Budget, Preference, Demand
Peter Berck
©2010, 2012
Outline
• What you can buy is described by budget
constraints. We learn to graph these and to
show how they change with income and price
changes.
• What you want is described by indifference
curves
• We put these together to get quantity
demanded and ultimately the demand curve
BUDGET
Buying Bundles
• A bundle is a collection of goods
– It is a list, showing how much of each good there
is.
•
(e.g., 2 apples, 3 green beans).
– In an economy with n goods, a bundle has n
elements
• some of which may be zero.
– In mathematical language, a bundle is an n
dimensional vector
What is Affordable?
• A 2-good world, so we can draw things.
– Bread, B, and wine, W
• Prices Pb and Pw
• Quantities B and W
• Income is Y
y = Pb B + Pw w
• Is the budget constraint
• all the (B,W) pairs that cost exactly y.
• Any (B,W) pair that lies on or below the
budget constraint is affordable.
• Any pair that lies above can't be purchased
with y.
Savings
• We would have more than two goods.
• Bread and Wine today and B and W
tomorrow.
• Now there is a reason to save money and buy
tomorrow.
• Money used to buy the tomorrow goods is
savings.
• Now back to 2 dimensions.
Slope Intercept
• Put W on vertical axis, B on horizontal
• W = y/Pw - Pb/Pw B
– Intercept
– Slope
– horizontal intercept is y/Pb.
• Graph by using two points: (0, y/Pw) and
(y/Pb)
Tradeoffs-• If you have a second helping of wine,
• You will have to give up something else,
bread.
• Slope of budget constraint is how much of the
vertical good (wine) you give up to get one
unit of the horizontal good (bread)
Can you find prices and income?
Or do you need to know that Pw=1
to get anywhere
At your seat.
• Show what happens if price of bread increases to twice
its previous value. Does the vertical intercept change?
the horizontal intercept, the slope? has the budget set
become larger or smaller.
• Now show what happens if income increases from 100
to 120. What happens to the vertical intercept, the
horizontal intercept and the slope. Has the budget set
become smaller or larger?
• For completeness, suppose the price of wine
doubles. What are the intercepts now?
Harder Case—Finger exercise*
• A sale. First 15 units of B at the normal price
and all additional units at half price.
– If B <= 15, budget constraint doesn’t change.
– If B > 15
• Then y- Pb 15 = Bsale (Pb /2 )+W Pw
• Total bread = 15 + Bsale
•
•
Take this home and graph it.
*Bob Solow taught that cute theoretical things are finger exercises.
PREFERENCE
Reality and Preference
• Budget constraints describe reality. What one
can do.
• Preference describes what one wants to do.
• Economists assume that people do what they
want to do within the constraints imposed by
reality—budget.
• Let’s look at preference.
Preferences
– Behavioral Assumption: Each person has his/her
own preferences over bundles.
– A person can rank two bundles A and B. Either
• A is preferred to B
• B is preferred to A
• A is indifferent to B
– One person may prefer A to B whilst another
prefers B to A.
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Candy bars and such
• When people choose their bundles of string
beans and broccoli, it is easy to say that their
choice reflects their preferences, but…
Individual Preference? Interdependent
preference? Commandment?
•
Why do we give money to beggars?
•
Meditation XVII. John Donne.
•
"The bell doth toll for him that thinks it doth: and though it intermit again, yet from that minute that that
occasion wrought upon him, he is united to G_d. Who casts not up his eye to the sun when it rises? but
who takes off his eye from a comet when that breaks out? Who bends not his ear to any bell which upon
any occasion rings? but who can remove it from that bell which is passing a piece of himself out of this
world? No man is an island, entire of itself; every man is a piece of the continent, a part of the main. If a
clod be washed away by the sea, Europe is less, as well as if a promontory were, as well as if a manor of
thy friend's or thine own were.. Any man's death diminishes me because I am involved in mankind, and
therefore never send to know for whom the bell tolls; it tolls for thee. (page 1213 of the Norton Anthology
of English Literature. Volume 1. WW Norton & Co. 1974)
•
Leviticus. XIX-7.
•
And when you reap the harvest of your land, thou shalt not wholly reap the corner of thy field, neither
shalt you gather the gleaning of thy harvest. And thou shalt not glean thy vineyard, neither shalt thou
gather the fallen fruit of thy vineyard: thou shalt leave them for the poor and the stranger. I am the Lord
your G_d. (Hertz)
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Veil of Ignorance
Beggar or Rich Man to Be? Would Ezra Berck (9/10/2010) vote for laws that
protect beggars at the expense of rich men right now?
Respect Preferences?
• Would you use the word, prefer, to describe the actions of an alcoholic or
a drug addict. Would you say, "she prefers alcohol to food?" If you said
that, would you still want to influence the addict to change their behavior?
Does your answer depend upon the damage addicts do to other people? If
it does, consider the poster-girl addict: she hurts no-one but herself and
dies with enough money in her pocket for her own burial. Do you
subscribe to the view that if a person thinks their choice makes them
better off then you (and the rest of society) ought also think that the
person's choice makes them better off? Do you have the same problems
answering these questions for a person who chooses cauliflower rather
than broccoli?
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Preference?
Do preferences lead to diabetes? Can your generation help itself in
the thralls of soda (which used to come in 6 oz bottles and was not
stocked in people’s refrigerators)? And 12” and larger plates?
• Do all people have meaningful preferences?
– Is the choice to smoke, use heroin a preference?
– Do people with severe mental disorders make
choices in the same way others do?
– Economists, as a group, will likely assert the
existence of preferences in cases where the
medical community would say illness.
Revealed Preference
• If choice A and B (perhaps bundles) are both
possible choices and A is chosen then we
conclude A is preferred to B.
• If we agree that impaired people have
preferences, and we observe them make a
bad choice, heroin, can we say that they
preferred heroin? Obesity? Ciggies?
• Again, economists would generally say yes,
they preferred it.
Interference
• I stop the addict against their wishes.
• 1. I don’t believe it is their preference
• 2. Their action hurts others, hence their
preference isn’t the only thing in play.
• 3. I have preferences over their well being.
(e.g. John Donne)
Non-Interference
• It is their personal responsibility.
• I believe they have made a choice based on
their preferences, that it does not unduly hurt
others, and that I should not allow my
compassion to overcome my respect for their
choices.
PROPERTIES OF PREFERENCE AND
INDIFFERENCE CURVES
Properties
– The preferences are assumed to have the
following reasonable properties:
• I. More is better. If bundle A has strictly more of one
good and does not have less of any good than bundle B,
then all consumers prefer A to B.
• II. Transitivity. A better than B better than C means A
better than C.
• III. A preferred to B means B is not preferred to A.
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More is Better
These points have
more bread or wine
or both.
Every consumer prefers
them to
A
Bread
?
A
Worse than
A
for all.
?
Wine
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Point, A, in Bread-Wine space is a bundle
27
Level Set
• A set of points that have the same height.
• Examples
– All the locations on Mt. Marcy that are 1,450 feet.
– z = xy; {(x,y)| k = xy} is a level set, where k is a
constant
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Mt. Marcy, NY
Same colored squares are all the same height.
They are in the same level set.
Light Blue squares are 50 units off the “floor”
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Indifference curves.
– Two bundles are indifferent (for a particular
consumer) if the consumer is equally happy with
either bundle.
• (If one added the teeniest bit of any good to one of the
bundles, then the consumer would prefer it.)
– Let A be a bundle. There is an indifference curve
through A.
– The indifference curve through A is the set of all
bundles that makes the consumer just as happy as
bundle A.
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Utility is an Ordinal Measure of
Happiness
• Think of Utility as height and amount of goods as
x1 and x2
• All bundles same height = level set = indifference
curve
• Theory only requires indifference curves not
utility. (We need to know which is higher, not
how much higher.)
• Ordinal means rank (one bundle better than
another) not absolute amount (one bundle is 17
utils better than another)
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Properties.
– Indifference curves slope down.
– They do not cross.
– Higher indifference curves are better.
– For reasons that I don't care to discuss, I always
draw them so that they look like a crescent moon.
(see p. 66 if you are curious.)
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A Demonstration
c
B
b
a
W
Every point on the higher indifference curve is better because b is preferred
to a by more is better, c is indifferent
to b because they are on the same indifference curve and therefore c is
preferred to a.
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Indiff. Curves Don’t
Cross
Use more is better
and transitivity to
construct the proof
B
a
c
b
W
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CHOICE OF BUNDLE
Choosing a Bundle
– Consumers can choose anything on or under their
budget constraints.
• Those are the only things that they can afford.
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Which Bundle?
B
Of the bundles a consumer can
afford, the consumer chooses
the one the consumer
likes
most.
e
Remember: Higher
indifference curve, like
more.
c
f
d
W
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Which??
• Choice will occur where an indifference curve
is tangent to the budget constraint.
• No point on the upper indifference curve lies
on the budget the constraint. The consumer
might like it but can't afford any such bundle.
• All points on the lower indifference curve are
inferior to the middle indifference curve.
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Find the bundle
How much bread and
how much wine are purchased?
B
If income is 2, what are the
prices of bread and wine?
6
4
2
2
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4
W
40
Change in income
– An increase in income shifts budget constraints up
in a parallel fashion.
– (x2 = y/p2 -p1/p2 x1; slope-intercept. change in y
does not change slope but increases intercept.)
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Inferior and Normal
– When income increases the quantity purchased of
a normal good also increases.
– When income increases, the quantity purchased
of an inferior good decreases
B
W
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DEMAND CURVES
Theory
• From among those bundles he can afford,
consumer chooses bundle that makes him
happiest (maximizes his utility)
• Y = p1x1 + p2x2
– gives bundles can afford
• Indifference curves
– shows preferences among bundles
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Choice at 3 Prices for Bread
Price of Wine is 1
100
80
Wine
High P
60
Medium P
40
Low P
20
0
0
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50
Bread
100
45
Price-Quantity Chart
The price of wine is 1.
Price
High
Med.
Low
100
80
In Numbers Quantity
$4/loaf
10
$2/loaf
22
$1/loaf
40
Wine
High P
60
Medium P
40
Low P
20
0
0
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50
Bread
100
46
price of bread
Demand Curve
Price
High
Med.
Low
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
10
20
30
In Numbers Quantity
$4/loaf
10
$2/loaf
22
$1/loaf
40
40
50
quantity of bread
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Income Shifts Demand
Price of Wine is 1
Income In Numbers Quantity
80
$4/loaf
10
80
$2/loaf
22
100
$2/loaf
30
120
100
High P
Wine
80
Medium P
60
Med. P;
High Y
40
20
0
0
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Bread
40
60
48
price of bread
One Point on a Demand Curve
Shifted Out by Increased Income
Income In Numbers Quantity
80
$4/loaf
10
80
$2/loaf
22
100
$2/loaf
30
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
10
20
30
40
50
quantity of bread
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Example from the book: Electricity
• What is the elasticity demand?
• Assume a flat supply curve and roughly
1,000,000 households in Montana.
– How much tax revenue would a $50 tax raise?
– How much electricity gets saved
– Research:
• What is the state budget in Montana?
• How much carbon per MW, assuming coal?
• How much does carbon sell for on the European trading
system?
Figure 4.5:
Budget Constraints at $50 and
$100/MWH.
4-51
© 2011 Pearson Addison-Wesley. All rights
reserved.
Figure 4.6:
The Chosen Bundle for Two Prices.
4-52
© 2011 Pearson Addison-Wesley. All rights
reserved.
Figure 4.7:
Demand Curve for Electricity.
4-53
© 2011 Pearson Addison-Wesley. All rights
reserved.