DEPARTMENT OF ECONOMICS
SAN JOSE STATE UNIVERSITY
MASTER’S COMPREHENSIVE EXAMINATION
DECEMBER 7, 2012
6:00 P.M. TO 9:30 P.M.
PROCTOR: J. HUMMEL
INSTRUCTIONS:
1.
Answer ONLY the specified number of questions from the options provided in each
section. Do not answer more than the required number of questions. Each section takes
one hour.
2.
Your answers must be on the paper provided. No more than one answer per page. Do not
answer two questions on the same sheet of paper.
3.
If you use more than one sheet of paper for a question, write “Page 1 of 2” and “Page 2 of
2.”
4.
Write ONLY on one side of each sheet. Use only pen. Answers in pencil will be
disqualified.
5.
Write ------ END ----- at the end of each answer.
6.
Write your exam identification number in the upper right-hand corner of each sheet of
paper.
7.
Write the question number in the upper right-hand corner of each sheet of paper.
Section 1: Microeconomic Theory—Answer Any Two Questions.
1A. Lydia spends all of her income on two goods: beer (B) and pizza slices (P). She also likes to
consume them in fixed proportions (3 pizza slices per bottle of beer). Suppose beer costs
$6/bottle and pizza slices are $2.00 each at Tom’s Tavern. Tom also offers a daily special for one
free beer for every 2 beers you buy.
a. Draw the budget constraint if she spends $60 per week on these two goods. (Draw beer
on the horizontal axis.)
b. Determine the combinations of beer and pizza slices that maximize utility.
c. How would your answer change if there were no free beer special? Determine the
substitution and income effects of this price change.
1B. The market demand for a pair of duopolists is given as P = 72 - Q, where Q = Q1 + Q2. Total
costs for each firm’s output are specified as TC1 = 12Q1 and TC2 = 18Q2. Determine the
equilibrium price, each firm's output and profit distribution for the following models:
a. Shared Monopoly (be sure to explain the sharing distribution).
b. Cournot Duopolists (each rival assumes output is fixed).
c. Stackelberg Duopolists (assume firm one is the leader).
d. Bertrand Duopolists (competitive case, be sure to explain the price in terms of the
different marginal costs).
(over)
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DEPARTMENT OF ECONOMICS
SAN JOSE STATE UNIVERSITY
MASTER’S COMPREHENSIVE EXAMINATION
DECEMBER 7, 2012
6:00 P.M. TO 9:30 P.M.
PROCTOR: J. HUMMEL
1C. Given a production function Q = f (K, L) = K0.5L0.5:
a. Derive the marginal product of capital and the marginal product of labor.
b. Derive the second order partial derivatives fKK, fLL, and use their signs to explain
whether the Law of Diminishing Returns prevails in the use of capital and labor.
c. Derive the second order partial derivative fKL and use its sign to explain how capital
and labor are related (substitutes or complementary to each other).
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