Question 1 Dayna’s Doorstops, Inc. (DD) is a monopolist in the doorstop industry

Question

Question 1 Dayna’s Doorstops, Inc. (DD) is a monopolist in the doorstop industry. Its cost is C =100 - 5Q + Q2, and demand is P = 55 - 2Q.

a. What price should DD set to maximize profit? What output does the firm produce? How much profit and consumer surplus does DD generate? (8 marks) b. What would output be if DD acted like a perfect competitor and set MC = P? What profit and consumer surplus would then be generated? (5 marks)

c. What is the deadweight loss from monopoly power in part (a)? (2 marks)  

d. Suppose the government, concerned about the high price of doorstops, sets a maximum price at $27. How does this affect price, quantity, consumer surplus, and DD’s profit? What is the resulting deadweight loss?

Explanation / Answer

Answer:

1.
MC=TC'
MC=5+2Q
MR=TR'
TR=(55-2Q)Q
MR=55-4Q
MC=MR
5+2Q=55-4Q
2Q+4Q=55-5
6Q=50
Q=8.33
****************************
P=55-2(50/6)=38.33
*******************************
When Q=0 P=55
CS=0.5*(55-38.33)*(8.33)=69.430
****************************
Profit=Tr-TC
Profit=(8.33*38.33)-(100-(5*8.33)+(8.33*8.33))
Profit=191.55
*******************************

b.
P=MC
55-2Q=5+2Q
50=4Q
Q=12.5
**********************************
c.
if Q=8.33
P=55-4*(8.33)=21.68

DWL=0.5*(38.33-21.68)*(12.5-8.33)=34.715

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