Problem Set #7 Name:________________

PPA 723

Professor John McPeak

1) Necessary and sufficient conditions. Circle the correct answer.

Condition A	Condition B	What type of condition is B for Establishing A?
A firm is producing at a profit maximizing level	A firm is producing in a technologically efficient way.	N,NS S,NN N,S
Marginal Cost is below Average Cost at quantity q	Average cost is downward sloping at quantity q.	N,NS S,NN N,S
The market is a perfectly competitive market	Price taking behavior by producers	N,NS S,NN N,S
There is no close substitute for the good produced by a firm	The firm is a monopoly.	N,NS S,NN N,S
MR (q*) = MC (q*)	The profit maximizing level of production is q*	N,NS S,NN N,S
A firm is producing at a profit maximizing level	A firm is producing in a economically efficient way.	N,NS S,NN N,S

N, NS : Necessary, not sufficient [If A, then B]

S, NN: Sufficient, not necessary [ A if B / If B, then A]

S, N: Necessary and sufficient [A if and only if B]

2) You know that the demand curve is defined by the following function: P=14-Q.

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

b. If total cost is defined by 2*Q, then you know MC is 2 for all possible levels of Q (why?). Is average cost different from marginal cost in this setting? Why or why not?

c. What level should the monopolist produce at if at all and why?

d. What is the implied selling price?

e. What is the implied profit?

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

g. Show the competitive case in comparison to the monopoly case on a single graph. Show consumer surplus and producer surplus on this graph.

3) You know that the inverse demand curve is defined by the following function: P=45-Q and costs are defined by 5*Q (so you know MC is 5 for all possible levels of Q). (2 points)

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

b. Draw the marginal revenue curve, the demand curve, and the marginal cost curve on a single graph.

c. What level of Q should the monopolist produce at?

d. What is the implied price?

e. What is the implied profit?

4) Continue with the information in the previous question, so you are still working with the information that P=45-Q, and MC =5.

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
Dead Weight Loss
Total Social Welfare

5) 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. Are all points on the expansion path described by each of the following terms? (circle yes if all points can be described by the term or no if all points can not be described by the term)

Technologically Efficient	Yes No
Welfare Maximizing	Yes No
Profit Maximizing	Yes No
Economically Efficient	Yes No

6) Circle the correct answer.

Statement	The statement is (circle the correct answer)
A natural monopoly has a downward sloping average cost curve over the entire range of feasible production levels	True False
In the long run, labor is the only variable that is not allowed to be variable.	True False
A monopoly firm is a price taker.	True False
It is possible to be on an isoquant while producing in a manner that is not technologically efficient.	True False
The slope of the isocost line is the negative ratio of the input prices.	True False
The bisection rule allows us to derive the marginal revenue curve from a linear demand curve.	True False