Download Sample Exam, December 2016, Section 1

DEPARTMENT OF ECONOMICS
SAN JOSE STATE UNIVERSITY
MASTER’S COMPREHENSIVE EXAMINATION
DECEMBER 2, 2016
6:00 P.M. TO 9:30 P.M.
PROCTOR: HUMMEL & LIU
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. Answer the following questions for a consumer with utility function U(x,y) = x1/3 y2/3 and a
budget constraint I = pxx + pyy, where “I” is the total amount of income the consumer has
available to spend, px is the price of x and py is the price of y.
a. What is the marginal utility of x? of y?
b. Define the economic meaning of the term “marginal utility.”
c. What is the marginal rate of substitution for the given utility function?
d. Define the economic meaning of the term “marginal rate of substitution.”
e. Using the Lagrange method, find the demand curves for x and y. Use lambda λ as the
Lagrange multiplier.
f. Define the economic meaning of the Lagrange multiplier as used in this problem.
(over)
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DEPARTMENT OF ECONOMICS
SAN JOSE STATE UNIVERSITY
MASTER’S COMPREHENSIVE EXAMINATION
DECEMBER 2, 2016
6:00 P.M. TO 9:30 P.M.
PROCTOR: HUMMEL & LIU
1B. Consider a firm that sells a product in two isolated markets. Suppose that such a firm also
has some monopoly power to influence the different prices it faces in the two markets by
adjusting the quantity it sells in each. Economists generally use the term “discriminating
monopolist” to describe a firm having this power. Suppose that the discriminating monopolist
faces two independent demand functions:
P1 = a1 –b1 Q1
P2 = a2 – b2Q2
for market areas 1 and 2, respectively. Suppose, too, that the cost function is C = c(Q1+Q2) and
all constants are positive.
a. How much should be sold in two markets to maximize total profit? What are the
corresponding prices?
b. What is the monopolist’s pricing strategy if it becomes illegal to discriminate?
c. Discuss the consequences of imposing a tax of 5 dollars per unit on the product sold in
market 1.
d. Discuss the effects of a tax imposed in market 2 of t dollars per unit of Q2.
1C. Once upon a time, in an ancient land perhaps not too far from US, an economy consisted of
three industries- fishing, forestry, and boat building. To produce 1 ton of fish requires the service
of  fishing boats. To produce 1 ton of timber requires  tons of fish, as extra food for the
energetic foresters. To produce 1 fishing boat requires  tons of timber. These are the only inputs
needed for each of these three industries. Suppose there is no external demand for fishing boats.
a. Find what gross output each of the three industries must produce in order to meet the
external demands of d1 tons of fish to feed the general population, plus d2 tons of timber to build
houses.
b. Based on the solutions from part (a), what are the sign restrictions should be imposed
on , and .
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