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DEPARTMENT OF ECONOMICS

SAN JOSE STATE UNIVERSITY

MASTER’S COMPREHENSIVE EXAMINATION

**INSTRUCTIONS: **

DECEMBER 5, 2014

6:00 P.M. TO 9:30 P.M.

PROCTOR: J. HUMMEL

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*

(

*x*

1,

*x*

2

) = 2

*x*

1

*x*

2

+ 3

*x*

1 where

*x*

1

and

*x*

2 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

* x*

1 and

* x*

2

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)

-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

**1B**

. Assume that for a consumer that their ordinary demand functions are:

*x*

*

(

*p x*

,

*p y*

,

*m*

) =

*m*

3

*p x y*

*

(

*p x*

,

*p y*

,

*m*

) =

2

*m*

3

*p y*

**a.**

Initially prices are

*p x*

* = 1*

,

*p y*

* = 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

*p x*

* = 1, p y*

* = 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*

?

**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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