McPeak                                                           Name:____________________________

PAI 723                                                          April 6, 2005

Quiz 2

 

All numbered questions are worth 2 points each, sub questions worth an equal share of these 2 points.

 

1) Production functions.  You are given the following production function:      

a. Define the marginal product of labor for this production function.  You can use words or refer to the given production function to define a formula.

 

 

 

 

 

b. Define the average product of labor for this production function. You can use words or refer to the given production function to define a formula.

 

 

 

 

 

 

 

c. Draw this production function and illustrate for a given input level of labor:

Point 1 representing an output level that is not technologically efficient given that input level;

Point 2 representing an output level that is technologically efficient given that input level;

Point 3 representing an output level that is not technologically feasible given that input level. 


2)   You know that the inverse demand curve is defined by the following function:  P=68-2Q and total cost is defined by 4*Q, so that you also know MC= 4 for all possible levels of Q. 

a.       Use the bisection rule to define the marginal revenue curve

 

 

 

 

 

 

b.      At what level of Q should the monopolist produce?

 

 

 

 

 

 

 

 

 

 

 

c.       What is the implied price?

 

 

 


3) Continue with the information in the previous question, so you are still working with the information that P=68-2Q and MC =4.

a.       If this were to become a perfectly competitive market for some reason, what would the market price and quantity in the market be if all firms had identical cost structures to the monopoly firm and the demand curve was unchanged?

 

 

 

 

 

 

 

b.      Show the competitive case in comparison to the monopoly case on a single graph.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c.       Calculate the value of the following areas under the competitive and the monopoly structure.

 

Competitive Market Structure

Monopoly Market Structure

Consumer Surplus

 

 

 

 

 

Producer Surplus

 

 

 

 

 

Total Social Welfare

 

 

 

 

 

 


4)  Isoquant and Isocost lines.

      a. Derive the expansion path graphically, using isoquant and isocost curves.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b.      Illustrate how a total cost curve can be derived from your graph in (a). 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c.       Is being on the expansion path a necessary condition or a sufficient condition to characterize the point as:

CHARACTERIZE AS

 

Profit Maximizing

Necessary    Sufficient 

Cost Minimizing bundle to produce target output level.

Necessary    Sufficient 

Technologically Efficient

Necessary    Sufficient 

Highest output level possible at given cost

Necessary    Sufficient 

Economically Efficient

Necessary    Sufficient 

 


5) Assume the rental rate of capital is 12 and the wage rate is 8. 

a.       Draw an isocost curve for a total cost level of 120.

 

 

 

 

 

 

 

 

 

b.      If the marginal product of labor is 4, what is the marginal product of capital at an economically efficient point?  Why?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c.       What is the technical name for the slope of an isoquant?


6) Perfectly competitive markets.

a. Note two out of the four main assumptions made by economists that underlie the perfectly competitive market model.

 

 

 

 

 

 

 

 

 

 

 

 

b. Illustrate why a perfectly competitive market maximizes social welfare.  Use the example a policy that limits the quantity of a good sold in the market to a level below the perfectly competitive market equilibrium quantity (the q too low example).    Note specifically the area of deadweight loss.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c. Using your graph in b, explain why it is difficult for cartels to maintain q at the “q too low” level because of the incentives each member faces at the low q. 

 

 


7) Complete the following table.

a) Quantity of Output

Total Cost

Average Cost

Marginal Cost

0

0

------------

---------

1

40

 

40

2

70

 

 

3

 

 

25

4

 

 

20

5

 

 

18

6

 

 

20

7

183

 

 

8

218

 

 

 

b. If the market price for the output produced is 20 and the market structure is perfectly competitive, what level of output is the profit maximizing level of output?  Why?

 

 

 

 

 

 

 

 

 

 

 

 


8) You are given the following information on the relationship between inputs and production level at various points.

Points

Labor

Capital

Output

A

1

2

1

B

2

4

4

C

4

8

8

D

8

16

16

E

16

32

24

 

a.  Illustrate these points using isoquants.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b. Contrast the returns to scale implied by movement between the points. (circle the correct answer)

From a to b I have (increasing, constant, decreasing) returns to scale.

From b to c I have (increasing, constant, decreasing) returns to scale.

From c to d I have (increasing, constant, decreasing) returns to scale.

From d to e I have (increasing, constant, decreasing) returns to scale.

 


9)  True or False.

Statement

True or False (circle)

In a two firm Cournot oligopoly, the combined quantity supplied by the two firms (q1 + q2) is equal to the quantity that would be supplied if either firm became a monopolist.

True               False

A monopoly firm chooses q* such that p=MC(q*)

 

 

True               False

If a monopoly is a natural monopoly, consumer surplus may be reduced by introducing a price ceiling.

 

True               False

A Cournot model of oligopoly behavior is based on each firm developing a best response strategy for the quantity they will supply to the market as a function of the other firm’s quantity supplied.

True               False

A monopsony is defined as a single firm being allowed to sell Sony products in a given country.

 

True               False

Granting patents is a way to authorize firms to operate as monopolists for a fixed period of time.

 

True               False

 


10) Costs.

a. If Variable Cost(q)= Cost(q), what is the value of Fixed Cost (q)?

 

 

 

 

 

 

 

 

 

b. Can Average Fixed Cost (q) be greater than Average Variable Cost (q) at some levels of q?  Explain briefly.

 

 

 

 

 

 

 

 

 

c.  If Average Cost increases when moving from output level q1 to output level q2, is the Marginal Cost of moving from q1 to q2 greater than, equal to, or less than Average Cost at q1? Explain briefly.