Econ 100A: Microeconomics
Course Pack
Jim Campbell
UC Berkeley
Fall 2022
This pack contains the material for our Microeconomics course. Our guiding questions for the
semester are where do prices come from and are they ‘right’ ? Why do some things have
higher prices than others? What is reflected in a price? Would it be better if prices were different
than they are?
In a more concrete sense, this course is about the fundamental tools that economists use to
think about decision-making by and interactions among economic agents like people, households,
firms, and governments. The way I see it, there are two broad uses for working on learning these
tools. First, it lets you in to some deep, philosophical questions if you are into big picture thinking
about how the world works. Second, this material forms the theory at the core of the modern,
sophisticated tools that economists use to answer specific, important policy questions, for example
about the effect of immigration, minimum wages, mergers and acquisitions, and innovation policy.
Try to find your own path here, because your thinking about these ideas might be quite different
than mine or your classmates, and that’s OK.
Each section in this pack should correspond to roughly 2-4 classes, give or take. In each section
you will find readings and resources (titles are clickable!), a list of concepts that you should know,
mathematical and analytical problems, and discussion prompts. The course pack is an implicit
contract for the course: if you can confidently and clearly use and explain the relevant concepts
and mathematical techniques, answer the practice problems, and sketch out well-reasoned and
well-supported arguments that address the discussion prompts, then you are well-prepared for
assessment in a given topic. Of course, the questions I will ask you on quizzes and exams are not
identical to the questions in the course pack—they will be new questions that ask you to apply
what you learned to novel problems and issues—but if you have understood the content of the
course pack, I consider you prepared to tackle those fresh questions.
How you get to that level of preparation is up to you! In class and in discussion sections,
we will work through the course pack: we will work on mathematical and analytical problems together to learn mathematical techniques and the application of core concepts in economic
models, discuss, in groups and as a class, subjective questions on microeconomic issues
to practice analyzing, applying, and critiquing the core ideas in microeconomic theory, and deliver and watch presentations on contemporary economic research to learn how research
economists use microeconomic tools and ideas to learn more about the world. I like to use our class
time in this course to demonstrate and discuss concepts and applications in this way rather than
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
giving traditional lectures, since I’ve found this more useful and valuable as a way to prepare you
for assessments. On top of that, four times during the semester the whole class will be assigned
a paper to read and respond to in a short written assignment, and once during the semester you
will present in your discussion section on another paper of your choice from those in the course
pack reading lists.
Apart from these readings I’ve just mentioned, there is no required reading for this class.
However, I recommend familiarizing yourself with the core concepts either in advance of or at the
same time as the classes when we apply those concepts, and you have some options for how to
do that. I don’t assign textbooks that cost money in my classes. To learn the core concepts, you
may use (i) my lecture notes (posted to bCourses), (ii) the Intermediate Microeconomics Video
Handbook (IMVH, linked via bCourses modules), (iii) the free textbook ‘Models in Microeconomic
Theory’ by Osborne and Rubinstein, (iv) a textbook that you buy if you choose (recommendations
are on the syllabus), or (v) any other high-quality resource of your choice (feel free to ask for
advice). I recommend using any of these resources in a combination that works for you in the
same way that you’d use a traditional textbook: use them to support your understanding and
learning when you need them, but there’s no need to religiously grind through them if you are
already comfortable with what we’re learning. I write the course pack and all of the assessments in
our course myself—there will be no ‘gotcha’ questions that refer to obscure stuff from deep inside
a reading or textbook.
My goal then is that what we do in class and sections should give you a good foundation to
succeed in your assessed work. I recommend taking notes on both what you read and what we
discuss in class, since taking good notes is proven to help you remember things later. Please
come to class and section, do your reading, and participate in discussions with a pen
and paper in front of you! And, as always, I strongly encourage you to take advantage of my
office hours and the GSIs’ office hours to meet with us if you have any questions or concerns or just
want to discuss something. I especially am always interested to know what topics in economics
you’re particularly interested in so that I can help you figure out how to best plan your next steps
after this course is done.
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Contents
0 General reference sources for economic news and analysis
5
1 Preferences and utility
6
2 The rational choice model
10
3 Demand
14
4 An application of consumer theory to labor supply
19
5 Choice under uncertainty and risk aversion
23
6 General equilibrium in an exchange economy
28
7 Producer theory
33
8 Perfect competition and partial equilibrium
38
9 General equilibrium with production
44
10 Monopoly and market power
48
11 Externalities
54
12 Game theory
60
13 Oligopoly theory
65
14 Markets with asymmetric information
71
A Math refresher
78
B Constrained optimization by Lagrangian method
79
C What do we do in discussion sections?
81
D Tackling discussion prompts
83
E Sample midterms
84
F Past final exam
88
G Tips for the essay exam
88
In the first section of our course, we will build the canonical models of choice in economics,
the foundation of the economic approach to studying human behavior. We will then build our
first equilibrium models, the canonical approach to decentralized interaction by “large” numbers
of people.
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Next we will build models of production, in which people and entities endeavor to turn things
into other, more complicated things. We will enrich and revisit our models of equilibrium under
so-called “perfect competition”, a core benchmark model in economics, and critically evaluate its
assumptions and curiosities. We will also explore with a critical eye some typical ways in which
economics evaluates the quality of an allocation of resources.
In the final section of our course we will construct models of so-called “market failure”, in which
decentralized decision-making are likely not to deliver a “good” outcome, for some definition of
the word good. We will consider in particular power discrepancies and what may happen when
there are not a “large” number of people involved in some economic interaction.
By this time, we will have studied much of the core bedrock of modern microeconomic theory,
taking us from roughly the late 19th century to the mid to late 20th century and pointing us
throughout the course to how contemporary economics has continued to develop. Your further
study in microeconomics, if you choose that path, will both use and expand on the ideas in our
course as you learn more about how economists seek to enrich our understanding of the world!
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Jim Campbell, UC Berkeley
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Econ 100A Course Pack, Fall 2022
General reference sources for economic news and analysis
This section is just for information and not even necessarily for our course! Just some useful links
to good places to read free, high quality articles about economic issues.
ˆ Our World in Data
ˆ National Bureau of Economic Research (includes the Reporter, interviews, lectures, and
more!)
ˆ The Brookings Institution and The Hamilton Project
ˆ U.S. Census Bureau
ˆ Federal Reserve Economic Data and St. Louis Fed publications
ˆ Pew Research Center
ˆ Economic Policy Institute
ˆ VoxDev
ˆ Journal of Economic Perspectives
ˆ NPR Planet Money and Hidden Brain podcasts
ˆ Microeconomic Insights
ˆ Econ Graphs (really cool interactive graphs, very neat)
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Econ 100A Course Pack, Fall 2022
Preferences and utility
1.1
References
ˆ Jim’s lecture notes “Preferences, constraints, and choice”
ˆ Video handbook section C1 (A2 is math background on level sets which can be helpful too!)
ˆ Osborne and Rubinstein, Chapter 1 and 4
ˆ Serrano and Feldman, Chapter 2
1.2
Readings
ˆ Kahneman, Daniel, Jack L. Knetsch, and Richard H. Thaler. 1991. “Anomalies: The
Endowment Effect, Loss Aversion, and Status Quo Bias.” Journal of Economic Perspectives,
5 (1): 193-206.
ˆ Bowles, Samuel. 2008. “Policies designed for self-interested citizens may undermine “the
moral sentiments”: Evidence from economic experiments. Science, 320 (5883): 1605-1609.
ˆ Cascio, Elizabeth U. and Na’ama Shenhav. 2020. “A Century of the American Woman
Voter: Sex Gaps in Political Participation, Preferences, and Partisanship since Women’s
Enfranchisement.” Journal of Economic Perspectives, 34 (2): 24-48.
ˆ Morgan, Mary S. 2014. “What if? Models, fact and fiction in economics.” Journal of the
British Academy, 2: 231-268.
1.3
Concepts
ˆ Preferences; utility function; indifference curves; marginal rate of substitution; well-behaved
preferences (convexity and monotonicity); perfect complements; perfect substitutes; monotonic transformation of a function
1.4
Problems
1. For each of the following utility functions, sketch two indifference curves: one for the utility
level u = 1 and one for the utility level u = 2. Remember to label the axes and the indifference
curves on your diagram.
a) u(x1 , x2 ) = x2
b) u(x1 , x2 ) = x1
c) u(x1 , x2 ) = min{x1 , x2 }
d) u(x1 , x2 ) = x1 + x2
e) u(x1 , x2 ) = x1 x2 (tricky! Try u = 4 and u = 9 if you get stuck...)
2. Jim likes both watching baseball (x1 , measured in ‘hours per day’) and teaching microeconomics (x2 , measured in ‘hours per day’). He has decided that his utility function for these
two goods is u(x1 , x2 ) = x31 x2 .
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a) Find M U1 , the marginal utility of an hour per day of watching baseball.
b) Find M U2 , the marginal utility of an hour per day of teaching microeconomics.
c) Find Jim’s M RS, his marginal rate of substitution of hours of teaching for watching
baseball.
d) Jim currently watches 8 hours of baseball per day and teaches microeconomics for 2 hours
per day. Find the value of his M RS at this point, and describe in words what this value
means.
e) Jim thinks he might have made a mistake. He thinks his utility function might actually
be u(x1 , x2 ) = 6 ln x1 + 2 ln x2 . How does the M RS for this utility function compare to
the M RS for the original one? Why?
3. Find the marginal rate of substitution of good 2 for good 1 for each of the following utility
functions:
a) u(x1 , x2 ) = 4 ln x1 + 2 ln x2
√
b) u(x1 , x2 ) = x1 + 2x2
c) u(x1 , x2 ) = f (x1 ) + x2 , where f is a generic function
d) u(x1 , x2 ) = x1 + x2
4. Using two or three non-technical sentences:
a) Give an example of a situation in which a consumer’s preferences are nonconvex. Sketch
a couple of indifference curves that match your example.
b) Explain the preferences of a consumer with upward-sloping indifference curves in a twogood world. Give an example of a utility function that generates upward-sloping indifference curves.
c) A typical assumption about a person’s preferences in an economic model is diminishing
marginal rate of substitution. Sketch a couple of indifference curves for an example of
preferences that instead have increasing marginal rate of substitution. Explain in words
what increasing MRS means and how that’s reflected in your picture.
5. Explain using one or two non-technical sentences:
a) What it means for preferences to be monotonic.
b) What it means for preferences to be convex.
c) The relationship between convexity and marginal rate of substitution.
6. Of the following utility functions, two represent exactly the same preferences. Which two
and why?
ˆ u1 = x1 x22
ˆ u2 = x1 x2
ˆ u3 = 2 ln x1 + ln x2
ˆ u4 = x21 x32
ˆ u5 = 3 ln x1 + 3 ln x2
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7. Part of a consumer’s indifference map:
a) What is this consumer’s marginal rate of substitution? What does that mean in words?
b) Give three examples of utility functions that could have generated this indifference map.
Please answer such that two of your utility functions represent the same preference
ordering, but the third represents a different preference ordering than the other two.
Explain your answer.
8. a) Two indifference curves for a single utility function cannot intersect. With the aid of
a diagram, explain why. What typically-assumed property of the preference relation
would be violated?
b) Say that a consumer’s marginal rate of substitution is always exactly zero. Suggest two
different utility functions, representing different preference orderings, that this consumer
might have. Explain in words what exactly it means to have an MRS that is always
zero.
9. a) Imagine that we knew that a consumer’s preferences can be represented by some utility
function u = f (x1 , x2 ). Say that bundle A has a utility u = 10 and bundle B has u = 5.
Is it correct to say that the consumer likes bundle A twice as much as they like bundle
B? Why or why not?
b) Say that a decision maker has preferences that can be represented by the utility function
u = 5 ln x1 + ln x2 . Is it correct to say that “this decision maker is always willing to give
up 5 units of good 2 for at least 1 unit of good 1”? Explain why or why not.
10. Consider a world with two goods, x1 and x2 . Person A’s preference ordering has marginal
x1
and person B’s preference ordering has marginal
rate of substitution given by M RSA = 2x
2
2x2
rate of substitution given by M RSB = x1 . You may assume that both A and B’s preference
orderings are monotonic.
a) Which person’s preferences are ‘convex’, in the sense that it is usually meant in this
context? Explain how you know this from the marginal rates of substitution, with the
aid of one or more sketches.
b) For the case of person B, give an example of a utility function that could have generated
this marginal rate of substitution.
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Jim Campbell, UC Berkeley
1.5
Econ 100A Course Pack, Fall 2022
Discussion
1. Brainstorm what a person’s preferences might look like for some real world or hypothetical
examples.
2. Do you think people know their own preferences? Does it matter?
3. Explain the relationship between preferences, utility functions, and indifference curves. Try
to be as precise as you can.
4. To what extent do you think people’s preferences are driven by social considerations versus
selfish considerations? What makes something social rather than selfish?
5. What are some standard assumptions that economics often make about people’s preferences?
How reasonable do you think those assumptions are? Brainstorm some examples in which
you think one of the assumptions is really plausible or really implausible.
6. “The way economists think about human behavior is far too restrictive, so their models are
useless.” Discuss.
7. Is there anything more to the concept of preferences than just a person’s subjective feelings
about the world?
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Econ 100A Course Pack, Fall 2022
The rational choice model
2.1
References
ˆ Jim’s lecture notes “Preferences, constraints, and choice”
ˆ Video handbook C2a,b,i,j,k
ˆ Osborne and Rubinstein, Chapter 2 and 5
ˆ Serrano and Feldman, Chapter 3
2.2
Readings
ˆ (Reading response 1) Small, Mario L. and Devah Pager. 2020. “Sociological Perspectives
on Racial Discrimination.” Journal of Economic Perspectives, 34 (2): 49-67.
ˆ Kahneman, Daniel, and Richard H. Thaler. 2006. “Anomalies: Utility Maximization and
Experienced Utility.” Journal of Economic Perspectives, 20 (1): 221-234.
ˆ Einav, Liran, and Leeat Yariv. 2006. “What’s in a Surname? The Effects of Surname Initials
on Academic Success.” Journal of Economic Perspectives, 20 (1): 175-188.
2.3
Concepts
ˆ Budget set; constraints; rational choice; the tangency method; revealed preference; quasilinear utility function; Cobb-Douglas utility function
2.4
Problems
1. For each of the following situations, write down an equation for the consumer’s budget
constraint, and sketch the budget set (with x1 on the horizontal axis and x2 on the vertical
axis). Label your axes, and write the slope of the budget line and the intercepts on your
diagram.
a) p1 = 4, p2 = 2, m = 60
b) p1 = 1, p2 = 5, m = 30
For this situation, just sketch the consumer’s budget constraint.
c) p1 = 5 and m = 30. The price of good 2 depends on the number of units the consumer
buys. The first 5 units of good 2 cost 3 per unit, but each unit after that costs 5.
2. In each of these cases in which the consumer has well-behaved preferences, find the consumer’s
optimal choice using the tangency method. Show your intermediate steps.
a) u = ln x1 + 4 ln x2 , p1 = 3, p2 = 2, m = 30
√
b) u = x1 + x2 , p1 = 8, p2 = 2, m = 12
c) u = ln x1 + 2 ln x2 , p1 = 2, p2 = 1, m = 30.
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Jim Campbell, UC Berkeley
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3. In each of these cases the consumer does not have well-behaved preferences. Find the consumer’s optimal choice by sketching a picture (with the budget set and a couple of indifference
curves) to illustrate.
a) u = min{x1 , x2 }, p1 = 3, p2 = 2, m = 20
b) u = max{x1 , x2 }, p1 = 2, p2 = 1, m = 10
4. Each summer Jim faces a dilemma. There are two goods in the world, Boston Red Sox
tickets (x1 ) and Pawtucket Red Sox tickets (x2 ). Jim has $200 to spend on tickets. Boston
tickets cost p1 = 50 each and Pawtucket tickets cost p2 = 10 each. Jim loves going to any
baseball game, but he likes going to Fenway a bit more than going to McCoy. His utility
function is u = 3x1 + x2 .
a) Sketch Jim’s budget constraint. Label the axes, the slope, and the intercept.
b) Calculate Jim’s marginal rate of substitution. Interpret how it compares to the price
ratio he faces.
c) What is Jim’s optimal choice of consumption bundle? Mark it on your diagram and add
to your diagram the indifference curve for Jim that passes through the optimal choice.
d) Explain why Jim prefers the point you found in c) to any other bundle in his budget set.
5. a) Explain using one or two non-technical sentences why the optimal choice for a consumer
with well-behaved preferences cannot be where M RS 6= pp12 .
b) Explain in a few sentences what the rational choice model in economics is, as if you were
talking to a friend who had never taken an economics course.
c) Take the following example. There are two goods. A consumer chooses to spend all of his
money on one of the goods. Suggest three different utility functions, each representing
a different preference ordering, that would rationalize this choice behavior.
6. There are two goods, x1 and x2 . Their prices are p1 = 2, p2 = 3. A consumer has utility
function u = x1 + x2 and income m = 30. Sketch the consumer’s budget set. Mark on your
diagram the consumer’s optimal choice, and the indifference curve that the optimal choice
lies on. Explain in words why this is the consumer’s optimal choice.
7. Jim is at a store that stocks two items, cookies (x1 ) and vegetables (x2 ), which each have a
price of $1 per unit. He has $20 to allocate between two goods. However, he can purchase
no more than 15 units of either good, since there are only 15 units of each at the store. Jim
has well-behaved preferences represented by the utility function u = 4 ln x1 + ln x2 .
a) Sketch Jim’s (non-standard) budget set.
b) Find Jim’s optimal choice. Mark it on your sketch of the budget set, and sketch the
indifference curve for Jim that passes though the optimal choice. Don’t try to precisely
plot out the indifference curve, but try to get the slope roughly correct at the optimal
choice.
c) If there had been no limit on the number of each good for purchase, would Jim have
gotten higher utility, lower utility, or just the same utility?
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8. A consumer has utility function u = x1 + 2x2 . Let m = 20 and p1 = 2. Above what value
of p2 will the consumer’s optimal choice be to spend all of their money on good 1? Explain
your answer (words, math, or diagram are all fine for the explanation, whatever you prefer).
9. Consider a model with two goods, Subway sandwiches (x1 ) and tickets to Drake shows (x2 ).
Each good must be consumed in a non-negative amount. Jim’s preferences over these two
goods can be represented by the utility function u = 10 − x1 − x2 .
a) Sketch a diagram illustrating two of Jim’s indifference curves for levels of utility of your
choice (please remember to label your axes and to label each indifference curve with its
utility level).
b) Say that Jim has m = 50 to spend and that p1 = 5 and p2 = 20. What is his optimal
choice of consumption bundle and why?
c) Write a different utility function that would represent exactly the same preferences as
u = 10 − x1 − x2 . Briefly explain your answer.
10. A consumer has well-behaved preferences that can be represented by the utility function
u = 6 ln x1 + 3 ln x2 .
a) Calculate the marginal utility for each good. Explain in words what your answers tell us
about this consumer’s feelings about these goods.
b) Say that we see the consumer choose the bundle (5, 5) from a standard triangular budget
set, but we don’t know everything about that budget set. We know that p1 = 4, but
not p2 or m. However, we can figure them out. What must p2 and m be and why?
11. Assume a standard, triangular budget set. For each of these two descriptions, use a diagram
and a short explanation to describe a situation in which:
a) There is a single point of tangency between the budget line and one of the consumer’s
indifference curves, but that point is NOT the consumer’s utility-maximizing choice.
b) The consumer’s utility-maximizing choice is on the budget line but is NOT a point of
tangency between the budget line and an indifference curve.
12. Consider the following two-good world with a non-standard budget set. A person has m = 50
to spend, the price of good 1 (x1 ) is $0 per unit, and the price of good 2 (x2 ) is $10 per unit.
a) Sketch (a portion of) this person’s budget set, and explain what makes it unusual.
b) Suggest a utility function such that the bundle (0, 5) would be the unique optimal choice
for this person from their budget set. On your diagram from a), add a couple of indifference curves for your chosen utility function, labeled with their utility level. Briefly
explain your answer.
13. Say that there are two goods, books (x1 ) and video games (x2 ). Jim and Stephanie both have
rational preference orderings over bundles of these goods, each person’s preference ordering
satisfies monotonicity, and each person’s marginal rate of substitution is constant.
a) Say that Jim’s marginal rate of substitution is higher than Stephanie’s. In plain English,
explain what this means in the context of this example. Suggest a utility function for
each person that would be consistent with the information given.
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Jim Campbell, UC Berkeley
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b) Keep the MRS assumption from a). Say that Jim and Stephanie face the same budget
set, and Stephanie’s optimal bundle is x1 = 10, x2 = 0. Based on this information, do
we know what Jim’s optimal bundle is? If so, what is it and why? If not, why not? A
sketch might help to illustrate your answer.
14. There are two goods, x1 and x2 . Jim’s well-behaved preferences over bundles of goods can
√
be represented by the utility function u = 3x1 + 4 x2 . The price of good 1 is p1 = 3, the
price of good 2 is p2 = 2, and Jim has m = 14.
a) Use the tangency method (or another valid method if you prefer) to find Jim’s optimal
choice of consumption bundle.
b) Consider the bundle (2, 4). Sketch Jim’s budget set, and sketch the indifference curve for
Jim on which that bundle lies (just the right general shape is OK, no need to precisely
plot it out). Explain why your sketch shows that this bundle cannot be Jim’s optimal
choice.
2.5
Discussion
1. How restrictive do you think the rational choice model is if you’re trying to model people’s
behavior? Be precise about your reasoning.
2. What, if anything, do we learn about a person by observing their choices? Does it matter
how many choices we observe?
3. There is evidence that sometimes people’s choice between two options depends on what
other unchosen options were available. That is, you choose A over B, but if C is available
you choose B over A. Can you think of a situation where that might be the case? Is this
compatible or incompatible with the standard rational choice model?
4. We have seen that a tangency condition between indifference curve and budget line is the
‘solution’ to a theoretical utility maximization problem, under some conditions. Do you
think the tangency condition bears any relationship to how people actually choose things in
real life?
5. “A consumer choice model in economics can say anything you want, it just depends on how
you write it.” Does that make sense, and would that be a good thing or a bad thing?
6. “The assumption that goods are divisible rather than discrete (for example that you can
have 2.15 units of something rather than just 2 or 3) is a much bigger deal than it’s made
out to be.” Do you agree or disagree?
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Econ 100A Course Pack, Fall 2022
Demand
3.1
References
ˆ Jim’s lecture notes “Demand”
ˆ Video handbook C2c,e,f; C3a,b; C4a,b,c,d; C6
ˆ Osborne and Rubinstein, Chapter 5
ˆ Serrano and Feldman, Chapter 4
3.2
Readings
ˆ Gneezy, Uri, Stephan Meier, and Pedro Rey-Biel. 2011. “When and Why Incentives (Don’t)
Work to Modify Behavior.” Journal of Economic Perspectives, 25 (4): 191-210.
ˆ Kleven, Henrik, Camille Landais, Mathilde Muñoz, and Stefanie Stantcheva. 2020. “Taxation and Migration: Evidence and Policy Implications.” Journal of Economic Perspectives,
34 (2): 119-142.
3.3
Concepts
ˆ Demand function; comparative statics; normal versus inferior goods; ordinary versus Giffen goods; complements versus substitutes; offer curve; Engel curve; demand curve; income
expansion path a.k.a. income-consumption loci; the Slutsky and Hicks decompositions; substitution and income effects; elasticity of demand
3.4
Problems
1. A consumer has utility u = x1 x22 , has income m, and faces prices p1 and p2 . Use the tangency
method to find the consumer’s demand functions. For each of the two goods, is the good
normal or inferior? Ordinary or Giffen? Are the two goods substitutes or complements?
2. Consider a two good model with a consumer whose utility function is u = ln x1 + 2x2 . (This
is an example of a quasilinear utility function.) Prices are p1 = p2 = 1 and the consumer
has income m. Derive the income expansion path for this consumer and sketch a diagram
to illustrate it. Describe her choice behavior in words, and suggest an example of two goods
that might fit this type of preferences and choice behavior.
3. Consider a two good consumer choice model in which a consumer with well-behaved preferences faces standard budget constraints with prices p1 and p2 and income m.
a) Say that for this consumer good 1 is normal and good 2 is inferior. Sketch a diagram on
axes x1 , x2 with two different budget lines, indifference curves, and optimal choices that
illustrates an example of what this looks like.
b) In the situation in a), what shape does this consumer’s Engel curve for each good have
and why?
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4. What shape does the income expansion path have for a Cobb-Douglas utility function and
how does it depend on the parameters of the utility function and of the budget? Explain
your answer with the aid of a diagram.
5. A consumer has utility u = 2 ln x1 + x2 , has income m, and faces prices p1 and p2 . Use the
tangency method to find the consumer’s demand functions. Derive an expression for the
consumer’s price elasticity of demand for good 1. Explain what you find.
6. There are two goods. A consumer has (non-well behaved) preferences represented by u =
min{x1 , x2 }: the goods are perfect complements. Her income is m, and she faces prices p1
and p2 that are finite and strictly positive. Write this consumer’s demand function for each
good.
Say that the price of good 1 falls. Using either the Slutsky or Hicks methods, how much of
the total change in demand is due to the substitution effect, and how much to the income
effect? Sketch a diagram to illustrate your answer and explain in words what’s going on.
7. Consider a two good model with a consumer who considers the goods to be perfect substitutes. That is, her utility function is given by u = x1 + x2 .
a) Sketch a diagram illustrating the derivation of the income expansion path for this consumer.
b) Sketch a diagram illustrating the offer curve for this consumer.
√
8. A consumer has a utility function u = x1 + x2 . She has income m = 2 and faces prices
p1 = 1 and p2 = 1. Say that the price of good 1 falls to p01 = 12 . Perform a Hicks and Slutsky
decomposition of the effect of this price change on the demand for good 1.
9. Jim’s preferences over minor league baseball tickets (x1 ) and minor league hockey tickets
(x2 ) can be represented by u = x1 . Jim has m = 30 to spend on tickets and initially faces
prices p1 = 3 and p2 = 6. Then the price of p1 increases to 6.
a) Sketch a diagram showing the budget lines, Jim’s optimal choices, and the associated
indifference curves labeled with their utility levels for both the original and new prices.
(We’ll be adding to this diagram in a moment, so make it big and clear.)
b) By adding to your diagram from a), use a graphical analysis to decompose the effect of
the price change on Jim’s optimal choice of x∗1 using the Slutsky method. What are the
substitution and income effects as a result of this price change?
c) What is the equation of the budget line that you added to your diagram in part b)?
Explain why that’s the equation of the budget line you added, with reference to both
the specific numbers in your equation and to the point of the Slutsky decomposition.
10. Say that there are only two goods in the world, lobster rolls (good 1) and bowls of ramen
(good 2).
a) Jim’s Engel curve for each good (for income above some minimal level) is a straight,
vertical line. Describe in plain English what Jim’s Engel curves mean. What standard
assumption about preferences in economics is inconsistent with Jim’s choices? Why?
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Jim Campbell, UC Berkeley
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b) Mo’s demand curve for lobster rolls slopes down, and, to him, these goods are substitutes.
Sketch a diagram that includes two budget lines and two choices for Mo (one on each
budget line) to show a situation that’s consistent this statement. Explain your answer.
11. The following diagram shows the decomposition of the effect of a change in price for a
consumer. The line marked O is the original budget line, N is the new budget line, and H
the hypothetical budget line constructed during the decomposition. The lines marked IC are
indifference curves.
a) Which price has changed and in what direction? Which type of decomposition
is this, and how do you know?
b) What is the size of the substitution effect, and what is the size of the income
effect in this case? Explain briefly what
those are. Based on the information in
the diagram: for each good, 1 and 2,
is the good normal, inferior, or can we
not say? Is the good ordinary, Giffen,
or can we not say? Explain.
√
12. A consumer has utility function u(x1 , x2 ) = x1 + 2 x2 . They have $20 to spend. The price
of good 1 changes. The following diagram shows their optimal choices before and after this
change, where ‘O’ is the original situation and ‘N’ is the new situation. We’re going to do a
Slutsky decomposition of the effect of this price change on demand for good 1.
a) What are the original prices, and what
are the new prices? What would the
equation of the Slutsky hypothetical
budget line be, and why?
b) Calculate (with the tangency method)
the consumer’s optimal choice from
that hypothetical budget. What is the
size of the substitution effect and what
is the size of the income effect as a result of this price change?
13. Consider a standard consumer choice model with two goods. Say that a person has demand
functions given by x∗1 = 0, x∗2 = pm2 .
a) Suggest a utility function that might represent this person’s preference ordering. Describe
that preference ordering in simple terms.
b) Let’s sketch the offer curve for this person for changes in the price of good 2. On a
diagram, sketch (i) three budget lines, (ii) the person’s optimal choice from each budget
line, (iii) the indifference curve on which each of the three optimal choices lies (following
the utility function you picked in part a), and (iv) the offer curve.
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Jim Campbell, UC Berkeley
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14. The diagram shows a situation before and after an increase in the price of good 1 in a
two good model. The original (O) and new (N ) optimal choices for the decision maker are
illustrated, as are the associated indifference curves.
a) On the diagram, add a line representing the Hicks decomposition’s ‘hypothetical’ budget
line. Mark the decision maker’s optimal choice (both the bundle H and the amount of
good 1 in the bundle x1,H ) from that budget line.
b) Explain what the point of the Hicks decomposition is and how that relates to where you
drew the budget line in part a).
3.5
Discussion
1. Explain what we mean by the concept of ‘revealed preference’. What is observed? What is
revealed?
2. “Goods might be ordinary in the aggregate, but at the individual level it’s a much different
story.” Discuss.
3. What kind of things do you think might have price inelastic / price elastic demand? Based
on what we’ve learned in this section, what kind of things determine which it is?
4. Brainstorm some examples of people who might want to know the price elasticity of demand
of something and why.
5. An important piece of information for policymakers is the marginal propensity of people to
save money. What do you suppose that means, and how does it relate to the kind of concepts
we’ve looked at in this section?
6. Do you think that people’s preferences are fixed? Do they change? When and why?
7. Should the ‘law of demand’ be called a ‘law’ ?
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8. “If you see someone buy one product instead of another, you can tell that they like it better.”
Is this interpretation consistent or inconsistent with the rational choice model? Why or why
not?
9. Does microeconomic theory overstate the role of prices in determining people’s choices?
10. Does consumer theory over-emphasize preferences relative to constraints?
11. “Would we really lose that much if we just assumed that everyone was financially selfinterested? Allowing for other possibilities makes our job more complicated and doesn’t
really add much.” Agree or disagree?
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Jim Campbell, UC Berkeley
4
Econ 100A Course Pack, Fall 2022
An application of consumer theory to labor supply
4.1
References
ˆ Jim’s lecture notes “Labor supply”
ˆ Video handbook C8 and C9 (particularly a, b, c from both)
ˆ Serrano and Feldman, Chapter 5
4.2
Readings
ˆ Albanesi, Stefania and Jiyeon Kim. 2021. “Effects of the COVID-19 Recession on the US
Labor Market: Occupation, Family, and Gender.” Journal of Economic Perspectives, 35 (3):
3-24.
ˆ Juhn, Chinhui, and Kristin McCue. 2017. “Specialization Then and Now: Marriage, Children, and the Gender Earnings Gap across Cohorts.” Journal of Economic Perspectives, 31
(1): 183-204.
ˆ Olivetti, Claudia and Barbara Petrongolo. 2017. “The Economic Consequences of Family
Policies: Lessons from a Century of Legislation in High-Income Countries.” Journal of
Economic Perspectives, 31 (1): 205-230.
ˆ Cassar, Lea, and Stephan Meier. 2018. “Nonmonetary Incentives and the Implications of
Work as a Source of Meaning.” Journal of Economic Perspectives, 32 (3): 215-238.
4.3
Concepts
ˆ Labor supply model
4.4
Problems
1. For each of the following situations, sketch a labor supply budget set. Put free time on the
x axis and money (or dollars of consumption) on the y axis. Use whatever time scale you
feel is appropriate (i.e. it could be the budget set for one day, one week, one year...).
a) 12 hours free per day; can work any amount of time at the rate $15/hr; zero non-labor
income.
b) Same as a), but law prevents working more than 10 hours per day.
c) Two possible jobs, must choose at most one to accept: one pays $1,000 per week for 40
hours work per week, the other pays $400 per week for 25 hours work per week. Zero
non-labor income.
d) 12 hours free per day; can work any amount of time at the rate $10/hr; $20 per day
non-labor income; after 8 hours, extra hours get overtime wage $15/hr.
2. Calculate marginal rate of substitution for the following utility functions, and discuss in words
what it implies about the person’s preferences. l is leisure and c is dollars of consumption.
a) u = c + 20l
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Jim Campbell, UC Berkeley
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b) u = cl
3. Jim is deciding how much to work. His total available time is 12 hours, which he must
allocate between labor and leisure. He likes consumption c and leisure L, and has wellbehaved preferences represented by u = cL. The price per unit of consumption is p = 2 and
the wage rate is w = 3.
a) What is Jim’s optimal choice of c and L? How many hours will he choose to work?
b) A mysterious stranger offers Jim nonlabor income m, but only if he agrees not to work
at all. At least how big must m be for Jim to want to accept this deal?
c) Say that Jim has nonlabor income m = 12 whether he works or not. What is his utility
if he doesn’t work at all? What is his new optimal choice of c and L? Does he work
more or less than in part a)?
d) If Jim has nonlabor income of m whether he works or not, at least how big must m be
for Jim to choose not to work at all?
4. Jim is facing a labor supply decision. His total available time is 12 hours. He has well-behaved
preferences for two goods, good 1, leisure L, and good 2, consumption c, represented by the
utility function u = L2 c. The price per unit of consumption is p = 1 and the wage rate is w.
a) Find Jim’s optimal choice of L and c (these could be a function of the parameter w).
How many hours does he work?
b) Now say that the wage is fixed at w = 14 . Jim’s laziness is upsetting his boss. His boss
offers the following deal: if Jim will agree to work 8 hours like a normal person, his boss
will pay a bonus b on top of his wage earnings. At least how big of a bonus must he
offer for Jim to be willing to accept this deal?
5. Jim is deciding how many hours to work. His well-behaved preferences depend on leisure
(L) and consumption (c) according to the utility function u = c2 L. He has 12 total hours
available. The price of each unit of consumption is p = 1 and the wage rate is w = 5.
a) Sketch his budget set over L and c (make L good 1 and c good 2).
b) What is Jim’s marginal rate of substitution between the two goods? What does it mean
that it is not constant?
c) What is Jim’s optimal choice of c and L? How many hours will he work?
d) Say that in addition to the job with hourly wage $5 that we considered so far, there is
another possible job available to Jim. This alternative job is salaried, and so he has no
discretion about how many hours to work. It pays $50 and he must work for 10 hours.
If he must choose either the wage job or the salaried job, which will he choose and why?
6. Ivan faces a labor supply decision. His well-behaved preferences
√ over the two goods ‘hours
of leisure’ L and ‘consumption’ c can be represented by u = 4 L + c. He has no non-labor
income and can choose how many hours to work at the wage rate w per hour. The price per
unit of consumption is p, and his available free time is T hours.
a) Sketch Ivan’s budget set, with axes, intercepts, and slope labeled (these will depend on
the parameters w, p, and T ).
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Jim Campbell, UC Berkeley
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b) Use the tangency method to find Ivan’s demand functions for leisure and consumption
(as functions of w, p, and T ).
c) Let’s think about Ivan’s “time expansion path” (that is, the analog of the income expansion path a.k.a. income-consumption loci but for changes in T ). Sketch it and explain
why it has this shape, with reference to Ivan’s demand functions.
d) In terms of parameters from the model, what is the most that Ivan would be willing to
pay to have an extra hour of free time (that is, to increase T by 1)? Why?
7. Consider a labor supply setting: there are two people, Saleem and Ritesh, with utility
functions uS = L3 c and uR = Lc. They face the same budget set: each one has $100 in
non-labor income and 10 free hours; consumption costs p = 1 per unit and the wage is w per
hour.
a) Sketch the budget set. Label axes, intercepts, and slope.
b) By thinking about each person’s marginal rate of substitution: for what values of w will
only one of the two people choose to work any hours? Which person? [Hint: this can
be done without having to derive the consumers’ demand functions.]
8. Consider a labor supply model.
√ The decision maker has utility over leisure L and consumption
goods c given by u = 2L + c. They have 10 available hours and no non-labor income. The
wage rate is w = 20 and the price per unit of consumption is p = 1.
a) Use the tangency method to find the consumer’s optimal choice of L and c. Based on
your calculations, if this person had more available hours, would they have worked more,
less, or the same number of hours?
b) Say that the situation is the same as before except that after 7 hours of work the wage
rate increases from w = 20 to w = 30. Sketch the budget set for this situation on the
usual axes, with axes, intercepts, and slopes all labeled.
9. A decision maker faces a labor supply decision. They have $120 non-labor income, face a
wage of $15 per hour, and have 12 available hours which they can allocate between working
for pay or ‘leisure’ (time not working for pay). Price per unit of consumption is p = 1. Their
preferences can be represented by u = c − L.
a) Sketch the consumer’s budget constraint on the usual axes, with intercepts, axes, and
slope labeled.
b) Mark the consumer’s optimal choice on your diagram from a), and sketch a couple of
indifference curves, including the one on which the optimal choice lies. Describe their
preferences in words, and how that preference leads to the optimal choice you found.
10. Stephanie got a raise! The diagram shows her budget set before and after a change in her
wage rate. She has 10 hours of available time. The price per unit of consumption is $2.
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Jim Campbell, UC Berkeley
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a) How much non-labor income
does Stephanie have? What
was her wage initially, and
what was it after the raise?
What is the slope of the new
budget line, and what does
that slope represent?
b) Say that Stephanie’s preferences can be represented by the utility function u = αL + c,
where α > 0. Say that Stephanie chose to work zero hours before the raise, but now
chooses to work 10 hours. What do we know about α? Explain carefully how you know.
4.5
Discussion
1. What do we know about the gender gap in earnings? What kind of policies might help to
reduce the gap, and what does the evidence look like for those policies?
2. In our labor supply model, would your utility function favor time or money? How might
that play out across the course of one’s life?
3. Do you find the labor supply model we’ve studied here to be a useful or compelling model?
In what ways might you critique it?
4. Brainstorm an interesting or useful application of the consumer choice model. Carefully
outline how the components of the model correspond to aspects of your application. What
kind of things could we learn from your example?
5. Does the standard model of consumer choice get more or less useful when we apply it to
decisions that aren’t strictly financial?
6. Are there some things in life that can’t or shouldn’t be analyzed using the tools of the
economic model of consumer theory and rational choice, or is anything fair game?
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Jim Campbell, UC Berkeley
5
Econ 100A Course Pack, Fall 2022
Choice under uncertainty and risk aversion
5.1
References
ˆ Jim’s lecture notes “Choice under uncertainty”
ˆ Video handbook C10a,b,c
ˆ Osborne and Rubinstein, Chapter 3
ˆ Serrano and Feldman, Chapter 19
5.2
Readings
ˆ (Reading Response 2) Kahneman, Daniel and Amos Tversky. 1979. “Prospect Theory:
An Analysis of Decision under Risk.” Econometrica, 47 (2): 263-291.
ˆ Moscati, Ivan. 2016. “Retrospectives: How Economists Came to Accept Expected Utility
Theory: The Case of Samuelson and Savage.” Journal of Economic Perspectives, 30 (2):
219-236.
ˆ Schildberg-Hörisch, Hannah. 2018. “Are Risk Preferences Stable?” Journal of Economic
Perspectives, 32 (2): 135-54.
5.3
Concepts
ˆ Expected Utility Theory; risk aversion; coefficient of absolute risk aversion; coefficient of
relative risk aversion
5.4
Problems
1. (From Varian 1992) An Expected Utility
maximizer has a Bernoulli utility function over
√
‘final wealth’ (w) given by u(w) = w. He starts with $4 and holds a lottery ticket that
pays $12 with probability 12 and pays $0 with probability 12 .
a) What is his expected utility?
b) What is the lowest price at which he’d sell the lottery ticket?
2. (Risk aversion)
a) Calculate the coefficient of absolute risk aversion for the utility function u =
√
x.
b) Calculate the coefficient of absolute risk aversion for the utility function u = ln x.
√
c) Individual A has Bernoulli utility function u = x and individual B has u = ln x, where
x is final wealth. Both are expected utility maximizers and have the same initial wealth,
w. If A rejects some gamble g, can we say if B will accept or reject g? Explain why or
why not.
d) Illustrate your answer to c) graphically.
e) Calculate the coefficient of absolute risk aversion for the utility function u(x) = −e−αx .
f ) Calculate the coefficient of relative risk aversion for the utility function u(x) =
23
x1−ρ
.
1−ρ
Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
3. An expected utility maximizer has zero initial wealth, and has a Bernoulli utility function
u = x2 , where x is ‘final wealth’. He holds a lottery ticket that pays $1 with probability 12
and pays nothing with probability 12 .
a) What is his expected utility?
b) What is the smallest amount of money he would accept to give up the ticket?
c) Calculate this individual’s coefficient of absolute risk aversion. Interpret it in words.
d) Calculate this individual’s coefficient of relative risk aversion. Interpret it in words.
√
4. An expected utility maximizer has Bernoulli function u(x) = x, where x is final wealth.
She has $10,000 today, but with probability 5% will lose everything.
a) Calculate her expected utility.
A firm offers her insurance, so that the firm will cover the loss if it occurs for a premium of
$C.
b) Write an expression for her expected utility if she buys the insurance.
c) What is the most she would be willing to pay for this insurance?
√
5. Stephanie is a risk-averse expected utility maximizer with a Bernoulli utility function u = x,
where x is final wealth. She currently has $1. She is offered a lottery ticket that costs $1. It
1
and zero with the remaining probability.
will pay $y with probability 100
a) Give one possible explanation in words of what it means that Stephanie is ‘risk-averse’.
b) Write an expression for Stephanie’s expected utility if she buys the lottery ticket.
c) What is the smallest prize y such that Stephanie is willing to buy the lottery ticket?
d) If instead of $1 both Stephanie’s initial wealth and the price of the lottery ticket were
$100, what would be the smallest prize y such that Stephanie is willing to buy the
lottery ticket?
e) Explain intuitively the difference between your answers to c) and d).
Now consider a different problem for Stephanie. Again assume she has $100 in initial wealth,
1
but with probability 10
she will lose it all. She is offered an insurance policy at a price c ≥ 0
that will cover the whole loss should it occur.
f ) Calculate Stephanie’s expected utility if she does not buy the insurance policy, and write
an expression for her expected utility if she does buy the insurance policy.
g) What is the largest c such that Stephanie is willing to buy the insurance policy?
Jim is an expected utility maximizer with a Bernoulli utility function u = x2 . He currently
has $1.
h) What is the smallest prize y such that Jim is willing to buy the $1 lottery ticket?
i) If Jim rejects some gamble g, can we say whether Stephanie will accept or reject it?
Explain.
6. Consider the following two lotteries:
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Jim Campbell, UC Berkeley
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A. Win $2500 with probability 0.9, else nothing.
B. Win $2000 with probability 1, else nothing.
a) Assume that an “outcome” is the lottery’s money prize. What must be true if an expected
utility maximizer prefers lottery B to lottery A?
Consider the following two lotteries:
C. Win $2500 with probability 0.45, else nothing.
D. Win $2000 with probability 0.5, else nothing.
b) Construct a compound lottery that is payoff-equivalent to lottery C, using a mix of lottery
A and a lottery that pays nothing with probability 1.
c) Construct a compound lottery that is payoff-equivalent to lottery D, using a mix of lottery
B and a lottery that pays nothing with probability 1.
d) Explain why an expected utility maximizer who prefers lottery B to lottery A also prefers
lottery D to lottery C.
7. Describe one of: the Allais, Ellsberg, or Machina paradoxes, or framing effects. What behavior does your chosen example capture that classical Expected Utility Theory does not?
8. Consider a situation in which a person (whose preferences over risky outcomes can be represented with the Expected Utility form) has $36 in wealth and is offered the chance to buy
a lottery ticket for $36. With probability 14 the ticket is worthless; with probability 34 the
decision maker will get $Z.
a) For what values of Z would no risk-averse person choose to buy this ticket? Explain.
√
b) If person’s Bernoulli function was u = x (where x is final wealth) what is the minimum
Z such that they’d buy the ticket? This person’s coefficient of absolute risk aversion is
1
; if the ticket had still cost $36 but the decision maker had started with more than
2x
$36 in wealth, would this minimum Z have been bigger, smaller, or the same? Why?
9. Say that a decision maker initially has $0 and has a Bernoulli function u(x), where x is cash.
Their preference ordering over lotteries that can be represented with the Expected Utility
form. They prefer (A) getting $1,000 with probability 12 and nothing with probability 12 over
(B) getting $600 for sure.
a) Express their preference with an inequality using Expected Utilities. Is this decision
maker risk averse, risk neutral, or risk loving (at least in this range of x)? How do you
know?
b) Consider a different choice between (C) getting $1,000 with X% chance and $0 with (1X)% chance and (D) getting $600 with 4% chance and $0 with 96% chance. For what
X do we know that the decision maker definitely prefers C to D? With reference to
your inequality from a), how do you know?
1
10. A decision maker has a Bernoulli utility function u = x 3 , where x is the amount of money
she has. Her preferences under uncertainty have the expected utility form.
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Jim Campbell, UC Berkeley
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a) Find expressions for the decision maker’s coefficients of absolute risk aversion and relative
risk aversion. In general, coefficients of risk aversion are related to what aspect of the
shape of the Bernoulli function?
b) Thinking about risky gambles that have positive expected cash value, does this decision
maker reject all such gambles, accept all such gambles, or accept some but reject others?
Explain why. Would your answer be different if her Bernoulli function had been u = x3
instead? Again, explain why.
11. Two decision makers, Jim and Saeromi, each currently have $50 in initial wealth. They face
1
a choice between two options: (A) gain $X for sure, or (B) lose $50 with
√ probability 2 and
1
gain $350 with probability 2 . Jim has a Bernoulli utility function u = x, where x is ‘final
wealth’. We don’t know Saeromi’s Bernoulli function, but we do know that her coefficient of
absolute risk aversion is always less than zero. Both people’s preferences can be represented
with the expected utility form.
a) For what values of X will Jim choose option A? How does this compare to the expected
cash value of option B, and why?
b) What does it mean that Saeromi’s coefficient of absolute risk aversion is less than zero?
For what values of X do we definitely know that Saeromi will choose option B over
option A? Explain.
12. Jim currently has wealth of $50 but he faces risk. With probability 15 , he will end up with
4
double his current wealth; with probability
√ 5 , he will end up with half his current wealth.
His Bernoulli utility function is u(w) = w, where w is his final wealth. His preferences over
lotteries can be represented by the Expected Utility form.
a) Say that Jim could pay some price p to eliminate the risk he faces. What is the most he
would be willing to pay? Is this more or less than the dollar amount of the expected
loss he currently faces, and why?
b) Make a rough sketch of Jim’s Bernoulli function. Explain in simple terms why we could
say that Jim has ‘diminishing marginal utility of money’.
5.5
Discussion
1. “Risk aversion is totally context dependent, so trying to figure out someone’s degree of risk
aversion is really not possible.” Discuss.
2. What special challenges are present when modeling choice under uncertainty that are not
present when modeling choice in a certain world?
3. Sketch and explain a diagram to show how concavity of the Bernoulli utility function corresponds to risk aversion. How might you go about finding out the level of risk aversion for a
person or a group of people? What kind of economic policy problems would that be useful
for?
4. Define the coefficient of absolute risk aversion and the coefficient of relative risk aversion.
What is the difference between them?
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Jim Campbell, UC Berkeley
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5. If a risk-averse person goes to Vegas and gambles, is that consistent or inconsistent with
Expected Utility theory?
6. Does the idea of rationality in economics allow for the possibility of regretting a decision?
7. “In reality people just don’t know that much about what the consequences of their choices
might be, and sometimes even what choices they have. That totally undermines the relevance
of standard economic models.” Agree or disagree? [Topic 14 also pretty relevant here]
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Jim Campbell, UC Berkeley
6
Econ 100A Course Pack, Fall 2022
General equilibrium in an exchange economy
6.1
References
ˆ Jim’s lecture notes “General equilibrium in an exchange economy”
ˆ Video handbook E2a-E2l
ˆ Osborne and Rubinstein, Chapter 10
ˆ Serrano and Feldman, Chapter 15
6.2
Readings
ˆ Alvaredo, Facundo, Anthony B. Atkinson, Thomas Piketty, and Emmanuel Saez. 2013. “The
Top 1 Percent in International and Historical Perspective.” Journal of Economic Perspectives, 27(3): 320.
ˆ Corak, Miles. 2013. “Income Inequality, Equality of Opportunity, and Intergenerational
Mobility.” Journal of Economic Perspectives, 27 (3): 79-102.
ˆ Hoynes, Hilary, Douglas L. Miller, and Jessamyn Schaller. 2012. “Who Suffers During
Recessions?.” Journal of Economic Perspectives, 26 (3): 27-48.
ˆ Attanasio, Orazio P. and Luigi Pistaferri. 2016. “Consumption Inequality.” Journal of
Economic Perspectives, 30 (2): 3-28.
6.3
Concepts
ˆ Exchange economy; Edgeworth box; endowments; Pareto improvement; Pareto efficiency;
general/competitive/Walrasian equilibrium; Walrasian auctioneer; the First and Second Theorems of Welfare Economics
6.4
Problems
1. Sketch an Edgeworth box and mark where the described allocation lies for each of the following cases:
a) Consumer A has an endowment of 3 units of good 1 and 4 units of good 2. Consumer B
has 3 units of good 1 and 1 unit of good 2.
b) Consumer B has all of the goods.
c) Consumer A has all of good 1 and consumer B has all of good 2.
2. Consider an exchange economy with two consumers, Jim (J) and Stephanie (S), and two
goods, peanuts (n) and Cracker Jack (c). Jim has an endowment of one bag of peanuts and
two bags of Cracker Jack, and Stephanie has an endowment of three bags of peanuts and
one bag of Cracker Jack.
a) Sketch an Edgeworth box to illustrate the feasible allocations in this economy. Put
peanuts on the horizontal axes and Cracker Jack on the vertical axes. Remember to
fully label your diagram and make it large enough to add to later.
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Jim Campbell, UC Berkeley
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b) Mark the endowment point on your diagram from a).
Jim doesn’t care for Cracker Jack and Stephanie doesn’t care for peanuts. Their utility
functions are
UJ = nJ ,
U S = cS .
(1)
(2)
Each consumer must consume a non-negative amount of each good.
c) On your diagram from a), sketch an indifference curve for each consumer that passes
through the endowment point.
d) Illustrate on your diagram which feasible allocations represent Pareto improvements over
the endowment point.
e) Illustrate on your diagram the Pareto efficient allocation(s) in this economy.
f ) Find a competitive equilibrium in this economy.
3. Consider an exchange economy with two goods, coffee (c) and donuts (d), and two consumers,
Jim (J) and TJ (T ). Jim has an endowment of 6 cups of coffee and 2 donuts, and TJ has
an endowment of 2 cups of coffee and 2 donuts. Jim only likes to consume coffee and donuts
together, so for him they are perfect complements. TJ, however, is watching his figure and
so cares only for coffee. Their utility functions are:
UJ = min{cJ , dJ },
UT = cT .
(3)
(4)
Sketch an Edgeworth box for this economy. Mark the endowment. Sketch an indifference
curve for each consumer, and show what allocations would be Pareto improvements over the
endowment. On a fresh diagram, show that there is a competitive equilibrium in which the
price ratio is ppdc = 1. Describe what each consumer buys and sells in this equilibrium.
4. Consider an exchange economy with two goods, x1 and x2 , and two consumers, A and B.
The consumers have utility functions as follows:
UA = 2 ln(x1A ) + ln(x2A )
UB = ln(x1B ) + 2 ln(x2B )
(5)
(6)
ωA = (ωA1 , ωA2 ) = (2, 2)
ωB = (ωB1 , ωB2 ) = (3, 0)
(7)
(8)
And endowments:
Normalize the price of x1 to be p1 = 1 and let the price of x2 be p2 . Find a competitive
equilibrium in this economy. To do this: find each consumer’s income. Then find each
consumer’s optimal choice as a function of p2 . Then find a value of p2 such that markets
clear at these optimal choices. Remember when you write down the competitive equilibrium,
you must write down an allocation for each consumer and the supporting price ratio.
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Jim Campbell, UC Berkeley
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5. Consider an exchange economy with two goods, x1 and x2 . Consumer A has preferences
represented by the Cobb-Douglas utility function
1
1
UA = (x1A ) 2 (x2A ) 2
(9)
and an endowment ωA = (1, 0). Consumer B has preferences represented by the CobbDouglas utility function
2
1
UB = (x1B ) 3 (x2B ) 3
(10)
and an endowment ωB = (0, 1). Find a competitive equilibrium.
6. Some questions about the exchange economy model:
a) Using an Edgeworth box diagram, explain what we mean by a Pareto improvement.
b) The Second Theorem of Welfare Economics mentions reallocating the endowment. With
the aid of an Edgeworth box diagram, explain what the endowment point is, and what
it means in theory to reallocate the endowment.
c) As a practical matter, is the idea of reallocating the endowment a realistic one? What
kind of real-world redistributive economic policies do you think are similar to the idea
of reallocating the endowment? Which are dissimilar?
d) In the exchange economy model, what exactly is a competitive equilibrium (also known
as a general or Walrasian equilibrium)? If the economy is in equilibrium, does that
mean things are good?
e) Using a couple of non-technical sentences and/or diagrams for each, explain the main
message of the first and second welfare theorems.
7. Consider a two-consumer, two-good exchange economy. Consumer A has utility function
UA (x1A , x2A ) = (x1A )(x2A )3 and endowment ωA = (4, 0). Consumer B has utility function
UB (x1B , x2B ) = 5 and endowment ωB = (0, 4). Normalize p1 = 1 and let the price of good 2
be p2 .
a) Write demand functions for consumer A in terms of prices.
b) Thus find a competitive equilibrium in which
p1
p2
= 1.
c) Show with an example that the competitive equilibrium in b) is not Pareto efficient.
d) Why does the first welfare theorem fail to hold in this economy?
8. Consider a two-consumer, two-good economy. Consumers A and B have utility functions:
UA = ln(x1A ) + 3 ln(x2A ),
UB = ln(x1B ) + ln(x2B ).
(11)
(12)
Consumer A has an endowment of ωA = (4, 4) and consumer B has an endowment of ωB =
(0, 0). Normalize the price of good 1 to 1 and let the price of good 2 be p2 .
a) Write expressions for each consumer’s demand for each good as functions of p2 .
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
b) Thus show that a competitive equilibrium exists with prices
tion in this equilibrium?
p1
p2
= 13 . What is the alloca-
The auctioneer likes using the price mechanism but dislikes how the equilibrium allocation
has turned out.
c) Find an equation for the contract curve in this economy.
d) Thus, invoking the second welfare theorem, show that the allocation xA = (2, 3), xB =
(2, 1) can be supported as a competitive equilibrium. How can the auctioneer implement
this allocation as a competitive equilibrium?
9. Using an Edgeworth box (properly labeled), sketch an example of the following situations in
an exchange economy:
a) Both consumers have well-behaved preferences and are at a utility maximizing bundle
given the prices that were called by the auctioneer, but we are not at a competitive
equilibrium. Why are we not at a competitive equilibrium in your diagram?
b) The two consumers have well-behaved preferences, we are at an allocation in which both
consumers have an identical bundle of goods, but that allocation is not Pareto efficient.
Explain in a few sentences how your diagram reflects this situation.
10. On Pareto efficiency:
a) Is it possible to have a Pareto efficient allocation in which some consumer is worse off
than she is at a different allocation that is not Pareto efficient? Explain. Illustrate in
an Edgeworth box.
b) In a two-consumer economy, it possible to have a Pareto efficient allocation in which
both consumers are worse off than they are at a different allocation that is not Pareto
efficient? Explain. Illustrate in an Edgeworth box.
11. Consider an exchange economy with two consumers, Tatiana and Martin, and two goods,
ice cream (i, good 1) and coffee (c, good 2). They each have Cobb-Douglas preferences
represented by, respectively, uT = i4T cT and uM = iM c2M , where iT is the amount of ice cream
in Tatiana’s bundle, and so on. Tatiana’s endowment is (9, 6) (ice cream first, coffee second);
Martin’s is (1, 6). Assume that all conditions of the two fundamental theorems of welfare
economics hold.
a) Sketch an Edgeworth box to represent this economy. Label the axes. Mark the endowment
point.
b) Consider three allocations. Allocation 1: Tatiana gets (8, 4) and Martin (2, 8). Allocation
2: Tatiana gets (1, 1) and Martin gets (9, 11). Allocation 3: Tatiana gets (8, 8) and
Martin gets (2, 4). Which of these, if any, can be supported as competitive equilibria?
Explain your answer.
12. Consider an exchange economy with two consumers and two goods. May has an endowment
ωM = (6, 2) and Joel has an endowment ωJ = (2, 6).
a) Sketch an Edgeworth box to represent this economy, with axes labeled and endowment
point marked. If we found a “Pareto improvement” relative to the endowment point,
what would that mean, in simple terms?
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
b) Consider an allocation in which May has (4, 0) and Joel has (4, 0). Is it possible for this
allocation to be Pareto efficient? If that is possible, give an example of a utility function
for each person that would make it so and briefly explain. If that is impossible, explain
why.
13. An exchange economy has two people, A and B, and two goods, j and k. Person A has an
endowment of 8 units of good j and none of good k; their preferences can be represented
by the Cobb-Douglas utility function uA = jA kA (where jA is the amount of good j that A
has, and so on). B has an endowment of no units of good j and 6 units of good k; their
2
preferences can be represented by the Cobb-Douglas utility function uB = jB kB
. Let the
price of good j be 1. Denote the price of good k with p.
a) Write demand functions for each consumer for each good as a function of p (for this
question, it’s not required to derive the demand functions). Explain what plays the role
of ‘income’ in the demand functions.
b) Find a competitive equilibrium in this economy. Explain why your answer is a competitive
equilibrium.
6.5
Discussion
1. Does the exchange economy model reflect something innate about human nature, or something constructed by our society?
2. Does general equilibrium theory offer any guidance about how we could reduce inequality in
society?
3. What, if anything, do the two fundamental theorems of welfare economics teach us about
economic policy?
4. What role is played by endowments in the exchange economy model? Discuss the relationship
between this aspect of the model and real-world debates about inequality, redistribution, and
fairness.
5. “Government shouldn’t get involved in dictating the prices of things. It should be left to the
market.” Discuss.
6. Can microeconomics help us to understand the causes and consequences of power disparities
in society?
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Jim Campbell, UC Berkeley
7
Econ 100A Course Pack, Fall 2022
Producer theory
7.1
References
ˆ Jim’s lecture notes “Producer theory”
ˆ Video handbook D (particularly D1 e, f, h, i, m; D2 a, c, h, i, l; D3 a, c, e, k)
ˆ Osborne and Rubinstein, Chapter 6
ˆ Serrano and Feldman, Chapter 8, 9, 10
7.2
Readings
ˆ Autor, David H. 2015. “Why Are There Still So Many Jobs? The History and Future of
Workplace Automation.” Journal of Economic Perspectives, 29 (3): 3-30.
ˆ Agrawal, Ajay, Joshua S. Gans and Avi Goldfarb. 2019. “Artificial Intelligence: The Ambiguous Labor Market Impact of Automating Prediction.” Journal of Economic Perspectives,
33 (2): 31-50.
ˆ Waldfogel, Joel. 2017. “How Digitization Has Created a Golden Age of Music, Movies,
Books, and Television.” Journal of Economic Perspectives, 31 (3): 195–214.
ˆ Cheng, Hong, Ruixue Jia, Dandan Li, and Hongbin Li. 2019. “The Rise of Robots in China.”
Journal of Economic Perspectives, 33 (2): 71-88.
7.3
Concepts
ˆ Production function; production possibility set; isoquants; marginal product; technical rate
of substitution; returns to scale; returns to an input; fixed versus variable costs; profit
maximization; marginal revenue
7.4
Problems
1. For each of the following production functions, calculate the marginal products and technical
rate of substitution. What is the nature of returns to scale in each case?
1
1
a) y = x13 x23
1
1
b) y = x12 x22
c) y = x1 x2
d) y = x1 + 4x2
For the production functions in a), b), and c), what shape do the isoquants have? What is
similar and what is different about the isoquants among the three cases?
2. A firm produces a single √
output y using a single factor of production x, according to the
production function y = 4 x. The price of y is p per unit and the price of x is w per unit.
a) Find expressions for the average product and the marginal product of x.
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
b) Set up and solve the firm’s profit maximization problem to find its optimal choice of
input, x∗ , as a function of the prices p and w.
c) With your answer to b) and the production function, write the firm’s optimal choice of
output, y ∗ , as a function of the prices p and w.
d) Say that w = 1. Using your answer to c), sketch the firm’s supply curve
√
3. A firm produces output y according to the production function y = 2 x. Output price is
p = 10 and input price is w = 5. Find the profit-maximizing choices of x and y and the
amount of profit that the firm makes.
4. Jim Corp. produces lecture slides y using two inputs, coffee (x1 , measured in cups) and labor
√ √
(x2 , measured in hours). Its production function is y = 10 min{ x1 , x2 }. That is, it needs
one cup of coffee and one hour of labor to achieve any output; coffee is useless without time
to work, and time to work is useless without coffee. Jim Corp. sells lecture slides on the
thriving black market for economics for a price of $12 per unit. Coffee costs $2 per cup and
labor costs $10 per hour.
Does Jim Corp.’s production function display increasing, decreasing, or constant returns to
scale? Assuming that Jim Corp. maximizes profits, what is its optimal choice of production
plan?
5. For each of the following cost functions, what are the producer’s fixed costs and variable
costs? Find expressions for marginal cost and average cost.
a) c(y) = 10 + 0.5y 2
b) c(y) = 3y
c) c(y) = 100 + 2y + 0.1y 3
6. Say that a firm uses two inputs, capital and labor. Give an example of a production function
such that has
i. Constant returns to scale and constant returns to labor.
ii. Constant returns to scale and diminishing returns to labor.
iii. Diminishing returns to scale and diminishing returns to labor.
7. Jim’s Bar produces drinks y using robot bartenders r and human bartenders h according to
the production function y = 5r + h.
a) What is the technical rate of substitution for this production function? Explain what in
means in words in this example.
b) Show whether this production function displays increasing, constant, or decreasing returns to scale. Explain what that means in words.
c) Sketch a couple of isoquants for this production function for the levels of output y = 10
and y = 20.
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
8. Kristal Corp. is organizing a one-day massage pop-up where they will produce massages y
2
using a single input, massage therapists x, according to the production function y = 6x 3 .
The price of massages is p = 50 and the wage rate for a massage therapist for the day is
w = 100.
a) Show whether this production function has increasing, decreasing, or constant returns to
massage therapists.
b) If Kristal Corp. wants to maximize their profit, what is their optimal number of massage
therapists to recruit for the event? How many massages will be provided?
c) If Kristal Corp. hires the profit-maximizing number of massage therapists, what is the
average product of a massage therapist? How much profit does Kristal Corp. make?
9. A firm in a perfectly competitive industry produces output y with a cost function c(y) =
8 + 5y + 2y 2 .
a) Sketch the firm’s marginal cost and average cost curves. (For the average cost curve,
your sketch can be rough, but I need the right shape and the right intersection with the
marginal cost curve.)
b) If the price in this market is p = 25, how much does the firm produce? Does the firm
make positive profit?
In the long run, this firm could shut down if it chose, but in the short run it cannot.
c) Below what price would the firm produce nothing in the short run? Why?
d) Below what price would the firm shut down in the long run? Why?
10. A producer in a perfectly competitive industry produces output y using a single input x
2
according to the production function y = 3x 3 . The price per unit of output is p = 10 and
the price per unit of input is w = 20. The producer has fixed costs of F .
a) If this producer’s goal is to maximize profit, what is their optimal choice of the amount
of input to use and output to produce? How does this depend on F and why?
b) If we were to sketch out this producer’s marginal revenue and marginal cost curves on
the usual axes (dollars on the y axis, output on the x axis), for each one, would it be
upward-sloping, downward-sloping, or flat? Why?
11. Jim Corp. produces economics quiz questions (y) using the inputs cups of tea (input 1, t)
and hours of labor (input 2, L). √
His daily output when he uses t cups of tea and L hours of
labor in a day is given by y = 4 t + 0.5L. His current production plan uses 4 cups of tea
and 12 hours of labor per day.
a) Find the marginal product of each input and the technical rate of substitution, given
this production function. What value do each of those three things take at his current
production plan? Explain what each of those things means in simple terms.
b) Does this production function have increasing, decreasing, or constant returns to scale?
What does that mean, in simple terms? What does your answer tell us about the nature
of Jim Corp.’s isoquant map and why?
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
12. A profit-motivated producer makes output y using two inputs, L (input 1) and K (input
2), in a perfectly competitive industry with the aim to maximize profit. The technical rate
of substitution is constant at 31 and the production function has decreasing returns to scale.
When L = 40 and K = 20, we know that y = 100.
a) Draw the isoquant for y = 100 on the usual axes, labeling its intercepts and slope. Even
though we cannot know exactly where the isoquants for y = 200 and y = 300 lie, add
to your diagram isoquants for those output levels that would be consistent with the
information that we do know.
b) Say that the price per unit of L is wL and the price per unit of K is wK . If the producer’s
optimal choice has y > 0 and they choose K = 0, what do we know about wK and wL
and why?
13. Two questions about producer theory:
a) The diagram shows a very rough
sketch of an isoquant map. Consider three production functions:
0.75
ˆ y = x0.75
1 x2
ˆ y = 0.2x1 + 0.2x2
0.3
ˆ y = x0.3
1 x2
Which of the three production
functions does the sketch most
closely resemble and why?
b) Say that a profit-motivated producer in a perfectly competitive industry had a cost
function c(y) = F + 0.2y + 0.1y 2 . How would the size of F impact the producer’s
decision of how much to produce in (i) the short run and (ii) the long run? Why?
7.5
Discussion
1. In producer theory, what distinguishes the ‘long run’ from the ‘short run’ ? If all input and
output prices stayed fixed at the same value, would a firm be more profitable at its optimal
choice of production in the long run or the short run?
2. Critique our producer choice model. What aspects of the real world do you think it does a
good or bad job of capturing?
3. While we have focused on profit maximization as an objective for the firm, economists have
modeled and considered many other possibilities as well. What are some other possibilities
you can think of? How would you work with a model of them?
4. Are producers in a ‘standard’ economic model of producer theory sociopathic (that is, having
a disregard for other people)? Does it matter?
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
5. Should we be worried about robots taking our jobs? Carefully discuss what determines
the outcome when the potential for automation increases in some task or industry. What
happens and why?
6. The ‘evil corporation’ is a common trope in pop culture. Brainstorm some examples of
corporations from movies, TV, or literature. What are they like? What do they do and
why?
7. Take a look at The Toaster Project (also at http://www.thetoasterproject.org/). What do
you think?
8. “Producers in the real world have to care about a lot more than what producer theory in
economics typically says.” Discuss.
9. Is producer theory a special case of consumer theory, or something distinct? Does it matter?
10. Is ‘profit’, in the sense that it’s meant in standard microeconomic models, something with a
measurable analog in reality? Does it matter to people?
11. “Businesses out in the real world aren’t doing calculus or thinking about equilibria. Economic
models that think about business that way are irrelevant.” Discuss.
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Jim Campbell, UC Berkeley
8
Econ 100A Course Pack, Fall 2022
Perfect competition and partial equilibrium
8.1
References
ˆ Jim’s lecture notes “Perfect competition and partial equilibrium”
ˆ Video handbook E1 (b, c, d useful for everyone; e, f, g, h, i if you’re not confident on supply
and demand stuff from Econ 1 or 2)
ˆ Osborne and Rubinstein, Chapter 9
ˆ Serrano and Feldman, Chapter 11
8.2
Readings
ˆ (Reading response 3) Sandel, Michael J. 2013. “Market Reasoning as Moral Reasoning: Why Economists Should Re-engage with Political Philosophy.” Journal of Economic
Perspectives, 27 (4): 121-40.
ˆ Graddy, Kathryn. 2006. “Markets: The Fulton Fish Market.” Journal of Economic Perspectives, 20 (2): 207-220.
ˆ Amiti, Mary, Stephen J. Redding, and David E. Weinstein. 2019. “The Impact of the 2018
Tariffs on Prices and Welfare.” Journal of Economic Perspectives, 33 (4): 187-210.
ˆ Oates, Wallace E. and Robert M. Schwab. 2015. “The Window Tax: A Case Study in Excess
Burden.” Journal of Economic Perspectives, 29 (1): 163-180.
ˆ Kahneman, Daniel, Jack L. Knetch, and Richard Thaler. 1986. “Fairness as a Constraint on
Profit Seeking: Entitlements in the Market.” American Economic Review, 76 (4): 728-741.
8.3
Concepts
ˆ Perfect competition; long run versus short run; consumer surplus; producer surplus; efficiency; deadweight loss; social welfare function (examples: utilitarian, minimax a.k.a. Rawlsian, Cobb-Douglas)
8.4
Problems
1. On perfect competition:
a) One of the assumptions of the model of perfect competition is that there is free entry
and exit to the industry in the long run. Explain what the ‘long run’ is and explain the
key implications of the free entry and exit assumption for the outcome of the model.
b) With reference to the assumptions of the model of a perfectly competitive industry,
explain why it is the case that a profit-maximizing firm chooses to produce at a point
where price is equal to the marginal cost of production.
2. Consider the following situations, assuming that the markets are perfectly competitive. Find
equilibrium price and quantity. Make a sketch of the situation. Calculate consumer and
producer surplus, and if applicable tax revenue and deadweight loss.
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
a) qS = pS − 5, qD = 25 − pD .
b) qS = pS − 5, qD = 25 − pD , per-unit tax t = 2.
c) qS = pS − 5, qD = 25 − pD , price ceiling at p = 10.
3. Derive the formula for price elasticity of demand in the case of the demand function qD =
25 − pD . What value does it take at a price of 10?
4. Consider a partial equilibrium model with demand curve QD = 40 − 21 PD and supply curve
QS = PS −20. Say that the price is $50. Sketch a graph to illustrate this situation. Calculate
consumer surplus and producer surplus, and, if applicable, deadweight loss.
5. A market has an inverse demand curve given by p = 85 − 12 qD and an inverse supply curve
given by p = 10 + qS .
a) Find the market equilibrium values for price and quantity.
Say that there is a negative shock to supply. The new inverse supply curve is p = 25 + qS .
b) Find the new market equilibrium values for price and quantity.
c) Illustrate your answers to a) and b) on a partial equilibrium graph. It should have price
on the vertical axis and quantity on the horizontal axis, and show the demand curve,
the old supply curve, the new supply curve, and the equilibrium points.
d) If the demand curve had been perfectly inelastic, would the increase in equilibrium price
due to the supply shock have been higher, lower, or the same? How would equilibrium
quantity have changed?
e) In general, when the supply curve shifts, what is the relationship between elasticity of
demand and the size of the change in equilibrium price?
6. A market has a demand curve qD = 50 − p and a supply curve qS = 21 p − 10.
a) Find the market equilibrium values for quantity and price.
b) Illustrate this situation on a partial equilibrium graph.
c) Calculate consumers’ and producers’ surplus at the equilibrium.
Say that a tax of $3 per unit is imposed in this market.
d) Find the market equilibrium values for quantity and prices (remember that the prices
paid by consumers and received by producers are no longer the same).
e) Draw another partial equilibrium graph to show the new situation.
f ) Using your graph, calculate consumers’ surplus, producers’ surplus, tax revenue, and
deadweight loss.
7. Consider a perfectly competitive market in which demand is given by QD = 65 − PD and
supply is given by QS = 2PS − 10.
a) What is the equilibrium price and quantity traded in this market?
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
b) Say that a price ceiling of $20 is imposed (that is, this good cannot be traded at a
price above $20). How many units are traded? Sketch a diagram of this situation.
Your diagram should show the demand and supply curves, including their intercepts,
the equilibrium, and consumer surplus, producer surplus, and, if applicable, deadweight
loss. (You don’t have to calculate these, just show them on the diagram).
c) How big of a per-unit tax would have to be placed on this good to have the same effect
on quantity traded as the price ceiling from part b)? Thinking in terms of surpluses, are
consumers as a whole better off, worse off, or just as well off under the tax as they would
be under the price ceiling? What about the same question for producers? Explain your
answers.
d) Say that a price ceiling of $30 is imposed. How many units are traded and why?
8. A firm in a perfectly competitive industry produces an output y that sells for p = 35 per
unit. Its cost function is c(y) = 25 + 5y + y 2 .
a) What are the firm’s fixed costs, and what are the firm’s variable costs?
b) Find expressions for marginal cost and average cost.
c) Write the firm’s profit function. Find the firm’s optimal output y ∗ . What profit does the
firm make?
d) Find the price in this industry in the long run.
e) Find the firm’s optimal output if the price is at the long run value you found in c). What
profit does the firm make?
9. A profit-maximizing firm in a perfectly competitive industry has a cost function c(y) =
450 + 10y + 12 y 2 . The firm’s average cost reaches a minimum at y = 30. They currently make
positive profit.
a) Find expressions for the firm’s average cost and marginal cost. Sketch their average and
marginal cost curves, on the usual axes. (The right general shape is enough for average
cost, but make sure the curves are in the correct position relative to each other.)
b) What do we know about the price in this industry at the moment? What will be the
price in this perfectly competitive industry in the long run? Explain your answers, with
reference to any assumptions of the perfectly competitive model that are important
here.
10. Tsunoda Corp. produces sushi (s) in a perfectly competitive industry with the goal to
maximize profit. Their cost function is c(s) = 500 + 0.5s + 0.05s2 . Sushi has a price of p.
a) Write Tsunoda Corp.’s profit function. Find their optimal choice of s, as a function of
p. Sketch their supply curve on the usual axes.
b) Based on the information we have, do we know how much economic profit Tsunoda
Corp. will make in the short run? Why or why not? What about the same questions,
but for the long run?
11. Consider an economy with three individuals, H, M and L, and let all have the same preferences. A social planner is considering which of three available plans to implement. The
utility of each person under each plan is summarized in the following table:
40
Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
H
M
L
Plan 1
7
3
1
Plan 2
3
2
2
Plan 3
5
4
1
a) The social planner does not want to choose a plan that is Pareto inefficient. Does this
rule out any of the three available plans? Why or why not?
b) Suggest a social welfare function such that Plan 1 is welfare-maximizing.
c) Give an ethical interpretation of the social welfare function you suggest in b).
d) Suggest a social welfare function such that Plan 2 is welfare-maximizing.
e) Give an ethical interpretation of the social welfare function you suggest.
12. There are two consumers, Jim and TJ, and six bottles of a single good, beer. Both Jim and
TJ like to consume beer but dislike when the other drinks beer, since then they have to put
up with the other being drunk. Their utility functions are as follows, where xJ is the number
of bottles of beer allocated to Jim and xT the number allocated to TJ:
UJ = xJ − (xT )2
UT = xT − (xJ )2
(13)
(14)
Consider an allocation xT = 6, xJ = 0.
a) Is an equal division of beer a Pareto improvement over this allocation? Explain why or
why not.
b) Under a utilitarian social welfare function, which would be a better allocation, the one
mentioned above or an equal division of the six bottles between Jim and TJ?
c) Under a minimax (Rawlsian) social welfare function, which would be a better allocation,
the one mentioned above or an equal division of the six bottles between Jim and TJ?
d) Assume that each person has to get a whole number of bottles (no fractions of bottles).
Show that under a utilitarian social welfare function, it’s better that some of the beer
be thrown away rather than allocated to either Jim or TJ. At least how many beers
should be thrown away to maximize social welfare under the utilitarian social welfare
function?
13. Jim and Saeromi have won a pool tournament and they’ve gotten a $200 prize. We’re going to
think about the social welfare-maximizing way for them to split the cash and how it depends
on their preferences and the social welfare function (SWF). Call the amount of money that
each gets J and S respectively. (For this question, we need accurate numerical answers, but
you can reason it out. Complicated calculations may not always be needed.)
a) For the following cases, what allocation of the cash would be welfare maximizing under
(1) the utilitarian SWF and (2) the minimax/Rawlsian SWF?
i. Increasing M U of money: uJ = J 2 and uS = S 2 .
√
√
ii. Decreasing M U of money: uJ = J and uS = S.
iii. Saeromi cares about Jim’s finances: uJ = J and uS = S + J.
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
b) Say that Jim covets the money more than Saeromi: UJ = 3J and US = S. Repeat a) for
this case. Next, find the welfare-maximizing allocation under the Cobb-Douglas SWF
with equal weights (hint: express welfare just as a function of J and use a first order
condition approach to maximize).
c) Under the utility function in a)i., what allocations of cash are Pareto efficient? What
about for the utility function in a)iii.?
14. There are two goods, x1 and x2 . Jim has a utility function given by uJ = x21,J x2,J and Martin
has a utility function given by uM = x1,M x22,M , where x1,J is Jim’s amount of good 1, and
so on. There are 5 total units of good 1 available, and 4 of good 2. Right now we are at
allocation X where Jim’s bundle is (3, 3) and Martin’s is (2, 1).
a) Find a reallocation of the goods among the two people that would be a Pareto improvement over this starting point. Explain what that means.
b) Relative to X, find (i) a reallocation of the goods that would be acceptable under a
utilitarian social welfare function, but unacceptable under a minimax social welfare
function, and (ii) a reallocation of the goods that would be acceptable under a minimax
social welfare function, but unacceptable under a utilitarian social welfare function.
Briefly explain your answers.
15. Consider an economy with two people, Bojack and Diane, and two goods, bags of chips c and
sodas s. Each person has Cobb-Douglas preferences: Bojack’s utility function is uB = cB sB
and Diane’s is uD = cD sD , where cB is the number of bags of chips Bojack has, and so on.
There are 10 total bags of chips and 10 total sodas in the economy.
a) Sketch an Edgeworth box to represent this economy. Mark an allocation Z in which
Bojack’s bundle is (8, 8) and Diane’s is (2, 2). Sketch the indifference curve for each
person on which their bundle lies (we need the right general shape and positioning for
the indifference curves, not a precise sketch). How do you know what the indifference
curves look like at that point?
b) Find a feasible allocation that is ‘better’ than Z under a utilitarian social welfare function.
Find a feasible allocation that is ‘better’ than Z under a minimax social welfare function.
Show your calculations and briefly explain why your allocations are ‘better’ in each case.
8.5
Discussion
1. If the world was perfectly competitive, would you want prices to be at equilibrium?
2. Carefully describe what happens in the perfectly competitive model if marginal costs are
really low. Are there any strategic or policy issues there?
3. Is it better to levy a per-unit tax on a good for which demand is elastic or a good for which
demand is inelastic? Support your answer with partial equilibrium diagrams, assuming for
the time being that the market for the goods is perfectly competitive. Lay out the expected
effects in each case, and then use your judgement to make a normative case one way or the
other.
4. “If something has zero marginal cost of production, then what’s best for society is if it’s free
to whoever wants it.” Discuss.
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5. Is the simple supply and demand model over-emphasized in economics education?
6. What exactly does ‘efficient’ traditionally mean in a supply and demand model? If we say
we want to try to have efficient outcomes, what value judgements does that imply? What is
left out?
7. Does “efficiency”, in the sense economics uses it, just mean that rich and powerful people
get whatever they want?
8. “It’s efficient for prices of things like bottled water to rise after a natural disaster, so laws
against price gouging are bad.” Discuss.
9. “The existence of prices is inevitable in human society because they derive from important
natural impulses.” Agree or disagree?
10. Are the ‘big ideas’ of perfect competition and equilibrium prices very sensitive to particular
modeling assumptions, or pretty flexible to a range of conditions?
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Econ 100A Course Pack, Fall 2022
General equilibrium with production
9.1
References
ˆ Jim’s lecture notes “General equilibrium with production”
ˆ Video handbook E2m
ˆ Osborne and Rubinstein, Chapter 12
ˆ Serrano and Feldman, Chapter 16
9.2
Readings
ˆ Slonim, Robert, Carmen Wang, and Ellen Garbarino. 2014. “The Market for Blood.”
Journal of Economic Perspectives, 28 (2): 177-96.
ˆ Prendergast, Canice. 2017. “How Food Banks Use Markets to Feed the Poor.” Journal of
Economic Perspectives, 31 (4): 145-62.
ˆ Glaeser, Edward, and Joseph Gyourko. 2018. “The Economic Implications of Housing
Supply.” Journal of Economic Perspectives, 32 (1): 3-30.
ˆ Banzhaf, Spencer, Lala Ma, and Christopher Timmins. 2019. “Environmental Justice: The
Economics of Race, Place, and Pollution.” Journal of Economic Perspectives, 33 (1): 185208.
ˆ Slattery, Cailin and Owen Zidar. 2020. “Evaluating State and Local Business Incentives.”
Journal of Economic Perspectives, 34 (2): 90-118.
9.3
Concepts
ˆ Robinson Crusoe economy; competitive/general equilibrium; Walras’ law
9.4
Problems
1. Consider a Robinson Crusoe economy: it’s Sunday morning and Jim is lounging around.
He is an economy of one and there are two goods, ‘pancakes’ (y) and ‘leisure’. Chef Jim
produces pancakes
√ using the input ‘labor’ (l), which is the inverse of leisure. His production
function is y = 4 l. Let the price of pancakes be 1 and the price of labor, the wage, be w.
a) Write Chef Jim’s profit function. Find Chef Jim’s optimal choice of production plan and
the amount of profit he makes, as a function of w.
Hungry Jim consumes pancakes and supplies labor to Chef Jim. He earns w per unit of labor
supplied, and also receives the profits from Chef Jim. Hungry Jim likes pancakes but dislikes
working: his utility function is U = 2y − 2l2 .
b) Write Hungry Jim’s utility function, substituting in what you know about y. Find Hungry
Jim’s optimal choice of consumption bundle as a function of w.
c) Find a competitive equilibrium in this economy.
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2. Consider an economy with one producer and one consumer. There are two goods, x, which
has a price of w, and y, which has a price of 1. The producer aims to maximize profit
2
by producing y with a single input x according to the production function y = 3x 3 . The
consumer aims to maximize her utility function u = y − x2 . She consumes y, supplies x to
the producer for w per unit, and owns the firm so receives its profits.
Is there a competitive equilibrium in this ‘Robinson Crusoe’ economy with w = 4? Sketch
a picture that represents this situation with w = 4 (you don’t have to plot out the various
functions with perfect accuracy, but things should be in roughly the right place).
3. Consider an economy with one producer and one consumer. The producer is a profit1
maximizer who produces output y using labor l according to a production function y = 8l 2 .
The consumer is a utility-maximizer who consumes y and supplies l; their utility function is
U = y − 2l2 . Let the price of labor be w and normalize the price of y to be 1. The consumer
receives any profits earned by producer Jim and earns w per unit of labor supplied.
a) Set up and solve the producer’s problem to get their optimal production plan and profit
as a function of w.
b) Set up and solve the consumer’s problem to get their optimal consumption bundle as a
function of w.
c) Thus find a competitive equilibrium in this economy.
d) Explain why there is not a competitive equilibrium in which w = 1.
4. Jim is trapped on a desert island and, therefore, in a Robinson Crusoe economy. As a profitmaximizing producer, Jim’s √
Coconut Corp., he can turn labor into coconuts according to the
production function y = 12 l. Labor costs w per unit and coconuts sell for 1 each. As a
utility-maximizing consumer, he has a utility function U = 4y − 23 l2 . He owns Jim’s Coconut
Corp. and so receives its profits, and he can work at the wage rate w and buy coconuts at a
price of 1 each.
a) Set up and solve Jim’s Coconuts Corp.’s profit maximization problem to find its optimal
choice of how much labor to hire and how many coconuts to produce.
b) Set up and solve Jim the consumer’s utility maximization problem to find his optimal
choice of how much labor to supply and how many coconuts to consume.
c) Find the competitive equilibrium in this economy.
5. Two questions about the perfectly competitive Robinson Crusoe economy:
a) Consider a Robinson Crusoe economy with an input good l, labor, and an output good y.
The profit-maximizing producer has a production technology with diminishing returns
to l and the utility-maximizing consumer has well-behaved preferences over y and leisure.
Sketch a diagram that illustrates both the producer and consumer’s optimal choices for
a case in which there is (i) excess demand for l and (ii) excess supply for y.
b) Consider a similar case as in part a) except that the production technology has increasing
returns to l (as an example, you could consider y = x2 ). In a few sentences, and
paying particular attention to the producer’s optimal choice, why would a competitive
equilibrium fail to exist in this economy?
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Jim Campbell, UC Berkeley
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6. On the topic of models of general equilibrium in an economy with production:
a) With reference to both the intercept and slope: why, in a Robinson Crusoe model, does
the isoprofit line for a producer coincide exactly with the budget line for the consumer?
b) What does the word ‘general’ mean in general equilibrium models? Why do only price
ratios matter in a general equilibrium model and not the absolute value of prices?
7. Consider a standard Robinson Crusoe model with a single output good, coconuts. As a
consumer, Robinson has well-behaved preferences over leisure and coconuts. As a producer,
Robinson uses labor (the opposite of leisure) to produce coconuts, according to a production
function with diminishing returns to labor. Labor has price w and coconuts have price p.
a) Say that right now we are not in equilibrium because w is ‘too high’ relative to p. Sketch
a diagram that illustrates this situation. Why is it not an equilibrium?
b) If the conditions of the first theorem of welfare economics hold, what do we know about a
competitive equilibrium, if one exists? Specifically in this Robinson Crusoe model, how
are the consumer’s preferences and the production technology related at such a point?
8. In a Robinson Crusoe economy, output y (whose price is 1) is made using labor l (whose price
is w). Robinson as a profit-maximizing producer hires l to produce y; the production function
has diminishing returns. Say that we know that the producer’s optimal choice is to hire w122
units of labor and that they make profit 12
. Robinson the utility-maximizing consumer owns
w
the production company, supplies labor, and consumes y. Their utility function is U = 3y−l2 .
a) Find the consumer’s optimal choice of l. Briefly explain how you calculated this.
b) What w would implement a competitive equilibrium in this economy? Why don’t we
need to calculate anything to do with y to find that answer?
9. Consider a Robinson Crusoe economy. Robinson the producer, a profit-motivated firm, can
hire labor x to produce fruit according to the production function y = f (x). Robinson the
consumer owns and so receives the profit of the firm, and dislikes working (x) but enjoys
eating fruit (y). His preferences over leisure and fruit are well-behaved. The price of fruit
is 1 and the price of labor is w. The diagram shows the production function and a few of
Robinson the producer’s isoprofit lines.
a) If Robinson the producer chooses their
optimal production plan, what exactly
does Robinson the consumer’s budget
line look like? With reference to relevant assumptions of the model, why?
b) Say that we knew that there are no prices
such that point A can be supported as
a competitive equilibrium in this economy. What do we know about Robinson the consumer’s preferences at point
A and why?
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Jim Campbell, UC Berkeley
9.5
Econ 100A Course Pack, Fall 2022
Discussion
1. “Microeconomics has no coherent way of thinking about tradeoffs among groups of people,
no matter how much it pretends otherwise.” Agree or disagree?
2. Say that an economy with production is at a competitive equilibrium. The welfare theorems
hold. If we look the equilibrium prices of this economy, what underlying information about
the economy do we learn?
3. Why do increasing returns pose a technical problem for the general equilibrium model? Is
this a big problem for applying this model to reality? How does this relate to what we learned
about market power earlier in the course?
4. Explain how the general equilibrium model accounts for ownership of the means of production
in an economy. Thinking about either the exchange economy or the economy with production,
how might imbalances in wealth and power come about and perpetuate themselves?
5. Are the prices in a general equilibrium model outcomes or suggestions?
6. Are market outcomes a cause of inequality or a symptom?
7. Do equilibrium prices in a general equilibrium model reflect some inherent truth about the
world, or are they just numbers?
8. Is being wealthy a choice?
9. Is the price of something the same as what it’s worth?
10. Do economic models based on the idea of ‘equilibrium’ have any practical significance or are
they just theoretical aids to thinking about the world?
11. Adding more people or more goods to a general equilibrium model doesn’t change the math
or the core technical results much. Does it add much to the interpretation or intuition of the
model?
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Jim Campbell, UC Berkeley
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Econ 100A Course Pack, Fall 2022
Monopoly and market power
10.1
References
ˆ Jim’s lecture notes “Monopoly and market power”
ˆ Video handbook G1 and G2 (in G1 you can safely skip f, j, k, and if you’re OK with the
concepts d and g are skippable too; for G2 you can safely skip e, i, j)
ˆ Osborne and Rubinstein, Chapter 7
ˆ Serrano and Feldman, Chapter 12
10.2
Readings
ˆ Lamoreaux, Naomi R. 2019. “The Problem of Bigness: From Standard Oil to Google.”
Journal of Economic Perspectives, 33 (3): 94-117.
ˆ Boldrin, Michele, and David K. Levine. 2013. “The Case against Patents.” Journal of
Economic Perspectives, 27 (1): 3-22.
ˆ Gilbert, Richard J. 2015. “E-Books: A Tale of Digital Disruption.” Journal of Economic
Perspectives, 29 (3): 165-184.
ˆ Shapiro, Carl. 2019. “Protecting Competition in the American Economy: Merger Control,
Tech Titans, Labor Markets.” Journal of Economic Perspectives, 33 (3): 69-93.
ˆ Kahle, Kathleen M., and René M. Stulz. 2017. “Is the US Public Corporation in Trouble?”
Journal of Economic Perspectives, 31 (3): 67-88.
ˆ “The Elusive Employment Effect of the Minimum Wage.” Journal of Economic Perspectives,
35 (1):3-26.
10.3
Concepts
ˆ Monopoly; monopsony; barriers to entry and exit; natural monopoly; price discrimination
(first, second, and third degree); two-part tariffs; bundling; antitrust
10.4
Problems
1. A monopolist faces a demand curve p(y) = 60 − y. The cost to produce y units is c(y) =
100 + y 2 . Find the monopolist’s optimal choice of output and price. Sketch a diagram
illustrating the demand, marginal revenue, and marginal cost curves. Compute consumer
and producer surplus and deadweight loss.
2. Good y is produced by a monopolist. Market demand for y is p(y) = 20 − 21 y, and the cost
to produce y units is c(y) = 40 + 4y.
a) Find the firm’s optimal choice of output, the associated price, and its level of profit.
The government regulator observes that there is a monopoly in the market for this good and
suspects that ‘too little’ is being produced.
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b) How do we know that it is socially efficient to produce more than you found in a)? Find
the socially efficient level of output and the associated price.
c) Show that if the regulator enforces the price you found in b), then without barriers to
exit the firm would prefer to shut down.
3. A monopolist produces y at cost c(y) = 6y. The inverse demand function for a single
representative consumer is p = 12 − y, which is known to the firm. Assume first that the
monopolist must set a uniform price p for this consumer.
a) Find the monopolist’s optimal choice of price and output, and the associated amount of
profit.
Now assume that the monopolist can set a two-part tariff that charges a lump-sum payment
followed by a price per unit.
b) By sketching the marginal cost and demand curves, find the profit-maximizing two-part
tariff that the monopolist would charge to this representative consumer. How much
profit does the monopolist make in this case?
4. A profit-maximizing monopolist faces a demand function P = 30−3Q and has a cost function
10 + 3Q.
a) First say they must set a single price for each unit of their good. Show that the monopolist’s optimal choice of price and output is different than the socially efficient price and
output.
b) Say now that they could use a two part tariff. What would their optimal two part tariff
be?
5. Third degree price discrimination: a monopolist produces good y at a cost c(y) = 10y, so
that marginal cost is a constant $10 per unit. Two distinct groups of consumers, A and B,
have demands for y as follows:
yA (pA ) = 120 − pA
yB (pB ) = 200 − pB
(15)
(16)
First assume that the firm can practice third-degree price discrimination and so can set a
different price for each group, pA and pB .
a) Find the firm’s optimal choice of yA and yB , and the associated prices for each group, pA
and pB .
Now assume that the firm is not able to practice price discrimination and must set one price
p for the whole market.
b) Write the demand curve for the market as a whole, by adding yA and yB under the
condition that pA = pB = p.
c) Find the firm’s optimal choice of y, and the associated price p. Does the firm do better
or worse than in a)?
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Jim Campbell, UC Berkeley
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6. Take a general version of revenue, R = p(y)y. Derive an expression for marginal revenue.
Express this in terms of price elasticity of demand. Using either this or verbal reasoning,
explain why a monopolist will not choose to produce at a point at which demand is price
inelastic.
7. A profit-maximizing monopolist operates in a market with an inverse demand curve given
by P = 200 − 21 Q.
a) Find expressions for the monopolist’s marginal revenue for (i) the ‘standard’ case in which
the monopolist sells each unit of output for a single, constant price and (ii) the case
in which the monopolist can use first degree price discrimination. Explain why your
answers are different.
b) Sketch the demand curve and the marginal revenue curve for the case in a)(i) on the
usual axes. At what prices is demand price inelastic and how do you know?
8. Scott has an idea for a video game that will surely waste the time of thousands of people. It
will cost 50 to produce the game, but since it will be sold online, once it is developed there
will be no cost to produce extra units. The cost to produce y is therefore
(
50 if y > 0
(17)
c(y) =
0
if y = 0.
Scott estimates that the inverse demand curve for the game will be p = 20 − y. He will
develop the game only if he expects positive profit.
a) Sketch the demand curve and the marginal cost curve.
b) Find an expression for marginal revenue.
c) What is Scott’s optimal choice y ∗ , p∗ ?
d) What is Scott’s profit at the optimal choice in c)?
Jim the economist is concerned that Scott’s monopoly power in the production of this game
will be bad for consumers. If Scott produces the game, Jim would like the price to be fixed
at the socially efficient price.
e) Using your sketch from a), find consumer surplus at Scott’s optimal choice from part c).
f ) Find the socially efficient output ysoc and the associated price.
g) Thus demonstrate that Scott would prefer not to develop the game if the price is fixed
at the socially efficient amount. Are consumers better or worse off than in c)?
9. A profit-maximizing monopolist produces a product that it sells to two consumers. Consumer
A has an inverse demand function P = 8 − Q and a consumer B has an inverse demand
function P = 20 − 2Q. The monopolist’s production costs are zero.
a) If the monopolist can practice third-degree price discrimination and sets a constant perunit price for each consumer, what price does it set for each consumer and how many
units does it sell to each? How much total profit does the monopolist make?
b) What would be the monopolist’s marginal revenue from consumer A at the point Q = 5?
How can marginal revenue be less than zero if price you’re selling the good for is positive?
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Jim Campbell, UC Berkeley
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c) If the monopolist can practice first degree price discrimination and makes each consumer
a personalized offer of a given quantity for a given total price, what quantity and total
price does it offer to each consumer? How much total profit does the monopolist make?
d) How do the situations in a) and c) compare in terms of (i) social efficiency and (ii)
consumer surplus to each consumer?
10. Construct an example in which a monopolist does better by bundling different products than
by selling them separately.
11. The diagram shows marginal cost, average cost, demand curve, and marginal revenue for a
profit-motivated monopolist which must set a single, constant price for its output.
a) At its optimal choice of quantity and
price, would this monopolist make positive, negative, or zero profit? At
the socially efficient quantity and price,
would they make positive, negative, or
zero profit? In both cases, explain how
you know from the diagram.
b) Say that a regulator gets to set the price
and wants to maximize quantity produced without forcing the monopolist
to make negative profit. What point on
the diagram tells us the price that the
regulator would choose? At that point,
is producer surplus positive, negative,
or zero? Explain your answers.
12. Jim’s Pinball Emporium is open for business. The inverse demand curve for a representative
customer is given by P = 3.50 − 0.25Q, where Q is the number of hours of pinball played.
Jim’s cost to provide Q hours of pinball to a representative customer is C(Q) = 10 + 0.5Q.
a) Jim decides to use a two-part tariff pricing structure, with a fee to enter the Emporium,
and then a price per hour of pinball. What would Jim’s profit-maximizing two-part
tariff be? Explain why the entry fee takes the value that you found.
b) Jim is bored of keeping track of how many hours people stay. He decides to switch to a
new policy: pay to enter, then a price of zero per hour. What’s the biggest entry fee
he can charge now? How much less profit would he get compared to the plan in a),
assuming he charges the biggest entry fee possible in both cases?
13. Consider a profit-motivated monopolist. The inverse demand curve for their product is
P = 21 − Q, and their cost of production is C(Q) = 3Q + 12 Q2 .
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Jim Campbell, UC Berkeley
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a) Consider the case in which the monopolist
cannot price discriminate and must set a single, constant price for their product. Find an
equation for marginal revenue and add a line
representing it to this diagram. Find and
show on the diagram their optimal choice
of price and quantity. Indicate areas representing consumer surplus, producer surplus,
and/or deadweight loss, as applicable.
b) Consider the case in which the monopolist can
use first degree (a.k.a. ‘perfect’) price discrimination. Find and show on the diagram
their optimal choice of quantity. Indicate areas representing consumer surplus, producer
surplus, and/or deadweight loss, as applicable. What is going on with prices in this
case?
10.5
Discussion
1. A patent grants temporary monopoly power to its holder. Are patents good or bad policy?
Are they too long or too short? Brainstorm some ways you could try to gather evidence to
help you answer these questions.
2. “Market power is nothing to worry about—new competitors could come along at any moment.” Agree or disagree?
3. Should the regulation of market power just be about its effect on the prices that consumers
pay, or should there be more to the story?
4. Are monopolies inevitable?
5. “In practice, all monopolies are natural monopolies.” Evaluate this statement.
6. An implication of the simple model of monopoly that we have studied is that the monopolist
will not choose to operate at a point at which demand is inelastic. Why is that and can you
think of any real-world situations where this would be particularly important?
7. “It’s only fair that people earn extraordinary profits from their own inventions, so we
shouldn’t worry too much about monopoly power.” Discuss.
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Jim Campbell, UC Berkeley
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8. Using an example, describe what second degree price discrimination is and how it can help
a firm with market power make more profit.
9. A frequent topic of policy debate is what the minimum wage should be. Why does the degree
of monopsony power in the market matter for the theory behind this debate? Support your
answer with diagrams showing the effects with and without monopsony power.
10. “Addressing market power should be easy. Most market power arises due to government
policies that could easily be changed.” Agree or disagree?
11. “Why should I have to subsidize shows I don’t watch? We’d be better off being able to pay
for shows separately instead of having to subscribe to a whole streaming service.” Discuss.
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Econ 100A Course Pack, Fall 2022
Externalities
11.1
References
ˆ Jim’s lecture notes “Externalities”
ˆ Video handbook H1 (videos c and g not super relevant for us)
ˆ Serrano and Feldman, Chapter 17
11.2
Readings
ˆ (Reading response 4) Ostrom, Elinor. 2000. “Collective Action and the Evolution of
Social Norms.” Journal of Economic Perspectives, 14 (3): 137-158.
ˆ Leape, Jonathan. 2006. “The London Congestion Charge.” Journal of Economic Perspectives, 20 (4): 157-176.
ˆ Goulder, Lawrence H. 2013. “Markets for Pollution Allowances: What Are the (New)
Lessons?” Journal of Economic Perspectives, 27 (1): 87-102.
ˆ Farrell, Joseph. 1987. “Information and the Coase Theorem” Journal of Economic Perspectives, 1 (2): 113-129.
ˆ Frischmann, Brett M., Alain Marciano, and Giovanni Battista Ramello. 2019. “Tragedy of
the Commons after 50 Years” Journal of Economic Perspectives, 33 (4): 211-228.
ˆ Currie, Janet and Reed Walker. 2019. “What Do Economists Have to Say about the Clean
Air Act 50 Years after the Establishment of the Environmental Protection Agency?” Journal
of Economic Perspectives, 33 (4): 3-26.
ˆ Auffhammer, Maximilian. 2018. “Quantifying Economic Damages from Climate Change.”
Journal of Economic Perspectives, 32 (4): 33-52.
ˆ Covert, Thomas, Michael Greenstone, and Christopher R. Knittel. 2016. “Will We Ever
Stop Using Fossil Fuels?” Journal of Economic Perspectives, 30 (1): 117-138.
11.3
Concepts
ˆ Externality; social costs and social benefits; Pigouvian tax and subsidy; quota; tradeable
permits; the Coase Theorem; tragedy of the commons
11.4
Problems
1. A pollutant is produced as a byproduct of production by a large number of profit-maximizing
polluters. The marginal private benefit of the pollutant to a polluter is M P B = 1000 − Q,
where Q is the total amount of the pollutant. There is no cost to the polluter to produce the
pollutant. However, the pollutant carries an externality effect on people in the area due to
its environmental impact, and the effect gets more severe the more pollution there is. The
marginal social cost of the pollutant is given by M SC = Q.
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a) What is the efficient amount of this pollutant? How much will be produced by the
polluters? Illustrate with a diagram.
b) What Pigouvian tax on the emission of the pollutant would result in the efficient amount
being emitted? Illustrate with a diagram.
c) Under a cap-and-trade system, what number of permits to emit a unit of this pollutant
would be efficient? What would be the price of the permit? Illustrate with a diagram.
d) What polluters end up emitting or not under the mechanisms in b) or c)? Is this fair or
not?
2. There are two firms. Firm 1 produces plastics (x). It can use a clean production process or
one that produces noxious fumes (f ). Costs to produce some level of x are lower when the
firm uses more the process that produces fumes: production costs for a given level of output
x and byproduct f are given by c1 (x, f ) = c(x) − f (1 − f ).
Firm 2 produces computer software (s). Its facilities are located next to firm 1’s plant. The
more fumes firm 1 produces, the more firm 2 must pay its employees to compensate them
for the unpleasantness. The cost to firm 2 is given by c2 (s, f ) = c(s) + f 2 .
Let the price of plastics be px and the price of software be ps .
a) Write firm 1’s profit function. Find the level of f that firm 1 will choose.
b) Write firm 2’s profit function. What is the marginal effect of f on firm 2?
c) Combining your answers to a) and b), find the socially efficient level of f .
d) Say the two firms were to merge. Write a profit function for the merged firm. Show that
the profit-maximizing level of f for the merged firm is equal to the socially efficient level
of f .
e) Explain why the merged firm is more profitable than the two firms were separately.
3. Consider an economy with two people, A and B. There are two goods in the economy:
‘noise’ (n, measured in hours)
and ‘cash’ (x). Consumer A likes to listen to music: her
√
utility function is UA = n + x. Consumer B likes to read books and so likes ‘quiet’ (q,
√
measured in hours): his utility function is UB = 2 q + x.
Each consumer has an endowment of $100 in cash. There are 10 hours of time, each of which
can be allocated to noise or quiet, so it must be that n + q = 10.
a) Sketch an Edgeworth box that represents the feasible allocations in this economy. Make
sure to clearly label the axes.
b) What is consumer A’s marginal rate of substitution between noise and cash?
c) What is consumer B’s marginal rate of substitution between quiet and cash?
d) Characterize the socially efficient allocations in this economy.
e) Say that there is a ‘right to be loud’. On your sketch from a), mark an endowment point
that captures this regime. Is this a Pareto efficient allocation?
f ) Say that there is a ‘right to quiet’. On your sketch from a), mark a different endowment
point that captures this regime. Is this a Pareto efficient allocation?
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Jim Campbell, UC Berkeley
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g) Say that trading of noise rights is allowed. Explain in words what would be a Paretoimproving trade from the endowment point in f).
h) Consider a competitive equilibrium reached from the endowment point in e) and another
competitive equilibrium reached from the endowment point in f). How will the distribution of noise compare in the two cases? How will the distribution of cash compare?
4. Jim has HBO and is very generous. He therefore allows his friends to come over to watch
‘Game of Thrones’, making his living room a common property resource for the group. There
are no costs associated with people coming over. However, there is an externality: the more
people are present, the harder it is to concentrate on the show, and so the benefit each person
enjoys is decreasing in the number of people present. If n people show up, everyone present
enjoys a benefit that is an equal share of a total value 10n − n2 . Assume that each person
decides to show up if the benefit they get exceeds the cost they must pay.
a) How many people will show up if each decides privately?
b) Find the socially efficient number of people in the room by equating marginal social cost
to marginal social benefit.
c) Jim is finding it hard to focus on the show, and is considering adding an entry fee: anyone
who comes to watch has to pay a tribute of t. What t should Jim set in order that the
socially efficient number of people show up?
5. A common property resource
produces value v depending on the number of users n according
√
to the function v = 100 n. Each user gets an equal share of that value. The cost of using
the resource is c = 10 per user (this is both the private and the social cost).
a) What is the socially efficient number of users?
b) Assuming that a person will use the resource if the value to them exceeds the cost, what
number of users will there be if everyone decides privately? Why is this different than
in a)?
c) Say that there is a tax t on the use of the resource. If the fee is introduced, the private
cost for a user will be 10 + t. What fee t would result in the socially efficient number of
users? What is a tax like this called in this context? Explain how it works.
6. Jim Corp. produces ‘writing’ (y)√
using√
the inputs ‘Jim’s coffee’ (j) and ‘music’ (m) according
to the production function y = j + m. The price per unit of writing is 4, the price per
unit of coffee is 2, and the price per unit of music is 1.
a) Solve Jim’s profit maximization problem to find his optimal choice of each input.
Jim’s music causes a negative externality for Stephanie Corp., who has the office next door
but prefers to work in silence. Stephanie’s output depends
on ‘Stephanie’s coffee’ (s) and
√
‘music’ (m) according to the production function y = s − 18 m. She also sells writing for
price 4, and pays 2 per unit of coffee, but she has no control over m and does not pay for it,
instead having to deal with whatever Jim chooses.
b) Solve Stephanie’s profit maximization problem to find her optimal choice of input. How
much would Stephanie be willing to pay for Jim to turn off his music so that m = 0?
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c) Show whether Jim would be willing to accept a payment this large to turn off his music
so that m = 0.
d) What is the socially efficient m in this two-person economy? Explain how and why it is
different to the amount of m that Jim originally chose.
e) What’s the social value of a pair of headphones?
7. Susan is deciding how many nights per week to open her club. Each night the club is open
it earns revenue 10, and the total cost of opening the club for n nights per week is 2n + n2 .
However, next door to Susan’s club is Jim’s bookstore. The more nights the club is open,
the more Jim’s noise-sensitive customers stop shopping at the bookstore: if the club is open
for n nights, the cost to Jim is n2 in lost revenue.
a) What is the marginal private cost to Susan of an extra night, as a function of n? What
is the marginal private benefit? How many nights, n∗ , will Susan open the club?
b) What is the marginal social cost of the club opening an extra night? What is the socially
efficient number of nights, nS for the club to be open?
c) If Susan had to pay a license fee f per night she wants to open the club. What f leads
her to choose the socially efficient number of nights? Explain your answer.
d) Say that there is no license fee like in part c). Jim is considering offering to pay Susan a
bribe of b if she agrees to open the club for nS nights instead of her preferred n∗ . Show
that the amount up to which Jim is willing to pay is bigger than the lowest amount that
Susan would be willing to accept. What values of b would make both parties better off
by making this deal than they would be at n∗ ?
8. Firm 1 is a profit-maximizer that√produces y1 using the inputs x1 and e according to the
√
production function y1 = 2 x1 + e. The price per unit of output y1 is 2 and the price of
each input, x1 and e, is 1.
a) Write firm 1’s profit function. Find firm 1’s optimal choice of e.
Firm 1’s choice of e causes an externality for Firm 2. Firm 2 produces y2 in a way that
√
depends on inputs x2 and e according to the production function y2 = x2 + 12 e. Firm 2 is
a profit-maximizer that chooses its amount of input x2 but has no control over e. The price
per unit of output y2 is 1 and the price per unit of input x2 is 1.
b) What is the effect on Firm 2’s profit of firm 1’s choice of e from part a)?
c) Find the socially efficient amount of e in this two firm economy and explain why it is
different than in a).
d) What Pigouvian tax or subsidy on e would induce firm 1 to choose the socially efficient
amount? Explain your answer.
9. La Noisette makes delicious desserts (d) according to a cost function c(d) = 10 + 41 d2 . Jim’s
1 2
Tea, next door, produces tea (t) according to a cost function c(t, d) = 10 + 10
t − d, which is
decreasing in d since the smell of delicious desserts makes Jim more productive. The price of
desserts is $5. The price of tea is $2. Both businesses are profit-motivated. No other party
is impacted by the amount of desserts, other than La Noisette and Jim’s Tea.
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a) Find La Noisette’s optimal number of desserts and the socially efficient number of desserts.
b) Find a mutually beneficial Coasian bargain in which La Noisette agrees to produce the
socially efficient quantity of desserts in exchange for a cash payment from Jim’s Tea.
In what range must the cash payment fall?
10. Consider a hypothetical environmental pollutant, whose private and social benefits and private costs are reflected in the diagram shown.
a) Is it possible that the socially efficient
amount of this pollutant is zero? If so,
what could make that the case? If not,
why not? Explain how you know based
on what the diagram illustrates.
b) In general, how would the imposition of a
Pigouvian tax on this pollutant change
the nature of this diagram? Explain
why. Give an example of a real-world
public policy that would fit the description of a Pigouvian tax, and explain
why.
11. Two roommates, A and B, live in an economy with three goods, cash (x), cooking TV shows
√
(c), and sitcom TV shows (s). A likes cooking shows: their utility function is UA = xA + 2 c
(where x√A is the amount of cash A has). B likes sitcoms: their utility function is UB =
3xB + 2 s. Their apartment has one TV so there is an externality problem: whenever one
type of TV show is on, the other one is not. Assume that each person has $200 in cash and
that they share the apartment and its TV for 20 hours per week.
a) Sketch a clearly and fully labeled Edgeworth box diagram (cash on the horizontal axes
please) to represent this economy. Do we know where the endowment point is in this
economy? If so, where is it? If not, why not?
b) The Coase Theorem could apply here under the assumptions that property rights are
well-defined and that there are no transaction costs of bargaining. If these assumptions
hold, how many hours of cooking shows and how many hours of sitcoms would the
theorem predict we’d see on this apartment’s TV? Show your work and explain your
answer.
11.5
Discussion
1. Who, if anyone, has responsibility to intervene in the presence of an externality? What tools
do they have at their disposal? Run through a couple of concrete examples.
2. Will externality problems ‘sort themselves out’, or do they require a more structured intervention by an authority? The Ostrom reading will be useful here.
3. If someone claims to be ‘offended’ by something another person is doing, does this count as
an externality? Where should the line be drawn in such cases? Are there implications for
society? For the law? For economics?
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4. Is there a case for a Pigouvian tax or subsidy of Facebook?
5. “A market for tradeable emissions permits is the cheapest way to control carbon emissions.”
Discuss.
6. “If there are different tools or ways to correct an externality, it doesn’t matter which one
you use as long as you get it done.” Do you agree or disagree?
7. “Without a strong legal system, there’s no hope of correcting market failures.” Discuss.
8. “Climate change is too big of a problem for traditional externality-correcting tools to solve.”
Discuss.
9. Would externality theory be irrelevant if people just cared more about each other?
10. Right now there are many online social networks that have zero price to join and zero price
to post. Are those prices ‘right’ ?
11. Would a world without externalities be socially desirable compared to the world we actually
live in?
12. Does the concept of ‘social benefit’ raise or diminish the importance of low-income households
in economic analyses, compared to other ways decisions might get made?
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Game theory
12.1
References
ˆ Jim’s lecture notes “Game theory”
ˆ Video handbook F1 a-d; F2a, g; F3a-c, g, h
ˆ Osborne and Rubinstein, Chapter 15.1-15.5, 15.8, 16.1-16.3
ˆ Serrano and Feldman, Chapter 14
12.2
Readings
ˆ Myerson, Roger B. 1999. “Nash Equilibrium and the History of Economic Theory.” Journal
of Economic Literature, 37 (3): 1067-1082.
ˆ Samuelson, Larry. 2016. “Game Theory in Economics and Beyond.” Journal of Economic
Perspectives, 30 (4): 107-130.
ˆ Rizvi, S. Abu Turab. 2007. “Aumann’s and Schelling’s Game Theory: The Nobel Prize in
Economic Science, 2005.” Review of Political Economy, 19 (3): 297-316.
ˆ Levitt, Steven, John List and Sally Sadoff. 2011. “Checkmate: Exploring Backward Induction among Chess Players.” American Economic Review, 101 (2): 975-90
ˆ Dal Bó, Pedro. 2005. “Cooperation under the Shadow of the Future: experimental evidence
from infinitely repeated games.” American Economic Review, 95 (5): 1591-1604
ˆ Mehta, Judith, Chris Starmer and Robert Sugden. 1994. “The Nature of Salience: An
Experimental Investigation of Pure Coordination Games.” American Economic Review, 84
(3): 658-673.
12.3
Concepts
ˆ Game, strategy, best response, mutual rationality, Nash equilibrium in pure strategies, backward induction, subgame perfect Nash equilibrium, discounting, infinitely repeated games
12.4
Problems
1. Two players, row and column, will simultaneously choose one of two actions, A or B. The
utility they get from an action depends on both their choice and the other player’s choice
in a way that is captured in the following payoff matrix, where in each cell the numbers are
row’s payoff first and column’s payoff second. (This payoff structure is the classic ‘prisoner’s
dilemma’.)
Column player
A
B
Row player A 2, 2 0, 3
B 3, 0 1, 1
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a) If row thinks that column will play A, what would their best option be? What if row
thinks that column will play B?
b) What is the unique Nash equilibrium of this game (that is: a strategy for each player
such that each is doing the best they can given what the other person is doing)?
c) Is the Nash equilibrium Pareto efficient or not?
d) Write down a different payoff matrix that would have the same answers to part a) and
b) but the opposite answer to part c).
Next, consider a version of a public good contribution game. There are four players. Each
has $10. They must each decide (independently) how much of their $10 to contribute to a
common pool that represents a public good; for each dollar in the common pool, all four
people in the group (including the contributor) receive $0.40 each. Each player’s total cash
at the end is the amount they kept of their original $10 plus any money they receive from
the public good.
e) If everyone contributes all of their money in the public good, how much does each person
end up with?
f ) If the other three players contribute $10 to the public good, how much cash does the
fourth player end up with if they contribute nothing to the public good? If each player
cares only about getting as much cash as possible, what would be the Nash equilibrium
of this game?
g) Games like these have been studied a lot in experimental economics. Two things that are
known to reduce free riding are (i) playing the game repeatedly rather than just once
and (ii) giving players the possibility to implement costly punishments to others (that
is, giving up some of your own money to reduce the money of someone else). Briefly
discuss how and why these things might matter. Are there other factors that you think
might reduce free riding in games like these?
2. Find the pure strategy Nash equilibria, if any exist, of each of the following games:
Player 1 U
D
Player 2
L
R
4, 4 0, 6
6, 0 2, 2
Player 1 U
D
Game 1
Player 1 U
D
Player 2
L
R
1, 1 0, 0
0, 0 1, 1
Player 2
L
R
4, 4 0, 3
3, 0 2, 2
Game 2
Player 2
Heads T ails
−1, 1
Player 1 Heads 1, −1
T ails −1, 1
1, −1
Game 3
Game 4
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T
Player 1 M
B
Player
L
C
4, 1 1, 2
3, 2 3, 3
2, 5 0, 4
Econ 100A Course Pack, Fall 2022
2
R
2, 3
4, 0
1, 1
Game 5
Make sure you can explain why your answers are Nash equilibria, and why other strategy
profiles are not!
3. For each of the following two scenarios, construct a 2 player simultaneous move game, with
2 pure strategies for each player, that satisfies the description.
There are two pure strategy Nash equilibria, but one player prefers the outcome in the first
of the equilibria and the other player prefers the outcome in the second of the equilibria.
There are two pure strategy Nash equilibria, one of which is Pareto efficient and the other
of which is Pareto inefficient.
4. Two players, Row and Column, will simultaneously and independently decide whether to
‘share’ or ‘steal’. Cash outcomes have a ‘prisoner’s dilemma’ structure. However, Column
feels shame s > 0 if they choose ‘Steal’. Row’s payoff is their cash outcome; Column’s is their
cash outcome, minus their shame if they ‘Steal’. The following matrix summarizes (each cell
has Row’s payoff first, and Column’s second):
Column
Share
Steal
5, 5
0, 8 − s
Row Share
Steal
8, 0
2, 2 − s
This game has a unique Nash equilibrium, but it depends on s. What is the Nash equilibrium
of this game, for different values of s? Explain.
5. By backward induction, find the subgame perfect Nash equilibria of the three player game
represented by the following extensive form:
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6. Rihanna is coming to town, and Jim and Stephanie are considering whether to buy a ticket
for the show. First Stephanie will decide whether to “buy” or “not buy”, and then Jim will
observe Stephanie’s choice and decide whether to “buy” or “not buy”. They would like to
go to the show, but only if they go together: each gets a payoff of 2 if they both buy, each
gets a payoff of 0 if neither buys, and if only one buys the buyer gets a payoff of -1 and the
other gets a payoff of 0.
a) If the two players had to make their choices simultaneously, what would be the set of
pure strategy Nash equilibria?
b) Sketch the extensive form of the game.
c) Find the set of pure strategy Nash equilibria.
d) Find the set of subgame perfect Nash equilibria.
7. Jim Corp. and Ivan Corp. are racing to release new Carly Rae Jepsen remixes to the market.
Each of them must decide whether to remix song A (“Julien”) or song B (“Stay Away”).
Since Ivan is a much less lazy person than Jim, this will proceed as a sequential move game.
First Ivan will choose whether to work on song A or song B, and then Jim will observe his
choice and decide whether to work on song A or song B.
Two things determine each person’s payoff: which song they pick and whether they pick the
same as the other person. If they work on the same song, they each get 0 because their songs
will compete with other, but if they work on different songs, they each get 2. In addition to
that, since song A is more famous, anyone who chooses song A gets an extra 1.
a) Sketch a game tree to represent the extensive form of this game.
b) Sketch a matrix that represents this game. Find the Nash equilibria in pure strategies.
What outcomes are possible in the pure-strategy Nash equilibria of this game?
c) Find the unique subgame perfect Nash equilibrium. Explain why this is different than
your answer to b).
8. Consider the following game:
(a) Seller offers good for sale at the price p1 ∈ [0, 1]. Buyer either accepts or rejects.
(b) If the buyer rejects, she offers to buy at the price p2 . Seller either accepts or rejects.
(c) Sale at stage 1: payoffs are p1 to the seller and u − p1 to the buyer, u > 1. Sale at stage
2: payoffs are δp2 to the seller and δ(u − p2 ) to the buyer. No sale: 0 to both.
Solve this game by backward induction. When is a sale made? What is the sale price?
9. Consider a 2 player game that infinitely repeats the following stage game:
Player 1 A
B
Player 2
A
B
2, 2 1, 5
5, 1 0, 0
Each player discounts the future at the rate δ according to the discounted utility model.
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Jim Campbell, UC Berkeley
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a) Say that player 2 uses the grim punishment strategy (“play A unless my opponent has
ever played B, in which case play B forever”). Write an expression for player 1’s payoff
(i) if they play B forever, or (ii) they use the grim punishment strategy.
b) Thus find a condition on δ such that there exists a subgame perfect Nash equilibrium
in which both players use the grim punishment strategy. Explain the intuition behind
there being such a threshold.
10. Consider a 2 player game that infinitely repeats the following stage game:
Player 1 A
B
Player 2
A
B
3, 5 0, 7
4, 1 2, 2
Player 1 discounts future payoffs at the rate δ1 , and player 2 at the rate δ2 . Find the threshold
patience for each player such that there exists a subgame perfect Nash equilibrium in which
both players use the grim punishment strategy (“play A unless my opponent has ever played
B, in which case play B forever”).
12.5
Discussion
1. If we’re modeling behavior, is mutual rationality an innocuous extension of individual rationality or is it a radically new idea?
2. Can game theory serve as a tool to help a person make strategic decisions, or is it just an
intellectual curiosity?
3. Would it be irrational for a person, playing in a well-defined game, to use a strategy that
was not part of a Nash equilibrium?
4. Does a strategy in the game theoretic sense bear any resemblance to what we would mean
by the word strategy in the real world?
5. Is game theory the right name for game theory?
6. What does Nash equilibrium have to say about the following game? What do you think
about that?
Player 2
L
R
0, 0
Player 1 U 1000, 1000
D
0, 0
1, 1
7. Which is more of an obstacle to good game theoretic modeling: the fact that strategy spaces
are really complicated in the real world, or the fact that preferences are really complicated
in the real world?
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Oligopoly theory
13.1
References
ˆ Jim’s lecture notes “Oligopoly”
ˆ Video handbook G3 (particularly d and j)
ˆ Osborne and Rubinstein, Chapter 15.3
ˆ Serrano and Feldman, Chapter 13
13.2
Readings
ˆ Adams, William James. 2006. “Markets: Beer in Germany and the United States.” Journal
of Economic Perspectives, 20 (1): 189-205.
ˆ Basker, Emek. 2007. “The Causes and Consequences of Wal-Mart’s Growth.” Journal of
Economic Perspectives, 21 (3): 177-198.
ˆ Kahn, Lawrence M. 2007. “Markets: Cartel Behavior and Amateurism in College Sports.”
Journal of Economic Perspectives, 21 (1): 209-226.
ˆ Berry, Stephen, Martin Gaynor, and Fiona Scott Morton. 2019. “Do Increasing Markups
Matter? Lessons from Empirical Industrial Organization.” Journal of Economic Perspectives, 33 (3): 44-68.
13.3
Concepts
ˆ Oligopoly; the Cournot model; the Bertrand model; the Hotelling model; collusion
13.4
Problems
1. Two firms produce an identical product and simultaneously choose what quantity to produce,
as in the Cournot model. The demand curve for the product is given by p = 10 − y, where
y = y1 + y2 is the sum of the outputs chosen by each firm. The cost to produce output is
c(yi ) = 2yi for each firm i = 1, 2.
a) Write the profit function for firm 1 and the profit function for firm 2.
b) Find reaction functions that define each firm’s optimal output for any output choice by
the other firm.
c) Find the Nash equilibrium, an output for each firm that is a mutual best response.
d) If this market had been served by a single monopolistic producer, what would its output
choice have been? How does the outcome in the Cournot equilibrium compare to the
monopolistic outcome?
e) Say that the firms ‘agree’ to each produce half of the monopolistic output. Show that
this is more profitable for each firm than the Cournot outcome. However, show that if
one firm does produce half of the monopolistic output, the best response by the other
is to cheat on the agreement.
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2. Two competing profit-motivated firms, 1 and 2, will simultaneously choose a quantity of
output (y1 for firm 1, y2 for firm 2). The inverse demand function in their industry is given
by p = 60 − y, where y = y1 + y2 . The cost of production for each firm i is c(yi ) = 12yi .
a) For each firm, derive a reaction function that gives their optimal choice of output as a
function of the other firm’s choice of output.
b) Thus find the Nash equilibrium of this game. Explain what that means. Show whether
this is bigger, smaller, or the same as (i) the output that would have been produced
if this industry was a monopoly, and (ii) the output that would have been produced if
this industry had been perfectly competitive. (In both cases, assuming that the cost
function is always c(yi ) = 12yi for any producer.)
c) Sketch the two reaction functions you found in a) on a diagram with y1 on the horizontal
axis and y2 on the vertical axis. Mark the Nash equilibrium on your diagram. Label
the intercepts with their appropriate values. What do those intercept values correspond
to? Why?
3. Jim and Norma are going to a cook-off and will both make delicious chili. Norma gets up
much earlier in the morning than Jim, so the two will decide sequentially how much chili to
make: first Norma will choose her output y1 , and then Jim will observe this and decide on
his output y2 .
The market demand for chili is p = 20 − y, where y = y1 + y2 , the combined output for
both producers. Marginal cost is constant at 4 for both Jim and Norma, so that the cost to
produce y units is 4y. Jim and Norma both aim to maximize profit.
a) Write Jim’s profit function.
b) Find Jim’s optimal choice of output as a function of the amount y1 produced by Norma.
c) Thus write Norma’s profit as a function only of y1 .
d) Solve to find Norma’s optimal choice of output.
e) Thus find Jim’s output and the market price in equilibrium.
f ) If Jim could just wake up earlier than Norma, he could be the quantity leader. How much
would it be worth to Jim to be the leader instead of the follower?
4. Jim and Martin are duopolistic producers of incisive economic analysis. These analyses are
valuable; the market demand curve is given by
p = 12 − y,
(18)
where y is the total number of analyses produced, the sum of y1 , the number produced by
Jim, and y2 , the number produced by Martin.
Martin can produce economic analysis very efficiently. He produces according to the cost
function c(y2 ) = 2y2 . Jim is lazy and suffers greatly to produce analysis. He produces
according to the cost function c(y1 ) = 4y1 .
a) Write profit functions for Jim and Martin.
The two producers must simultaneously decide how much analysis to produce.
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b) Find y1∗ (y¯2 ), Jim’s optimal choice as a function of Martin’s output.
c) Find y2∗ (y¯1 ), Martin’s optimal choice as a function of Jim’s output.
d) Thus find a pair y1∗ , y2∗ such that Jim and Martin are both making optimal choices given
the choice made by the other.
e) What is the market price at the output pair from d)?
f ) Who earns more profit, Jim or Martin?
5. Two identical firms will compete in a Stackelberg setting: first firm 1 will choose and commit
to an output y1 and then firm 2 will observe firm 1’s choice and choose an output y2 . The
price in the market is given by the inverse demand function p = 12 − y, where y is the sum
of their outputs. The cost of production for each firm is 2yi , where yi is their output.
a) Set up and solve firm 2’s profit maximization problem to find their reaction function
(optimal y2 as a function of y1 ).
b) Using your answer to a), set up and solve firm 1’s profit maximization problem to find
their optimal choice of output, y1∗ , and therefore firm 2’s optimal choice of output, y2∗ .
What does the price end up being?
6. Two profit-maximizing firms produce an identical product and will compete in Cournot
fashion by simultaneously choosing how much to produce. Demand for the product is given
by p = 6 − y, where y is the total output produced by both firms, y1 + y2 . Firm 1 has a cost
function c1 (y1 ) = y1 , and firm 2 has a cost function c2 (y2 ) = 2y2 .
a) Set up firm 1’s profit maximization problem and solve to find its reaction function y1∗ (y2 ),
its optimal choice as a function of firm 2’s choice.
b) Set up firm 2’s profit maximization problem and solve to find its reaction function y2∗ (y1 ),
its optimal choice as a function of firm 1’s choice.
c) Find an output pair y1∗ , y2∗ that is a mutual best response. What is the price and how
much profit does each firm make?
Shady “consultant” Jim has a proposal for firm 2. He offers to steal firm 1’s secrets, thus
making firm 2’s cost function the same as firm 1’s.
i. steal firm 1’s secrets, thus making firm 2 just as efficient in production as firm 1. This
would lower firm 2’s cost function to c2 (y2 ) = y2 , or
ii. sabotage firm 1, increasing firm 1’s cost function to c1 (y1 ) = 2y1 .
d) Assuming they could get away with it, which of these two proposals is most valuable to
firm 2? What is the most that they would be willing to pay Jim for this professional
service?
e) Jim, being fair-minded, gives firm 1 a chance to counter-offer: if firm 1 is willing to pay
more than firm 2, he will not enact the proposal that firm 2 chose in part d). Show
whether firm 1 would be willing to outbid firm 2.
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7. Jim runs a lemonade stand. There are two lemonade stands on his street. Jim (firm 1) and
his competitor (firm 2) must simultaneously set the price for which they will sell lemonade
this summer (i.e. the Bertrand model). The lemonade stand with the lower price will attract
and serve all 200 customers; if the two stands have identical prices they will each serve half
the market. The cost of producing lemonade is a constant 25 cents per cup.
a) Carefully characterize what Jim’s best response would be for each possible price that his
competitor could set.
b) What pair of prices set by Jim and his competitor would be a mutual best response (that
is, each has set the best possible price given the price set by the other)?
Now assume that each lemonade stand can serve a maximum of 100 customers. Further
assume that each customer is willing to buy precisely one cup of lemonade so long as the
price does not exceed $1.
c) Explain why the pair of prices in b) is no longer a mutual best response.
d) Explain why for each firm to set a price of $1 is a mutual best response in this modified
game.
8. Two profit-maximizing firms will simultaneously choose a price for their (identical) products
as in the Bertrand model. You may assume that prices can’t include fractions of pennies.
Each of the 100 potential customers in the market will buy one unit of the product from
whichever firm has the lower price; if the prices are the same, the two firms will split the
consumers half each. We are interested in what choices by the two firms are mutual best
responses (that is, each firm has chosen a price that is optimal for them given the price that
the other firm chose).
a) Say that both firms have a marginal cost of production that is constant at $1. Show that
(i) it isn’t a mutual best response for both firms to set a price of $5, but (ii) it is a
mutual best response for both firms to set a price of $1.
b) Now say that firm 1’s marginal cost of production is constant at $1 and firm 2’s is constant
at $3. Is there a mutual best response in which one of the firms prices at $3? Which
firm, and what does the other one do in that case? Is this mutual best response unique?
Briefly explain your answers.
9. Consider the basic version of the Hotelling spatial duopoly model. Explain the setup of the
model in a few non-technical sentences using an illustrative example of your choice. Explain
why the unique mutual best response is for both firms to locate at the midpoint.
10. Consider a Hotelling variation. Two firms, Pat Corp. and Carlos Inc., are going to sell drinks
at a block party, which is a line from 0 to 1, and they each want to serve as many people as
possible. Price is fixed and not chosen by either firm. Each must simultaneously choose a
location. Potential customers are uniformly distributed along the block, each willing to buy
exactly one drink. They’ll buy from the closer firm; if they’re equally close they’ll pick one
at random. However, the twist is that customers refuse to walk more than 14 to get a drink.
If they have to walk more than that, they won’t buy a drink at all.
a) In the basic Hotelling model we saw in class, it was a Nash equilibrium for both firms to
locate at the midpoint of the line. Carefully explain why that isn’t true in this case.
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b) Find a Nash equilibrium in this model. Carefully explain why it’s a Nash equilibrium.
11. In each of period t = 0, ...∞ each of two firms must choose whether to set a ‘high’ or ‘low’
price. The payoff to firm 1 in period t, denoted π1,t , depends on the choice made by both
firms as follows:
Firm 2
High Low
2
−2
Firm 1 High
Low
4
0
P
t
The total payoff to firm 1 is Π1 = ∞
t=0 δ π1,t , where 0 < δ < 1. (This is called the discounted
utility model of preferences over time!)
Say that firm 2 is following a strategy such that it will play ‘high’ in every period unless in
some period firm 1 plays ‘low’, and then firm 2 will play ‘low’ in every subsequent period.
a) What is firm 1’s total payoff if it plays ‘high’ in every period?
b) What is firm 1’s total payoff if it plays ‘low’ in every period?
c) Find a condition on δ such that firm 1 prefers to play ‘high’ rather than ‘low’ in each
period. Explain your answer.
d) If the payoff in the (low, high) case was bigger than 4, how would the threshold δ be
different? Why?
12. Two competing firms will play a repeated game indefinitely, in time periods t = 0, 1, 2, ..., ∞.
In each period the firms will simultaneously choose whether to ‘collude’ or ‘defect’. Payoffs
in each period are as in the following matrix, where the first number in each cell is firm 1’s
payoff and the second number firm 2’s payoff, and X > 3:
Firm 2
Collude Defect
Collude
3, 3
−1, X
Firm 1
Defect X, −1
0, 0
The total payoff to firm i is Πi =
period t.
P∞
t=0
δ t πi,t , where 0 < δ < 1 and πi,t is their payoff in
a) If this game was played only one time, what is the unique Nash equilibrium? Explain
why and what that means in simple terms, referring to the properties of each good.
b) Say that firm 2 uses a trigger strategy: it will play ‘collude’ every period unless firm 1
ever plays ‘defect’, after which it will play ‘defect’ forever. What would firm 1’s total
payoff be if it (i) also used this same trigger strategy, or (ii) always played ‘defect’ ?
How do these depend on δ and why?
c) Say that firm 1 has δ1 = 12 and firm 2 has δ2 = 34 . Is there an equilibrium in which both
firms use the trigger strategy? How and why does your answer depend on X?
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Jim Campbell, UC Berkeley
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13. Jim and TJ are Cournot duopolists. They each make an identical product. They will
simultaneously choose a quantity of output, yJ and yT respectively. The market for this
product has an inverse demand curve p = 15 − 21 y, where y = yJ + yT is the total quantity
of output produced by both Jim and TJ. Their production costs are identical: production
costs for each person i are c(yi ) = 3yi .
a) Say that both people are profit-motivated. Derive reaction functions for each person
(their optimal choice given the choice made by the other person). Thus find the quantity
produced by each person and the price in the Nash equilibrium of this game.
b) Now say that Jim is not profit-motivated, but spite-motivated. He has one goal: to
ensure that TJ cannot make positive profit, no matter what yT he picks. At least how
much output yJ will Jim choose to produce? Explain the economic intuition behind
your answer.
13.5
Discussion
1. Compare and contrast the Cournot and Bertrand models and their predictions. Which one
is the ‘right’ way to think about a duopoly?
2. Can selfish people play nice?
3. Suggest and describe a variation or extension of the Hotelling model that you think might
be useful or interesting. What happens in your model?
4. Take an example of a real-world industry that you think might be characterized as an
oligopoly. How do the players compete? Do you think it’s close to any of the oligopoly
models we’ve studied?
5. Is market structure just driven by consumer preferences?
6. “At the end of the day the most applicable ideas in oligopoly theory are found in the most
basic versions of the models. You can add things to them, but the basics are most of the
story.” Discuss.
7. “The concept of a strategy in simple oligopoly models so different from how firms actually
operate that it makes the models irrelevant.” Discuss.
8. “An oligopoly model that doesn’t include prices is useless. That’s the most important thing
we need to consider.” Discuss.
9. Is the distinction between the Cournot and Bertrand models just a theoretical thing, or are
there distinct real-world situations where we can see their differences in action?
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Jim Campbell, UC Berkeley
14
Econ 100A Course Pack, Fall 2022
Markets with asymmetric information
14.1
References
ˆ Jim’s lecture notes “Asymmetric information”
ˆ Video handbook section I (particularly I1a,c and I2b,d)
ˆ Osborne and Rubinstein, Chapter 14
ˆ Serrano and Feldman, Chapter 20
14.2
Readings
ˆ Weiss, Andrew. 1995. “Human Capital vs. Signalling Explanations of Wages.” Journal of
Economic Perspectives, 9 (4): 133-154.
ˆ Geruso, Michael, and Timothy J. Layton. 2017. “Selection in Health Insurance Markets and
Its Policy Remedies.” Journal of Economic Perspectives, 31 (4): 23-50.
ˆ Leeson, Peter. 2012. “Ordeals.” The Journal of Law and Economics, 55 (3): 691-714.
ˆ Lazear, Edward P. 2018. “Compensation and Incentives in the Workplace.” Journal of
Economic Perspectives, 32 (3): 195-214.
14.3
Concepts
ˆ Hidden type; adverse selection; signalling; hidden action; moral hazard; incentive contracts;
incentive compatibility constraints; participation constraints
14.4
Problems
1. Consider a used car market with a large number of sellers and buyers. Each seller has a used
car whose quality is a random variable drawn from a uniform distribution with support [0, 1].
Each seller knows the quality of the car they are selling. If the car is of quality q, the seller
is willing to sell if and only if they receive a price p ≥ q.
Each buyer cannot tell the quality of a car before they purchase it. If the buyer knew that
a car was of quality q, they would be willing to pay up to 45 q for the car. Since they cannot
infer quality before purchase, each buyer is willing to pay up to 45 q̄ for a car of expected
quality q̄.
a) Explain why if buyers could observe the quality of a car before buying, all cars would be
traded.
b) Say a price p = 12 prevails in the market. What is the expected quality among the pool
of cars that will be offered for sale at this price?
c) What is the most that a buyer would be willing to pay for a car from the pool that would
be offered for sale at price p = 12 ?
d) Thus explain why p =
1
2
cannot be a market clearing price.
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Jim Campbell, UC Berkeley
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e) Say some price p ∈ (0, 1] prevails in the market. What is the expected quality among the
pool of cars that will be offered for sale at p?
f ) What is the most that a buyer would be willing to pay for a car from the pool that would
be offered for sale at price p?
g) Thus explain why no p > 0 can be a market clearing price.
2. A product can be either ‘high quality’ or ‘low quality’. There are many sellers, each with
one item to sell, and many buyers. The quality of each product is known to its seller, but
buyers cannot verify quality before buying. The going rate for high quality products would
be $100 and the going rate for bad quality products would be $60.
Sellers can choose whether to offer a money back guarantee, so that if a product turns out
to be of low quality the buyer can return it for a full refund. The failure rate of high quality
products is 5% and the failure rate of low quality products is 50%. For the seller the expected
profit per unit sold is the sales price of the product minus the expected cost of giving a refund.
We are going to check whether it can be sustainable for only sellers to offer a money back
guarantee only on high quality products and not on low quality products.
a) Is it incentive compatible for sellers with a good phone to offer a money back guarantee
on good products? Why or why not?
b) Is it incentive compatible for sellers with a bad phone to not offer a money back guarantee
on bad products? Why or why not?
c) Thus explain why a money back guarantee can be a credible signal of the quality of a
product in this market.
3. Many small firms make computers and many consumers would like to buy a computer. A
computer that was known to be good would sell for $1000 and a computer known to be bad
would not sell. However, buyers cannot verify the quality of a computer before buying.
It is possible for a firm to offer a warranty on a computer, so that the firm will pay for any
repairs the computer might need. For a good computer, the expected cost of repairs is $100;
for a bad computer, the expected cost of repairs is $500.
The firm’s profit per unit if it sells the unit and offers a warranty is the sales price minus the
expected cost of repairs; if it sells the unit and does not offer a warranty it is the sale price
only; if it does not sell the unit it is zero.
a) Say that good firms offer a warranty and bad firms do not. Will a computer with a
warranty sell, and if so for what price? Will a computer without a warranty sell, and if
so for what price?
b) Under the regime in a), what is the expected profit per unit of a seller of good quality
computers?
c) Under the regime in a), what is the expected profit per unit of a seller of bad quality
computers?
d) Under the regime in a), is it incentive compatible for a seller of good quality computers
to offer a warranty? Why or why not?
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Jim Campbell, UC Berkeley
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e) Under the regime in a), is it incentive compatible for a seller of bad quality computers
not to offer a warranty? Why or why not?
f ) Thus explain why a warranty cannot be a credible signal of good quality in this market.
4. A job candidate has either ‘high’ or ‘low’ ability to do a one-time job for a potential employer.
The candidate knows whether they’re high or low ability, but the potential employer does
not. The employer would value the high ability candidate’s work at $5,000 for this job, but
would only value the low ability candidate’s work at $1,000; they believe that a candidate
is likely to be high ability with probability p, and are willing to offer to pay up to their
expected value of the candidate’s work.
a) What would determine whether or not there would be an ‘adverse selection’ problem in
this example? Explain why.
Say that the candidate can take a particularly difficult test before applying for the job. The
test is annoying—candidates would be willing to sacrifice cash to avoid the hassle of taking
it. The test is completely unrelated to the candidate’s ability to do the job. Despite this,
the test is a credible signal of the candidate’s ability.
b) What must be true about the amount of cash that different candidates would be willing
to sacrifice to avoid this test? Why?
c) In the context of this example, what exactly would we mean by an ‘incentive compatibility
constraint’ ?
5. Jim has had what might be a million dollar idea, but he is a busy guy and so has decided to
hire an employee to undertake the project on his behalf.
If the project succeeds it will generate revenue of $1 million; if it fails it will generate no
revenue. Whether the project succeeds depends on both luck and on how much effort the
employee makes: the probability of the project succeeding is 34 if the employee exerts high
effort, but only 14 if the employee exerts low effort.
Jim would like to maximize π = E(R) − E(w) (expected revenue minus expected wage). The
employee has a utility function u = E(w) − c(e), where c(e) is the cost of effort and is equal
to 50, 000 for high effort and 0 for low effort. The employee can get u = ū = 0 by working
elsewhere, and so will not accept any contract that yields less than this utility.
a) Write the employee’s participation constraint for high effort.
b) Write the employee’s incentive compatibility constraint for high effort.
c) Say that Jim can observe the employee’s effort and offers a contract that pays zero if the
employee exerts low effort and $100,000 if the employee exerts high effort. Show that
high effort satisfies the incentive compatibility and participation constraints.
d) Now assume that effort is unobservable. If Jim offers a contract that pays a flat wage of
$100,000, show that high effort is not incentive compatible.
e) If effort is unobservable and Jim offers the contract in d), what is Jim’s expected profit?
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Jim Campbell, UC Berkeley
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Continue to assume that effort is unobservable to Jim. Say now that Jim offers a contract
that pays the employee $200,000 if the project is a success and $0 if the project is a failure.
f ) Is high effort incentive compatible? Why or why not?
g) Will the employee accept the contract? Why or why not?
h) What is Jim’s expected profit?
6. Jim is putting together a softball team and would like to hire the crafty veteran Toru to
launch some home runs. If Toru plays for the team, the success of the team will depend on
how much effort he exerts and on luck: they will win only if Toru tries hard and they get
lucky. Jim likes to win and hates to lose; his happiness h in each combination of luck and
effort is as follows:
Low effort
High effort
Bad luck (probability= 12 ) Good luck (probability= 12 )
0
0
0
100
Toru’s utility function is UT = E(w) − c(e), where E(w) is the expected wage he earns if he
plays for Jim’s team, and c(e) is the cost of effort, which is 4 if he puts in high effort and
0 if he puts in low effort. Toru currently enjoys reservation utility ū = 10 playing for Jim’s
hated rival TJ, so Toru will not accept a contract that offers less utility than this.
Unfortunately Jim is not very good at telling apart high from low effort and so cannot simply
refuse to pay Toru unless he tries hard; he can only condition wage on the observable outcome
(his happiness at the team’s outcome). Jim’s utility function is UJ = E(h) − E(w): expected
happiness minus the expected wage he must pay.
a) Write Toru’s participation constraint for high effort (that is, so that he prefers to accept
and put in high effort than to reject the contract).
b) Write Toru’s incentive compatibility constraint for high effort (that is, he prefers to accept
and put in high effort than accept and put in low effort).
c) If Jim offers Toru a constant wage of $15, what effort will Toru do? What is Jim’s utility?
Say that Jim offers a contract that pays Toru $x if the team wins (that is, when h = 100)
and nothing if the team loses.
d) Say that Jim offers $x if the team wins and nothing if the team loses. What is the
smallest x such that Toru will accept the contract and put in high effort?
e) Show that Jim does better by offering the $x you found in d) than by offering the contract
in c).
f ) Say that instead of what we had assumed in this question so far, Toru instead was the
type of person who loves to put in high effort. How might you change the model to
account for this? How might it change the analysis?
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7. Ivan’s going on vacation and is hiring Jim to look after his vegetable garden. He’s worried
because Jim is, notoriously, super lazy, and Ivan won’t know how hard he works; all he’ll see
when he gets back is whether the veggies grew. He knows that success requires both hard
work and good luck: hard work makes good veggies more likely but sometimes even with
hard work the veggies fail, and sometimes even with no work at all the veggies thrive.
a) Ivan, hoping to induce Jim to actually work, is considering offering Jim a performancerelated contract: he’ll pay more if the veggies thrive. Explain in the context of this
example what the ‘incentive compatibility’ and ‘participation’ constraints are.
b) How would (i) how lazy Jim is and (ii) how much hard work matters relative to luck
influence Ivan’s problem?
14.5
Discussion
1. Two important provisions of the Affordable Care Act were the ‘individual mandate’ that
everyone must purchase health insurance or else pay a tax penalty and the requirement that
insurers cannot deny coverage because of pre-existing medical conditions. Discuss these in
the context of models of asymmetric information. What is the relationship between them?
2. Brainstorm some examples of real world settings in which the hidden type model may be
relevant. How do things play out in your example? Do institutions exist to help with the
potential adverse selection problem?
3. Two important extensions of the basic incentive contracting model are to (i) contracting for
a job that includes more than one type of task and (ii) contracting for a team. What special
issues do you think there might be in these cases?
4. A famous model in economics shows that a college degree can be valuable even if it adds
nothing to one’s skill since it could serve as a signal of underlying traits. Describe carefully
how this would work. Why might this be an interesting question for policymakers?
5. “Adverse selection is a nice theory but has nothing to do with real insurance markets.”
Discuss.
6. “Market failures, for example from information asymmetry or externalities, might exist, but
that doesn’t justify interfering in other people’s business.” Discuss.
7. “If people were just honest, asymmetric information wouldn’t cause any economic problems.”
Agree or disagree?
8. In the context of markets with asymmetric information, can a signal that’s costless ever work
as a credible signal?
9. If you were starting a business and launching a product, would asymmetric information
theory have any lessons or warnings for you?
10. Does sharing more of one’s private information help to facilitate more trade, better trade,
neither, or both?
11. Would it be better if everyone had an ownership interest in the business they’re employed
in?
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Jim Campbell, UC Berkeley
14.6
Econ 100A Course Pack, Fall 2022
Some holistic discussion prompts
Since this is our last topic, I’m putting here some old final exam prompts that don’t fit neatly
into one topic or another. For any discussion prompts in the course, you are of course welcome
to tackle them in whatever way you feel is best, with economics from around our course rather
than just restricting your attention to any one topic. However, for these prompts, I think it’s
even more important to take a more holistic, reflective approach! Our final exam will feature
prompts of all sorts, but I particularly like writing prompts that can be addressed with lots of
different perspectives, interpretations, and theoretical approaches, since it gives you the room to
be creative and show off the breadth and depth of your knowledge!
1. “When it comes to questions of public policy, standard microeconomic models restrict our
thinking. They are not imaginative enough.” Agree or disagree?
2. Is there a meaningful difference in microeconomics between ‘good decisions for society’ and
‘decisions that society will find acceptable’ ?
3. Does microeconomics offer any guidance as to what goods or services, if any, should be
produced by government agencies and employees?
4. Does microeconomic theory model people as too antagonistic with each other?
5. “Microeconomics sees money as a means to an end, but to understand the real world you
have to understand that it can be an end in itself.” Discuss.
6. Does the U.S. government influence the prices of things too much, too little, or just about
enough?
7. “Just talking about social welfare functions is too late—microeconomics makes inherent value
judgements at a fundamental level.” Agree or disagree?
8. “The terminology ‘market failure’ presupposes ‘market successes’ that just don’t necessarily
exist.” Discuss.
9. Can microeconomic theory teach us anything about how big or interconnected our society
should be?
10. Does the nature of production and/or cost functions in the tech industry raise any particular
concerns from microeconomic theory, or is it just the same kind of thing as other industries?
11. Is “more, better markets” the right solution to so-called market failure?
12. Are there any deep insights in microeconomic theory, or is it all just an assortment of unrelated thoughts?
13. Does microeconomics really need a model of behavior and choice in order to be useful?
14. “Microeconomic policy tools have not been used strongly enough at all in recent years. We
could be doing so much more.” Discuss.
15. If we think about the regulation of business and industry, does 100A-level microeconomics
give us enough tools and ideas to do this well enough, or is there too much more that we
need to consider?
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Jim Campbell, UC Berkeley
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16. Is standard microeconomics only relevant to a world that has prices, currency, and money,
or are those things just incidental?
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Jim Campbell, UC Berkeley
A
Econ 100A Course Pack, Fall 2022
Math refresher
The Video Handbook’s section A has lots of helpful math primers!
1. Find the derivative of the following functions (where a, b and c are constants):
a) f (x) = a + bx
b) f (x) = a + bxc
c) f (x) = ln(x)
d) f (x) = x3 − 8x2 + 30x − 5
e) f (x) = 10 +
5
x
2. Find the value of x that maximizes the function
f (x) = 100 + x − x2 .
(19)
[Remember to check both first and second order conditions.]
3. Simplify these expressions:
a) y =
x3
x−2
b) y =
xa−1
xb2
1
b−1
xa
x
1 2
4. Consider the following function of two variables:
1
f (x1 , x2 ) = 10x1 − x21 + 20x2 − x22
a) Find
δf
,
δx1
the partial derivative of f with respect to x1 .
b) Find
δf
,
δx2
the partial derivative of f with respect to x2 .
(20)
5. Consider the following function of two variables:
f (x1 , x2 ) = 10xa1 xb2
a) Find
δf
,
δx1
the partial derivative of f with respect to x1 .
b) Find
δf
,
δx2
the partial derivative of f with respect to x2 .
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(21)
Jim Campbell, UC Berkeley
B
Econ 100A Course Pack, Fall 2022
Constrained optimization by Lagrangian method
This will be a demonstration of how to use the Lagrangian method to solve a constrained optimization problem, adapted slightly from the appendix of chapter 5 of your textbook. Our focus is
how to apply the Lagrangian method rather than analyzing how it works; I encourage you to refer
to a calculus text of your choice if you are interested in the mathematics.
Consider the following utility maximization problem:
max U = c ln x1 + d ln x2
(22)
such that p1 x1 + p2 x2 = m
(23)
x1 ,x2
Note that in this problem the prices p1 and p2 and income m are fixed parameters, as are c and d
in the utility function. x1 and x2 are what we’re interested in finding. In doing so, we are finding
the demand function of our consumer with the utility function U for a given income and set of
prices.
To solve this problem, we set up the Lagrangian:
L = c ln x1 + d ln x2 − λ(p1 x1 + p2 x2 − m)
(24)
λ, Lambda, is the Lagrange multiplier.
By Lagrange’s theorem, a solution (x∗1 , x∗2 ) to a generic Lagrangian satisfies the following firstorder conditions:
δL
=0
δx1
δL
=0
δx2
δL
=0
δλ
(25)
(26)
(27)
For our problem, this yields:
δL
c
=
− λp1 = 0
δx1
x1
δL
d
=
− λp2 = 0
δx2
x2
δL
= p 1 x1 + p 2 x2 − m = 0
δλ
(28)
(29)
(30)
We are looking for an x1 , x2 and now λ such that all these equations are satisfied simultaneously.
We have three equations in three unknowns, and we are need to end up with an x1 and x2 just as
a function of the parameters. There are plenty of ways to proceed.
One way, for example, is to solve 29 for λ:
d
− λp2 = 0
x2
⇒λ=
79
d
p 2 x2
(31)
(32)
Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
We can substitute this into 28:
d
c
−
p1 = 0
x1 p 2 x2
c p 2 x2
⇒ x1 =
d p1
(33)
(34)
Then we can use this in 30:
p1
c p 2 x2
+ p 2 x2 − m = 0
d p1
⇒ x∗2 =
d m
c + d p2
(35)
(36)
We’re done for optimal x2 . We can then go back to 34 to find:
x∗1 =
c m
c + d p1
(37)
And we’re done. We have x1 and x2 just as a function of the fixed parameters c, d, m, p1 and p2
that satisfy the Lagrangian first-order conditions. This is the solution to our consumer’s utility
maximization problem.
a) To practice the Lagrangian method, use it to work through a numerical example of the
problem we just solved with general parameters:
max U = ln x1 + 2 ln x2
(38)
such that x1 + 4x2 = 12
(39)
max U = x21 x2
(40)
such that 4x1 + x2 ≤ 120
(41)
x1 ,x2
b) One more for practice:
x1 ,x2
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Jim Campbell, UC Berkeley
C
Econ 100A Course Pack, Fall 2022
What do we do in discussion sections?
In Econ 100A, we meet for three hours per week as a whole class (these are called the ‘lecture’
meetings, although they are not just ‘lectures’ !) and for two hours per week in discussion sections
of 30 students each. In our course, our core goal is to enable you to incorporate new ideas from
economics into your thinking and writing about the world—all of our assessments are geared
towards your ability to use, explain, and discuss the concepts and ideas we learn. Discussion
sections are therefore an absolutely crucial venue for learning.
The small, collaborative scale of discussion section meetings allows you all to work together
to master concepts and techniques and to practice the kinds of skills that enable you to succeed
on assessments. In this appendix section, I will discuss some of the things we do in discussion
sections, so that you can understand the rationale for our approach. The precise blend and balance
of activities remains up to the instructor of your discussion section, but this will serve as a rough
and partial guide. Throughout, we rely on active learning techniques, which are backed by years
of pedagogical research that indicate their irreplaceable value in your learning journey.
C.1
Collaborative work on practice problems
What? Work in small groups on practice problems from the course pack. Walk through the
problem step by step and write notes and explanations. Come together as a class afterwards to
demonstrate your group’s proposed solution and discuss areas of difficulty.
Why? This will let you practice the material from the main class meetings in real time, reinforcing
it in discussion section right after seeing it in class. Working together forces you to explain the
methods and concepts and therefore to identify any gaps in your knowledge and understanding.
Discussing the techniques with a group helps you to remember it better, and means less cramming
before exams since you will have done the work in real time. The majority of the course pack
practice problems are old exam questions, so you’ll get to know the right style for the exams.
C.2
Collaborative work on discussion prompts
What? Work in small groups on discussion prompts from the course pack. Think of different
perspectives on the prompts and on how to explain core technical ideas in simple language. Discuss
a range of possible interesting and creative ways to answer the question. Expand on your ideas and
knowledge to write a collaborative and detailed plan for a one-hour essay based on the prompt your
discuss. Come together as a class afterwards to share different perspectives and to constructively
identify areas of improvement in other groups’ ideas. Swap essay plans with other groups to read
and provide constructive feedback. Think of evidence and sources that might help support your
arguments.
Why? On midterms we prioritize explanations; the final exam is all about producing essay-length
writing that incorporates economic ideas. Being able to find a rich variety of perspectives and to
explain in simple language the core ideas and your own arguments is a crucial skill. Working with
others on this helps you to identify complementary ideas and to find perspectives and ideas that
you may have overlooked. Creating essay plans and critiquing other group’s plans will, by the end
of the semester, give you a rich library of notes to help you during reading week as you prepare to
tackle our essay-based final exam.
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Jim Campbell, UC Berkeley
C.3
Econ 100A Course Pack, Fall 2022
Delivering and discussing presentations on non-required readings
What? Once during the semester, with a small group of fellow students, present on the nonrequired readings from one of the topics in our course. Deliver a presentation that goes beyond
just a simple summary of the readings—what do you want to teach the rest of your discussion
section about them and this topic? What are the big lessons you took from the readings? How do
they connect to the material from the topic? What questions would you like to pose your fellow
discussion section students for them to think about going forward?
Why? This assignment serves a purpose for both the presenters and the audience. For the
presenters: you get to become an ‘expert’ on one topic during the course, learning it in more depth
than you may have time for with the other topics. It also gives you practice being a teacher: what
do you want to convey about the topic and readings? How can you express that in an interesting
and understandable way? For the audience: taking notes on other groups’ presentations gives you
a library of knowledge about a huge range of readings in the course, without necessarily having to
read them all yourself. This library will be invaluable when you are thinking about real examples
and connections to draw on in your final exam essays!
C.4
Policy debates and role-playing
What? Debate public policy questions from the perspective of different stakeholder groups who
may care about the question. Within smaller groups, take on different roles and brainstorm
arguments and counterarguments for your stakeholder’s preferred policy positions. Look for areas
of agreement and consensus with other groups and stakeholders as you come back together as a
whole class. Put yourself in the shoes of policymakers who have to make tough decisions that
balance competing interests.
Why? On a practical level: to prepare you to write rich, persuasive analyses of policy questions
on the final exam and on the midterms. Bigger picture: to practice assimilating what we learn
into questions of importance to society, combining your new economics training with your other
knowledge and experience to move beyond opinion and into looking for informed solutions to
tough questions. Practice writing and discussing difficult ideas at a high level with generosity and
understanding.
C.5
Interactive activities and experiments
What? Participate in games and experiments that help us to understand the nature of economic
decision-making and the kind of laboratory work that economists engage in to better understand
behavior in the economy. Come up with strategies in smaller groups, and meet as a whole class
to discuss what we can learn from these kind of scenarios and on what ideas we can think of to
advance our understanding of economic behavior in the future.
Why? These activities will help you to get a better handle on experimental methods in economics,
a key part of the modern economist’s toolbox. You will feel the kind of tension and tradeoffs that
economists seek to study and understand, and learn core economic ideas at a deeper level by seeing
them in action in simple, controlled settings.
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Jim Campbell, UC Berkeley
D
Econ 100A Course Pack, Fall 2022
Tackling discussion prompts
One important way to really learn the concepts in our course and to prepare for the final exam is to
tackle the discussion prompts in the course pack (and, later, prompts from an old final exam that
I’ll post for practice!). The goal should be to really pick out different arguments for and against
the premise of the (subjective) questions, figure out where there are gaps in your knowledge or
understanding, and identify information or citations that you think could enhance your arguments.
I recommend producing essay plans for examples of some of the old exam prompts based on these
goals, and ideally to work on it with your peers so that you can help each other identify different
arguments, weaknesses in your arguments, gaps in your knowledge, and so on.
The target audience for your essays should be your peers! Imagine someone who is interested
in the question but doesn’t know economics. You have to make your case while clearly explaining
the issues and concepts. That means that a great way to prepare is to write a timed practice essay
from one of your essay plans (or a fresh prompt) and have a peer, friend, or family member read it.
If they find it unclear, you have work to do! To elevate your essays, be creative! What would be
an interesting take on the question? What would be a fun thought experiment, whether realistic
or not? What would the counterfactual look like?
Here are some other questions you could ask yourself when discussing prompts with others or
thinking them through yourself:
1. What economic terms or concepts would I need to clearly explain or define before I’d be able
to make my argument?
2. What are some different arguments on different sides of the question? (Remember questions
don’t just have two sides! We can always view these subjective questions through different
lenses.)
3. What real-world analogies or examples could I use to help my reader to understand the
issues?
4. What pieces of information would I like to seek out to boost my argument? (This could be
citations of research papers, facts and figures, etc.)
5. How can I take my ideas on this topic and organize it into an essay that clearly lays out the
concepts and makes a strong argument?
6. What are the really key issues and tipping points that could lead someone to favor one
argument over another? How does the economics inform those?
7. What would the person reading my essay be thinking while they read it? Am I making it
easy for them to agree with me, or will they be confused or unconvinced?
You should be aiming to go in to the final exam with notes! The essays you write will have to
be fresh (they will be fresh prompts after all) but preparation will help. Are there pieces of evidence
you want to cite if you end up writing about topic X? Do you have good working definitions of
key concepts in plain English? Have you thought about how you’d like to structure your answer?
All of this and more will take your final exam performance to the next level! (One last thought:
this is weird, but the better your notes, the less you will find you need them in the exam! The
information will be right there in your head if you have prepared well!)
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Jim Campbell, UC Berkeley
E
Econ 100A Course Pack, Fall 2022
Sample midterms
In this section are sample midterms that cover the provisional topics that we intend to cover
on each of this semester’s three actual midterms. Most of these questions already appear in the
relevant course pack topics above, but this should give you an idea of the typical format and length
of a midterm. To be crystal clear: questions on the exams are always new and not from the
course pack!
E.1
Example of midterm 1
1. There are two goods in the world, good 1 (x1 ), which has a price of $25 per unit, and good
2 (x2 ), which has a price of $10 per unit. Jim has $100 to spend, and his well-behaved
preferences can be represented by the utility function u = x31 x2 .
a) How many units of good 2 must Jim give up to get an extra unit of good 1? If we were
to sketch this problem, what would that correspond to on the diagram?
b) Find Jim’s optimal choice of consumption bundle.
2. Consider the following two-good world with a non-standard budget set. A person has m = 50
to spend, the price of good 1 (x1 ) is $0 per unit, and the price of good 2 (x2 ) is $10 per unit.
a) Sketch (a portion of) this person’s budget set, and explain what makes it unusual.
b) Suggest a utility function such that the bundle (0, 5) would be the unique optimal choice
for this person from their budget set. On your diagram from a), add a couple of indifference curves for your chosen utility function, labeled with their utility level. Briefly
explain your answer.
3. Consider a labor supply model.
√ The decision maker has utility over leisure L and consumption
goods c given by u = 2L + c. They have 10 available hours and no non-labor income. The
wage rate is w = 20 and the price per unit of consumption is p = 1.
a) Use the tangency method to find the consumer’s optimal choice of L and c. Based on
your calculations, if this person had more available hours, would they have worked more,
less, or the same number of hours?
b) Say that the situation is the same as before except that after 7 hours of work the wage
rate increases from w = 20 to w = 30. Sketch the budget set for this situation on the
usual axes, with axes, intercepts, and slopes all labeled.
4. The following diagram shows the decomposition of the effect of a change in price for a
consumer. The line marked O is the original budget line, N is the new budget line, and H
the hypothetical budget line constructed during the decomposition. The lines marked IC are
indifference curves.
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
a) Which price has changed and in what direction? Which type of decomposition
is this, and how do you know?
b) What is the size of the substitution effect, and what is the size of the income
effect in this case? Explain briefly what
those are. Based on the information in
the diagram: for each good, 1 and 2,
is the good normal, inferior, or can we
not say? Is the good ordinary, Giffen,
or can we not say? Explain.
E.2
Example of midterm 2
1. Two decision makers, Jim and Saeromi, each currently have $50 in initial wealth. They face
1
a choice between two options: (A) gain $X for sure, or (B) lose $50 with
√ probability 2 and
1
gain $350 with probability 2 . Jim has a Bernoulli utility function u = x, where x is ‘final
wealth’. We don’t know Saeromi’s Bernoulli function, but we do know that her coefficient of
absolute risk aversion is always less than zero. Both people’s preferences can be represented
with the expected utility form.
a) For what values of X will Jim choose option A? How does this compare to the expected
cash value of option B, and why?
b) What does it mean that Saeromi’s coefficient of absolute risk aversion is less than zero?
For what values of X do we definitely know that Saeromi will choose option B over
option A? Explain.
2. Consider an exchange economy with two people, A and B, and two goods, x1 and x2 . A’s
preferences can be represented uA = x1,A x2,A and B’s uB = x41,B x2,B , where x1,A is the
amount of good 1 that A has, and so on. Their endowments are ωA = (3, 0) and ωB = (0, 5).
Normalize the price of good 1 to 1, and let the price of good 2 be p.
a) Find each consumer’s demand for each good, as a function of p.
b) Thus find a competitive equilibrium in this economy.
3. A profit-maximizing firm in a perfectly competitive industry has a cost function c(y) =
450 + 10y + 12 y 2 . The firm’s average cost reaches a minimum at y = 30. They currently make
positive profit.
a) Find expressions for the firm’s average cost and marginal cost. Sketch their average and
marginal cost curves, on the usual axes. (The right general shape is enough for average
cost, but make sure the curves are in the correct position relative to each other.)
b) What do we know about the price in this industry at the moment? What will be the
price in this perfectly competitive industry in the long run? Explain your answers, with
reference to any assumptions of the perfectly competitive model that are important
here.
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
4. Consider a standard Robinson Crusoe model with a single output good, coconuts. As a
consumer, Robinson has well-behaved preferences over leisure and coconuts. As a producer,
Robinson uses labor (the opposite of leisure) to produce coconuts, according to a production
function with diminishing returns to labor. Labor has price w and coconuts have price p.
a) Say that right now we are not in equilibrium because w is ‘too high’ relative to p. Sketch
a diagram that illustrates this situation. Why is it not an equilibrium?
b) If the conditions of the first theorem of welfare economics hold, what do we know about a
competitive equilibrium, if one exists? Specifically in this Robinson Crusoe model, how
are the consumer’s preferences and the production technology related at such a point?
E.3
Example of midterm 3
1. The diagram shows marginal cost, average cost, demand curve, and marginal revenue for a
profit-motivated monopolist which must set a single, constant price for its output.
a) At its optimal choice of quantity and
price, would this monopolist make positive, negative, or zero profit? At
the socially efficient quantity and price,
would they make positive, negative, or
zero profit? In both cases, explain how
you know from the diagram.
b) Say that a regulator gets to set the price
and wants to maximize quantity produced without forcing the monopolist
to make negative profit. What point on
the diagram tells us the price that the
regulator would choose? At that point,
is producer surplus positive, negative,
or zero? Explain your answers.
2. La Noisette makes delicious desserts (d) according to a cost function c(d) = 10 + 41 d2 . Jim’s
1 2
Tea, next door, produces tea (t) according to a cost function c(t, d) = 10 + 10
t − d, which is
decreasing in d since the smell of delicious desserts makes Jim more productive. The price of
desserts is $5. The price of tea is $2. Both businesses are profit-motivated. No other party
is impacted by the amount of desserts, other than La Noisette and Jim’s Tea.
a) Find La Noisette’s optimal number of desserts and the socially efficient number of desserts.
b) Find a mutually beneficial Coasian bargain in which La Noisette agrees to produce the
socially efficient quantity of desserts in exchange for a cash payment from Jim’s Tea.
In what range must the cash payment fall?
3. Two competing profit-motivated firms, 1 and 2, will simultaneously choose a quantity of
output (y1 for firm 1, y2 for firm 2). The inverse demand function in their industry is given
by p = 60 − y, where y = y1 + y2 . The cost of production for each firm i is c(yi ) = 12yi .
a) For each firm, derive a reaction function that gives their optimal choice of output as a
function of the other firm’s choice of output.
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
b) Thus find the Nash equilibrium of this game. Explain what that means. Show whether
this is bigger, smaller, or the same as (i) the output that would have been produced
if this industry was a monopoly, and (ii) the output that would have been produced if
this industry had been perfectly competitive. (In both cases, assuming that the cost
function is always c(yi ) = 12yi for any producer.)
c) Sketch the two reaction functions you found in a) on a diagram with y1 on the horizontal
axis and y2 on the vertical axis. Mark the Nash equilibrium on your diagram. Label
the intercepts with their appropriate values. What do those intercept values correspond
to? Why?
4. Jim and Rahul are going to a party after work and each must decide whether to pick up
some beer. However, Rahul likes to work very hard and so will be leaving later than Jim.
Therefore the two will play a sequential move game. First, Jim will decide whether to “buy
beer” or “not”, and then Rahul will observe Jim’s choice and decide whether to “buy beer”
or “not”.
If one of the two buys beer, each drinks a good amount of beer, which gives each a payoff of
5. If neither brings beer, each drinks no beer and gets 0. However, if both buy beer, they
cannot help but drink too much and so get a payoff of −1 (and a hangover). In addition,
buying beer is costly and so subtracts 3 from the payoff of whoever buys beer.
a) Sketch a game tree to represent the extensive form of this game.
b) Find the unique subgame perfect Nash equilibrium. Find a Nash equilibrium that is not
subgame perfect and explain why it isn’t.
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Jim Campbell, UC Berkeley
F
Econ 100A Course Pack, Fall 2022
Past final exam
Choose TWO of the following prompts and write a persuasive essay for each. You have 2hr 15min.
You will be graded on (i) how well you displayed knowledge of relevant economics and (ii) how
well you constructed a well-reasoned and persuasive argument for a point of view. Good luck!
1. There is strong evidence that people sometimes make choices as if they care about what
other people get, not just what they themselves get. Is that consistent or inconsistent with
how we model preferences and choice in microeconomics?
2. It is ever possible to figure out if someone chooses in a way that’s consistent with the utility
maximization model?
3. “If you saw people’s demand functions, the income effect would be much more significant
than the substitution effect.” Do you agree or disagree?
4. Do we choose our job or does our job choose us? Discuss with reference to the labor supply
model or other applications of the consumer choice model to issues of job choice.
5. Thinking either of specific examples or in general, do you think that in 20 years production
functions will look more similar or more different to production functions today?
6. Can we make industries look more like the perfect competition model, or are we stuck with
what we’ve got?
7. Is there reason to be concerned that big firms in tech industries might inherently end up
with excessive market power? How might you be able to tell if that were the case?
8. Does the auctioneer in a general equilibrium model bear any resemblance to any real-world
institutions?
9. “More often than not, using the market mechanism to allocate things leads to good outcomes.” Do you agree or disagree?
10. To what extent do you think different policies to reduce carbon emissions using the tools of
externality correction are fair?
11. “It would be easier to get consensus on what public goods to provide if there was less income
inequality.” Do you agree or disagree?
12. What’s the point of oligopoly theory if different models have such different predictions?
13. “The adverse selection problem is a nice theory, but it’s nothing to worry about in practice.”
Discuss, with reference to specific examples.
G
Tips for the essay exam
In our final exam, you’ll have two hours and ten minutes to choose two prompts and write two
essays in response. The prompts on our final will come from across all areas of the course, so
to prepare you can focus on a few areas that particularly interested you. The prompts span the
whole course to make sure that whatever areas you focused on in your preparation there will be
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
options that you can work with! However, there is not a one-to-one mapping between prompts
and topics—I encourage you to use whatever economic knowledge you think would be relevant
and interesting for a question, not what you think we want to hear, and I encourage you to mix
and match, drawing on whatever aspects of the course you like to creatively tackle your chosen
prompts.
Your essays will be graded according to (i) how well you demonstrated knowledge of the relevant
economics and (ii) how well you constructed a well-reasoned argument in response to the question.
If you like, you are welcome to bring in any facts, diagrams, or numbers that help you to make
your case. Your target audience should be someone who is interested in the question but hasn’t
necessarily taken a course in microeconomics before—think one of your peers or relatives who
hasn’t studied economics but wants to know more.
The essay prompts are subjective and normative: there are no right or wrong answers. Different
people with knowledge of economics may reasonably disagree on these issues, and so your focus
should be on making a strong, persuasive case for a particular point of view, not on trying to find
some hidden truth. I think that an OK essay will make an argument that is based on economics;
a good essay will present different perspectives and adjudicate; a great essay will present different
perspectives and really try to identify the key reasons when and why one perspective would be the
most convincing. For a top grade it is not enough to just mechanically describe some models or
ideas from our course—you must use the economics we learned and the knowledge you gained to
make a convincing and interesting argument.
To study for the final, I recommend picking out a few topics and deeply reviewing and updating
your notes based on any of these: essay plans you created with other students in response to
discussion prompts, lectures, readings and reading presentations you saw in lecture, your own
knowledge or research, or facts and figures. You could practice by attempting essays in response
to course pack prompts (I’d give yourself about 50 minutes to write, to see how the time limit
will feel) and by writing out single page essay plans to help you remember what kind of concepts
and arguments you might be able to incorporate during the final. Of course you have to write the
essay for the final from scratch in real time to properly answer the question being asked, but by
preparing in advance you might be able to prepare ideas to draw on to help you in the moment!
There is no formal upper or lower bound on the word count. Figure out how much you
personally are capable of coherently writing within the time limit and work to that capacity. Essays
that are very short are unlikely to have enough content to really satisfy the two requirements that
I mentioned above. Just to give you some sense, since people always, always ask me about word
counts, I personally used to aim for 800-1000 words per essay as a baseline, since for me personally
that amount is achievable in the time limit. Finally, it is absolutely crucial that you properly
credit sources. If you use words from another source, you must use quotation marks and properly
credit the source material. If you use ideas from another source, even if it’s not directly the same
words, you must credit that source also. An exception: when it comes to uncited material directly
from the lecture notes or video handbook, you can consider that ‘common knowledge’ and use it
freely, as long as you use your own words to express those ideas. For example, if you are giving
a definition of ‘utility function’, you can use either (i) use your own words to express a definition
without having to cite the lecture notes or anything like that, or (ii) quote a definition directly
from a high-quality source with proper attribution. As always, please avoid low-quality sources
like random websites.
Finally: I have been a writing instructor in the past. I’m happy to give advice or suggestions
to take your writing to a higher level! Please try making essay plans or doing practice essays and
have someone else read them (could be me, your peers, your GSI...) to see where the strengths
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Jim Campbell, UC Berkeley
Econ 100A Course Pack, Fall 2022
and weaknesses are. Writing is a crucial but difficult skill but collaboration on the process can
really make your writing better!
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