Added Instructions for Microeconomics Interfield Candidates
Examiners: Borcherding and Denzau
May 25, 2011
Interfield students do not answer Sections B & C. Instead follow these instructions:
1. For Section A answer [A-I] or [A-2] and THREE questions from [A-3] through
[A-7] for 20 points instead of 10 points.
2. For Section A' answer question [A'-I] and TWO questions from [A'-2] through
[A'4] and question [A'-5] below, for a total of35 points instead of20 points.
[A' -5] Many countries, especially in the developing and emerging worlds, impose rigid
price control on key commodities like rice, cooking oil, gasoline, electricity, water and
such. Why? Answer by analyzing who gains and who loses.
3. Answer the C' interfiled game theory section below for 40 points:
C' Interfield Game Theory: Economics 315 (35 Points)
Answer either [C'-I] or [C'-2]
[C'-I] Consider a market with 2 participants, 1 and 2. They each have a constant
marginal cost, but at levels that may differ, CI and C2; i.e.,
with CI = 18, C2 = 6.
Cost of firm j = Cj qj.
Let total quantity in the market be Q,
Q = ql + q2,
and inverse demand be
P(Q) = 312 - ql - q2.
a)
b)
c)
What is the equilibrium price and quantities?
What are the profits of the firms?
Suppose that they can collude successfully. What would the outcome be?
[C'-2] There are two firms producing similar commodities. Firms set quantities as their
strategic variable. Demand price for each firm is
PI(ql" q2) = 74 - 2ql - q2
P2(ql" q2) = 41 - ql - 2q2
Assume that costs are linear in quantity for both, with no fixed costs, and that marginal
costs are 4 for firm 1, and 1 for firm 2.
What are the equilibrium prices and quantities?
a)
b)
What are the profits?
a)
What happens to equilibrium outputs if the marginal cost for ql falls to 2?
1
Ph.D. Qualification Examination in Microeconomics
Examiners: Borcherding, Denzau and Tasoff
May 25, 2011/100 points/Six Hours
You have one hour to read and outline your thoughts and another five hours to answer the
three sections of the exam. Note that each section allows for choice. Follow instructions,
answering no more than is required. Note also question weights and answer accordingly.
Good luck.
Section A: Economics 313 Questions (20 points)
There is a Section A" based on Economics 318 required of students in the current
program who came in under the 20 I0-11 rules. Students answering Section A" will not
be required to answer Section A' (this examl).
Answer ONE question [A-I] or [A-2]
[A-I] A price-searching firm faces the inverse demand curve, P = A - 5q. The intercept
A, is a random number, 100 or 200, with equal probabilities. The average cost is constant
at 10.
a. The firm sets its price, but does not know what A will be until after its decision is
made. What should that price be if it is risk neutral?
b. Suppose, the firm could find out, in advance, with certainty what A would be?
How much would the firm be willing, to pay for this information?
c. How would your answer change, if you were told the firm is owned by a widow­
lady, with five children and no other source of income? Should she sell her firm?
To whom is she likely to do that?
[A-2] When two goods, X and Y, are similar, but differ in time costs per unit consumed,
e.g. an evening meal, full prices will differ depending on opportunity cost of time used:
a.
Predict the change in the ratio of consumption of X and Y, when X is at­
home consumption and Y is at-restaurant consumption, as wage rises.
b. Is the analysis commensurate with the Alchian-Allen apples example? How?
c. What do you do about the pesky third good, Z, "everything else," which could
have positive or negative cross effects?
d. If high-wage earners dine out relatively more than low-wage earners, how
come they all seem to put in $200,000 (and more!) to home gourmet kitchens?
Would you not predict they'd prefer more modest, utilitarian cooking
facilities?
e. How does your analysis change for affluent retired people vs. those on more
modest pensions?
Answer TWO questions from [A-3] through [A-7] (10 points)
[A-3] This summer you plan to visit friends in Korea. Bringing them seeds for Italian
and Mexican garden herbs would make them happy, but customs laws probihit such
importation. You have a choice between cheap Wal-Mart seeds (=$0.89/packet) and
expensive nursery packaged seeds (=$2.99/packet). Compare your choice behavior of the
two qualities of seeds to a world without a prohibition against seed imports with respect
to the following three states:
(a) The only penalty is confiscation of the seeds;
(b) The penalty is a $100 fine for small quantities (under a kilo), plus their
confiscation;
(c) The penalty is confiscation of the seeds plus 100 times their original value.
[A-4] Gasoline prices are currently very high in California. Over time this leads to
various substitutions. Describe them and various speeds of adoptions.
[A-5] Describe the economic relationship between house prices and house rentals and
how changes in their ratio might or might not signal "froth" or "bubbles" in the housing
market.
[A-6] Optimal tax theory claims that taxes on final goods and services should favor
substitutes for leisure and tax more heavily its complements. This could require
Solomonic-knowledge of cross-effects but suppose such knowledge were available to
you. Offer the tax rate differentials (higher or lower) for the following - beach balls,
cigarettes, prayer books, calculus texts, take-out food at lunch time from M-F - with
(clever) explanations.
[A-7] Joe Schmelk has been operating his cattle feed lot at the edge of town for 25
years. The land around him used to be fanned, but now some of the farmers are selling
out to real estate developers. The quarter-section on the east side of Joe's lot was bought
by a developer who is putting in large single-family homes. Within a couple of years, the
homeowners' association has come to Joe and demanded that he control the odors
coming from his feedlot. They threaten to sue him as a nuisance if he does not control it
adequately.
a. Give an economic analysis of this situation.
b. If the current situation is inefficient, then is government intervention required
to deal with it? Why, or why not?
c. Joe thinks that the homeowners have already been compensated for t6he
presence of his feed lot. Explain why he thinks this.
2
Section A': Political Economy Questions (20 Points)
Answer question [A'-I] and any TWO from [A'-2] through [A'-4]
[A'-l] Back in the early 1980s George Stigler argued that public policy analysis was a
"scientific" but not "welfare enhancing activity," because the analysis of "why" would
not alter "what should be." He reasoned, in what he called "the Chicago credo," that
interest groups were already well informed and scholarly understandings would hardly
change those opinions. Buchanan and Friedman thought this view in error. Why did
Buchanan and Friedman believe policy analysis was, on net, useful? Could Stigler be
right? When and how?
[A'-2] Voting is generally a social act, say Downs and most public choice theorists. If
this is the case, why is voting turnout in Claremont high in presidential elections but low
in these same precincts when only location races are at issue? Are Claremonteros
unsocial about their own government but responsible in their national citizenship duties?
[A'-3] Some hardcore public choice economists hold that political markets are just as
likely to be optimally organized as those for private goods and services. Critically
evaluate this statement.
[A'-4] Ignoring transaction costs, if X is a public good, its equilibrium quantity supplied
must rise as the populations sharing the consumption increases. True, false, or uncertain?
3
Section A": Behavioral Economics (20 points)
Answer either [A"-l] or [A"-2] but not both.
[A"-I]
Xiao has no access to savings or credit. He earns a daily income and fully spends it in the same
day. Xiao is indifferent between $10 today and S15 next week. If asked to choose between
$10 in 37 weeks or $x in 38 weeks, Xiao will reveal that he is indifferent when x = 10.01.
(a) Show mathematically that Xiao cannot be an exponential discounter.
(b) Using the (quasi- )hyperbolic discounting model below to find Xiao's weekly discount
rate IS and degree of present bias
/3.
(c) Suppose Cynthia is a money lender and offers Xiao cash now at an annual interest rate
i, What is the highest annual interest rate i that Xiao will accept assuming that Xiao
will make one payment in exactly one year?
(d) Carlos is another money lender but must do a credit check on Xiao first and so can give
him cash tomorrow at the soonest. What is the highest annual interest rate i that Xiao
will accept assuming that Xiao will make one payment in exactly one year from the time
he receives his cash?
(e) Explain the intuition for your answers in part (c) and (d) in four sentences or less.
4
[A"-2]
Consider the chicken game below where x > O.
C
S
C
S
-x, -x
O,3x
3x,O
x,x
(a) Find the unique Nash equilibrium assuming that both players are purely self-interested.
(b) Now assume that both players have Charness-Rabin preferences.
Specifically player
i E {I, 2} has preferences
if
Xi
2' Xj,
ifxi:::;Xj.
Find the values of the parameters p and a for which (C, C) is a Nash equilibrium.
(c) Now assume that both players have Rabin fairness preferences. Recall that player i
maximizes
where the kindness function is given by
and the perceived kindness function is given by
Find the values of x for which (C, C) is a fairness equilibrium.
(d) Briefly compare and contrast the interpretation of the (C, C) equilibrium under the
distributional preferences and under the fairness preferences.
5
Section B: Economics 316 (30 points)
Answer either [B-1] or [B-2] but not both.
[B-1]
Consider a pure exchange economy, representable by an Edgeworth Box, with endowments
WI
= (6,4),
W2
= (3,3), and utility functions
Ul(Xll,X2t}
= x~{2x~{2, and
U2(X12,X22) =
2/3 1/3
X12 X22 .
(a) Show that consumer l's Walrasian demand is homogeneous of degree zero in the price.
(b) Find all the competitive equilibria of this economy.
(c) Find the set of Pareto optimal allocations of this economy.
(d) Find prices and transfers that make the allocation
equilibrium with transfers.
Xl
= (3,3.5), X2 = (6,3.5) a price
[B-2] Suppose a consumer's direct utility function is
U = XI I/2 X2 112.
a.
Derive the expenditure function, and the indirect utility function.
Let P2 = 64, and income $160. Suppose that PI rises from $1 to $16.
b.
What is the initial utility level? The final utility level after the price
change?
c.
Suppose the consumer demands compensation for the price increase. How
much is the compensation if
1.)
the consumer gets compensated for the price increase at their
original consumption levels?
2.)
the consumer is not to be harmed by the price increase?
d.
What is the least costly policy to restore the consumer to their original
level of satisfaction:
Policy A ­
a price subsidy for good 1 of $15;
Policy B ­
an income supplement; or
Policy C ­
an in-kind free-to-the-consumer provision of units of good
1, sufficient to enable the person to buy what they would have bought at the old
price?
6
Section C: Economics 317 (30 points)
Answer either [C-l] or [C-2] but not both.
(C-ll
Consider the game below.
L
1,2
U
M
5,0
D
-1,6
R
2, -1
i.a
1, 1
(a) Find all the Nash equilibria.
(b) Suppose this game is repeated an infinite number of times and players discount stage
payoffs using the discount factor J. Find the smallest delta for which it call be a suhgame
perfect equilibrium for the players to alternate between (.!\-f, L) and (D, L).
(c) Draw the set of fl'llsible average payoffs ill
71'1-71'2
space. Shade in the region that can be
supported as a subgame perfect equilibrium.
(d) Construct a Pareto optimal subgarne perfect equilibrium in which both players earn the
same aueraqe payoffs (note that the question is not askinq for equal net-present utility).
(C-21
A chef goes to the farmer's market to buy some lemons for
i\
lemon liqueur she is making.
She wants very juicy lemons. The juiciness of a lemon j is uniformly distributer!
011
[0,1/.
Both the chef and t he farmer have utility that is quasilincar in money, The value of a lemon
to the chef in dollars is aj2 where a > O. The value of a lemon to the fanner in dollars is J.
(a) What is the Pareto optimal allocation for
1\
lemon as a function of j.
(b) Suppose j is unobservable to the chef. She makes a take-it-or-leave-it otfl~r to buy it at
price p. Solve for E{aj'2/p ~ j/
iL'i
a function of p.
(c) What is the Bayesian :'lnsh equilhriurn of this game'? flint: think mre/1111.1I.
(d) Graph E[<lJ'z/p ~ j}
iL'l ;\
function of p. Where does it intersect with the 1,5-dl~l{rt'e line'!
Is this the "qllilibrilllll? Explain ill t hrr:e sPlltPllel'S or less.
2