (a bumper crop of applies).
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Lecture17
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However, tournament pay is not perfect – there are disadvantages as well. One disadvantage might be that
it will not promote cooperation in a team setting. If you and I are in a winner take all science project, might
I light your science project on fire just before judging? Or if we are both candidates to be the new CEO
and I have a great idea for your division, might I keep it to myself?
If the winner becomes clear (if it is too tough to win), effort might be reduced. Do professional golfers
give up (play more conservatively) when they are way behind Tiger Woods? Does this defeat the purpose
of the big first prize?
Might there be ludicrous risk taking to win the tournament? When I watch “Poker After Dark”, those
players do very risky stuff that they would not do if it were not winner take all. Is the product enhanced?
Or is the lack of 2nd prize causing effort to be lower?
Race for the Chase? Jeff Gordon would have put Jimmy Johnson into the wall a couple of weeks ago if not
for the Race for the Chase. A tournament within the tournament.
You could write a book about tournament pay.
What should I read?
With a few tweaks, I have stolen almost all of this from Chapter 7.
5