301_mid2s09.pdf

Midterm Exam 2

ECO 301 – Summer 2009

Instructor: Dr. Michael Malcolm

Instructions: You can use any written materials you would like and a calculator in

completing this exam.

Statement of academic honesty:

This exam entirely reflects my own work. I have not received assistance from

anyone or given assistance to anyone in completing this exam.

Signature: _________________________________

Name:

_____________________________________

The marginal product of capital for a firm is equal to 100, while the marginal product of labor is equal to 40. The price of capital is $5 per unit, while the price of labor is $2 per unit.

a. Demonstrate that this firm is minimizing costs.

Gale starts with total wealth of $200,000 and a utility function of U W

( )

= W . She has a

chance to bet $50,000 of her wealth that President Obama will be reelected. It is an “even bet”, meaning that she gains $50,000 if Obama is reelected and loses $50,000 if Obama is not reelected.

An individual lives for two years. Each year, he has 2000 hours to allocate to labor or leisure. Designate his leisure hours in the first year as N₁ and his leisure hours in the second year as N₂.

He earns a wage of w₁ for each hour of labor supplied during the first year and w₂ for each hour

of labor supplied during the second year. Designate his consumption in year 1 as C₁ and his

consumption in year 2 as C₂. He can borrow or save, and the relevant interest rate is r.

a. Write down the present value budget constraint that relates N₁ and N₂ to C₁ and C₂.

b. Write down the future value version of the budget constraint you derived in (a).

Consider a pure exchange economy. The consumers are Anna (A) and Bob (B); the two goods traded are fish F and cheese C. There is 1 unit of fish and 1 unit of cheese available. Anna’s utility function is UA =F C2 and Bob’s utility function is UB =FC2. Throughout this problem

(

FA,CA

)

denotes Anna’s allocation of fish and cheese, and

(

FB,CB

)

denotes Bob’s allocation of fish and cheese.

a. Consider the allocation

(

FA,CA

)

=

(

0.5, 0.5

)

and

(

FB,CB

)

=

(

0.5, 0.5

)

. Is this allocation

Pareto efficient? Explain your answer.

b. Consider the allocation

(

FA,CA

)

=

( )

1, 0 and

(

FB,CB

)

=

( )

0,1 . Is this allocation Pareto

efficient? Explain your answer.

c. Consider the allocation

(

FA,CA

)

=

( )

1,1 and

(

FB,CB

)

=

( )

0, 0 . Is this allocation Pareto

A single-price monopoly manufactures hats, and its cost of producing q hats is given by the cost

function

( )

1 2 4

C q = q . The demand curve that the firm faces is P=90 2− q.

a. Find the profit-maximizing price and quantity.

can obtain hats from a supplier for $12. Suppose that the firm’s demand function rises to 162 2

Consider a firm whose production function is q= L+K. The price of a unit of labor is fixed at

1

w= and the price of a unit of capital is fixed at r=8.

a. Suppose that the level of capital is fixed at K =10 in the short-run. Find the short-run cost function. Your answer should depend only on q.

b. Find the marginal cost function.

d. Find the long-run cost function. Again, your answer should depend only on q.

e. Find the long-run average cost function.

of its input usage (over the long run).

Extra Credit (+ 3 points max)

Suppose that this firm operated in a competitive market and could sell each unit of output for 10

p= . How much output would it produce to maximize profit over a short-run time horizon

when capital is fixed at K =10?

Extra Credit (+ 3 points max)

Suppose that this firm operated in a competitive market and could sell each unit of output for 10