Download Sample Exam, December 2014, Section 1

DEPARTMENT OF ECONOMICS
SAN JOSE STATE UNIVERSITY
MASTER’S COMPREHENSIVE EXAMINATION
DECEMBER 5, 2014
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. A consumer’s utility function is given by
U(x1, x2) = 2x1 x2 + 3x1
where x1 and x2 denote the number of items of two goods G1 and G2 that are bought. Each item
costs $1 for G1 and $2 for G2.
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 above utility
function?
d. In a sentence or two tell me what is the economic meaning of the term “marginal rate
of substitution.”
e. Write down a general formula for the marginal rate of substitution between x and y.
The formula should not depend on the form of the utility function above.
f. Use Lagrange multipliers to find x1 and x2 that maximize the value of U if the
consumer’s income is $83.
g. Estimate the change in optimal utility if the consumer’s income rises by $1.
(over)
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DEPARTMENT OF ECONOMICS
SAN JOSE STATE UNIVERSITY
MASTER’S COMPREHENSIVE EXAMINATION
DECEMBER 5, 2014
6:00 P.M. TO 9:30 P.M.
PROCTOR: J. HUMMEL
1B. Assume that for a consumer that their ordinary demand functions are:
m
x* (px, py, m) =
3px
2m
3p y
 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 a own-price change.
d. In a sentence, tell me in general, what is the income effect of a own-price change.
e. Mathematically, decompose the total change in the quantity of y, owing to the price
change of y (from 2 to 5), into the substitution effect and the income effect?
y* (px, py, m) =
1C. Tom spends all of his income on two goods: beer (B) and pizza slices (P). He also likes to
consume them in fixed proportions (2 pizza slices per bottle of beer).
a. Write down Tom’s utility function for beer and pizza.
b. Suppose, for a moment Tom was consuming a bundle of 2 beers and 2 slices of pizza.
Does this bundle maximize Tom’s utility? Carefully explain why or why not.
c. Draw a graph with beer on the horizontal axis, and pizza on the vertical axis.
-Draw and label the 2 beers, 2 slices bundle from part (b).
-Draw one of Tom’s indifference curves through that bundle.
-Label the indifference curve with the level of utility it represents.
d. Suppose beer costs $6/bottle and pizza slices are $2.00 each at Grande Pizza. Tom
spends $60 per week on these two goods.
-Write down the formula for Tom’s budget constraint.
- On the same graph as above draw Tom’s budget constraint.
e. Given the budget constraint in part (d) what would be the optimal bundle of beer and
pizza for Tom?
- Draw and label that bundle on your existing graph.
- Draw the indifference curve that goes through that bundle.
- Label the indifference curve with the level of utility it represents.
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