DEPARTMENT OF ECONOMICS
SAN JOSE STATE UNIVERSITY
MASTER’S COMPREHENSIVE EXAMINATION
DECEMBER 6, 2013
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. The state of Georgia will be voting on a law that would legalize marijuana in the state. The
leader of the Athens, GA, “Organic Free-Range Marijuana Growers Co-Op and Tofuery,” Stiple
Mike, is against the legalization. His group currently supplies the town’s illegal marijuana, and
they are concerned about falling prices. He says:
“If the price of marijuana drops, I think people are going to probably buy less of it.
Therefore, they will spend less money on marijuana. People are going to buy food instead of
buying marijuana with the extra money they have, which happens with casual users.”
For simplicity, assume that consumers only get utility from marijuana consumption and
food, both of which are purchased at market prices with income consumers get from jobs that
have nothing to do with food or marijuana.
Assuming Stiple Mike’s statement is true, answer the following questions:
a. Is the own-price elasticity of uncompensated demand greater than, equal to, or less
than one (in absolute value)? Rigorously show your work.
b. Is the cross-price elasticity of uncompensated demand for food with respect to
marijuana prices positive or negative?
c. Is marijuana a normal or inferior good? Explain in detail why.
d. Is food a normal or inferior good? Explain in detail why.
e. What could explain Stiple Mike’s seemingly counter-intuitive belief that falling prices
would lead to less marijuana consumption?
(over)
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DEPARTMENT OF ECONOMICS
SAN JOSE STATE UNIVERSITY
MASTER’S COMPREHENSIVE EXAMINATION
DECEMBER 6, 2013
6:00 P.M. TO 9:30 P.M.
PROCTOR: J. HUMMEL
1B. Answer the following questions for a consumer with the following utility function:
(1) U(x,y) = x1/2 + y1/2. And this budget constraint: (2) I = pxx + pyy, where “I” is the total amount
of income the consumer has available to spend. In some texts, this same variable is referred to as
“M.”
a. In a sentence or two tell me what is the economic meaning of the term “marginal
utility.”
b. Write down a general formula for the marginal utility of x. The formula should not
depend on the form of the utility function above.
c. What is the mathematical expression for marginal utility of x, for the utility function
in equation (1)?
d. In a sentence or two tell me what is the economic meaning of the term “marginal rate
of substitution.”
e. Write down the general formula for the marginal rate of substitution of x for y using
only marginal utilities. The formula should not depend on the form of the utility function above.
f. Now find the marginal rate of substitution of x for y, given the utility function in
equation (1).
g. In a sentence or two tell me precisely what the result you calculated in part (f) means.
1C. Solve the utility maximization problem, max U(x, y) = xy, subject to budget constraint,
2x + y = 100, using the Lagrange method. 100 represents the income level.
a. Find the optimal quantities demanded of the two goods and the value for the Lagrange
multiplier.
b. Suppose income increases from 100 to 120. What is the approximate increase in the
optimal value of U(x,y)? (You must use the property of the Lagrange multiplier to calculate.)
1D. Consider a monopolist firm that sells a product in two isolated markets. Suppose that the
monopolist faces the demand functions:
P1 = 100 – Q1 (market 1)
P2 = 40 – Q2 (market 2)
The total cost function is C = 10 (Q1 + Q2). Q1 and Q2 are the quantities sold in market 1 and 2
respectively; P1 and P2 are the corresponding prices. How much should be sold in the two
markets to maximize total profit? What are the corresponding prices?
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