AMERICAN UNIVERSITY
Department of Economics
Comprehensive Exam
Preliminary Theory
January 2014
Total Exam Pages: 3
COMPREHENSIVE EXAM IN PRELIMINARY THEORY
Directions: Complete all questions in Parts I - III. Read the questions carefully. Please
show all of your work, and make sure to explain and discuss if the question indicates.
Your grade depends on the quality of your explanations. Answers should be expressed in
your own words. Also, no electronic aids are permitted.
Part I: Basic Concepts
Define and discuss the significance of each of these terms. Keep your discussions
concise. Limit your discussion of each term to no more than two paragraphs (or a
maximum of 125 words).
Moral Hazard
Say’s Law
Compensating Variation
Liquidity Trap
Part II: Microeconomics
Answer both questions in this part.
1. Suppose there are two persons, A and B, and two goods, X and Y. Person A has 90
units of good X and 35 units of good Y. Person B has 30 units of good X and 25 units of
good Y. Thus, the total supply of good X is 120 and the total supply of good Y is 60.
However, this existing allocation of goods between the two persons may not be their
utility-maximizing bundles. Suppose the utility function for person A is uA = XAYA and
for person B is uB = XBYB. Let pX be the price of good X and let the price of good Y be
normalized to 1.
a. Write down the budget constraint for person A and that for person B.
b. Maximize person A’s utility subject to her budget constraint, and do the same for
person B.
c. Derive everyone’s demand for good X and for good Y.
d. Given the fixed supplies of good X and good Y, find the market clearing price.
e. Explain why, in part d, we need only find the market clearing price for one of the two
goods.
2. Consider a competitive industry with a large number of potential entrants. Every firm
has an identical cost structure: the LRAC (long run average cost) curve of a typical firm
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is U-shaped and reaches a minimum at an output level of 20. The minimum average cost
is $10 per unit.
a. Draw the LRAC and MC (marginal cost) curve for a firm in long run equilibrium,
given the information above. Label your graph carefully and indicate the minimum
average cost and output point. What price per unit is compatible with long run
equilibrium? How much does each firm produce? What are the firm’s long run profits?
b. Suppose that Market Demand is Q = 1500 - 50 P. How much output is sold in long run
equilibrium? How many firms are there in long run equilibrium?
c. Suppose that the short run cost function is given by C*(q) = 0.5 q2 - 10 q + 200, where
q denotes the firm’s output. Derive the short run average cost and marginal cost curves.
At what level of output does short run average cost reach a minimum?
d. Using the number of firms found in part b, derive the industry short run supply
function.
e. Draw the industry supply and market demand curves and point out the long run
equilibrium price and industry quantity.
f. Now suppose that Market Demand permanently increases to QD =2000 - 50 P. Holding
the industry supply curve constant (or more specifically, holding the number of firms
constant), what is the new equilibrium price and industry quantity? How much does each
firm produce and what are its profits?
g. What happens in the long run? Is there entry or exit?
h. Assume the industry is one of constant cost; that is, it has neither external economies
nor diseconomies of scale. Find the new long run equilibrium price, industry quantity,
and quantity produced per firm. How many firms are there in the new long run
equilibrium?
i. Draw the new market demand and new industry supply curves on your diagram from
part e, and show the new equilibrium points, and trace the long run expansion path.
Part III: Macroeconomics
Answer both questions in this part.
3. In the following Diamond Overlapping Generations (OLG) model, each person lives
for two periods. Thus, in each period, two generations live side-by-side: the young and
the old. Only the young work; the old are retired. Let
(1) Yt = Ct + It
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be the aggregate GDP identity, where Y is output, C consumption, and I investment.
Aggregate consumption is given by:
(2) Ct = Lt c1t + Lt-1 c2t
where Lt is the number of young people, Lt-1 the number of old people, c1 consumption
per young person, c2 consumption per old person. The population growth rate is n= (Lt –
Lt-1)/Lt-1. Investment is given by the change in capital stock (assuming no depreciation):
(3) It = Kt+1 - Kt
a. Derive the steady-state GDP identity in per worker units; that is, in terms of the young
population. (In other words, divide through equation (1) by Lt and, using the rest of the
information given, find the steady-state.)
b. The steady state lifetime utility function of the typical person is:
(4) V = u(c1) +  u(c2)
where  is the time discount factor. The social planner would maximize (4) subject to the
steady-state per capita GDP identity that you derived in part a. Assume output per
worker is y = f(k), where k is the capital per worker. Derive and discuss the necessary
conditions for welfare maximization.
4. Consider the following Solow model:
k = sy - (n + g + δ)k
where s is the savings rate, n the growth rate of labor,  the depreciation rate, and g the
growth rate of technical efficiency. Assume n =  = 0 and g = 0.05. Let y = k . Output
y, capital k, investment i, and consumption c are all in per worker efficiency units.
a. Find the steady-state values of y, k, i, and c if s = 0.3.
b. Find the steady-state values of y, k, i, and c if s = 0.8. Does a higher savings rate
result in greater steady-state consumption?
c. Define the golden rule of capital accumulation, and find the golden rule level of
capital per efficiency worker in this example. Call this kGR.
d. What rate of savings, s, will assure that kGR will be achieved. Find the steady-state
values of y and c associated with this golden rule level of capital per efficiency worker.
e. Why does this model predict cross-country convergence in the long run (i.e., poorer
economies catching up to the richer countries in per-capita output levels)? Specify the
assumptions required and the roles they play in this prediction.