Question

Consider a monopoly firm facing a demand curve Q = 100 – P. This firm has fixed costs =$1000 and constant marginal cost =$20. Total costs are $1000 + $20Q and average costs are $1000/Q + $20.

a. What is the firm’s profit maximizing level of output? What price does it charge to sell this amount of output? How much profit does it make? What is consumer surplus at this level of output? Show your work.(8)

b. Suppose this firm was regulated by the government, and that the regulation required that the firm charge a price equal to marginal cost. Calculate the number of units demanded and profit at this level of output. Is this policy sustainable? Why or why not?(7)

c. As an alternative, consider a regulation that is meant to allow the firm to earn a “reasonable rate of return” for operating. After analyzing the firm’s costs, the regulator allows the firm to charge $36 per unit produced. Calculate quantity demanded and profit under this policy. Is this a sustainable price? Why or why not?(7)

Answer 1

a)

Q = 100 - P  

P = 100 - Q  

MR = 100 - 2Q

MC = 20  

MR = MC  

100 - 2Q = 20

100 - 20 = 2Q

80 = 2Q

Q = 40

P = 100 - 40

= 60

Profit = TR - TC

= PQ - (1000 + 20Q)  

= 6040 - 100 - 2040

= 2400 - 100 - 800

= 2400 - 900

= 1500

CS = 1/2(100 - 60)(40)  

= 1/24040

= 800

b)

Now monopoly firm is regulated by the government to charge price equals to marginal cost i.e. P = MC

P = MC

100 - Q = 20  

100 - 20 = Q  

Q = 80

P = 100 - 80 = 20  

Profit = TR - TC  

= PQ - 1000 - 20Q

= 2080 - 1000 - 2080  

= 1600 - 1000 - 1600

= - 1000

Since at P = MC monopolist produces 80 units of output and making a loos of 1000 therefore this policy is not sustainable

c) Now regulators allow monoploy firm to charge price $ 36

Q = 100 - P

Q = 100 - 36

Q = 64

so at price P = 36 monopoly firm is producing 64 units of output and

Profit = TR - TC  

= PQ - 1000 - 20Q

= 3664 - 1000 - 2036  

= 2304 - 1000 - 720

= 584

At this price monopolist is making a positive profit of $ 584 wchich is less than in part (a) but still it is a positive thus this policy is sustainable.