DEPARTMENT OF ECONOMICS
SAN JOSE STATE UNIVERSITY
MASTER’S COMPREHENSIVE EXAMINATION
MAY 1, 2015
6:00 P.M. TO 9:30 P.M.
PROCTOR: R. RAGAN
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. Tom spends all of his income on two goods: beer (B) and pizza slices (P). He considers beer
and pizza to be substitutes for one another. Two pizza slices give him the same utility as one
bottle of beer. Beer costs $6/bottle and pizza slices are $2.00 each at Flames Eatery. Tom spends
$60 per week on these two goods.
a. Write down a utility function for beer and pizza that represent Tom’s preferences.
b. What is the mathematical expression for Tom’s budget constraint.
c. If Tom was consuming a bundle of 2 beers and 2 slices of pizza, would that bundle
maximize Tom’s utility? Carefully explain why or why not.
d. Draw a two-dimensional graph with beer on the horizontal axis, and pizza on the
vertical axis. (Suggestion: Use a whole page so your graph is big, clear and readable. You will
add more to it in part (f) later.)
-Draw and label the 2 beers, 2 slices bundle from part (c).
-Draw and label the indifference curve through (2,2) with the level of utility it represents.
-Draw and label Tom’s budget constraint on the graph.
e. Given Tom’s budget constraint, mathematically determine the optimal bundle of beer
and pizza for Tom?
f. On the graph from part (d)
- Draw and label the bundle from part (e) on your existing graph.
- Draw the indifference curve that goes through that bundle.
- Label the indifference curve with the level of utility it represents.
(over)
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DEPARTMENT OF ECONOMICS
SAN JOSE STATE UNIVERSITY
MASTER’S COMPREHENSIVE EXAMINATION
MAY 1, 2015
6:00 P.M. TO 9:30 P.M.
PROCTOR: R.RAGAN
1B. Assume that a consumer has the following ordinary demand functions:
2m
x* (px, py, m) =
2 px + 3py
3m
2px  3py
a. Initially prices are px = 1, py = 2 and income is m = 3000. Calculate the optimal
amount of x and y for this consumer.
b. The price of y changes, and now prices are px = 1, py = 5. Income is still m = 3000.
Calculate
 the optimal amount of x and y for this consumer.
c. In a sentence, tell me in general, what is the substitution effect of an own-price change.
d. In a sentence, tell me in general, what is the income effect of an own-price change.
e. Mathematically, determine the total change in the quantity of y, owing to the price
change of y from $2 to $5.
f. Mathematically, determine the size of the income effect, owing to the price change of y
from $2 to $5.
g. Mathematically, determine the size of the substitution effect, owing to the price change
of y from $2 to $5.
y* (px, py, m) =
1C. A firm produces and sells a product in two separate markets. When the price in market 1 is
P1 per ton, and the price in market 2 is P2 per ton, the demand in tons per week in the two
markets are, respectively,
Q1 = a – bP1
Q2 = c – dP1
The cost function is C(Q1,Q2) = e + f(Q1 + Q2), and a, b, c, d, e and f are positive constants.
a. Find the firm’s profit as a function of prices P1 and P2.
b. In the case a = 100, b = d = 1, c = 40, e = 10 and f = 0, find the pair of prices that
maximize total profit.
c. In the case a = 100, b = d = 1, c = 40, e = 10 and f = 0, suppose a tax of t per unit is
imposed in market 1, find the pair of prices that maximize profit.
d. In the case a = 100, b = d = 1, c = 40, e = 10 and f = 0, and a tax of $2 per unit (t = 2)
is imposed in market 1, find the pair of prices that maximize profit.
e. In (d) how much tax revenue is generated?
f. Based on (d), what is the loss in profit when a tax of $2 is imposed in market 1
compared to (b)?
g. Suppose it becomes unlawful to discriminate by price, so that the firm must charge the
same price in the two markets. In the case a = 100, b = d = 2, c = 40, e = 10 and f = 1, find the
price that maximizes the firm’s profit when it becomes unlawful to discriminate by price.
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