Question

5. A monopolist produces under a constant average cost equal to 10 and no fixed cost. The demand for the monopolist’s output is given by Q = 52 − P.

a. What are the price and output that yield the maximum profit? What is then the monopolist’s profit?

b. What would be the level of output supplied in this market under perfect competition?

c. What would be the consumer surplus under perfect competition? Does it exceed the

sum of the monopolist’s profit and consumer surplus in the market under monopoly?

d. How much is the social deadweight loss related to the market monopolizatio

Answer 1

)Q = 52 - P

P = 52 - Q

Average cost = Total cost/Quantity = 10
Total Cost = 10Q

A) Monopolist profit = Totat revenue - total cost

Total revenue = 52Q - Q2

Profit =  52Q - Q2 - 10Q

Differentiate with respect to Q and equate with 0

52 -2Q - 10 = 0

Q = 21

P = 31

These are equilibrium price and quantity

Profit = 52(21) -(21)2 - 10(21) = $441

B) Under perfect compeitition , equilibrium condition P = MC

MC = 10

10 = 52 - Q

Q = 42

P = 10

C) Consumer surplus under perfect compeitition :

CS = 0.5 x (52 - P) x ( Q ) = 0.5 x (52 - 10) x 42 = 0.5 x (42) x(42) = 882

Consumer surplus under monopoly :

CSm = 0.5 ( 52 - P ) x Q = 0.5 x (52 - 31) x 21 = 0.5 x 21 x 21 = 220.5

Total suplus under monopoly = CSm + profit = 220.5 + 441 = 661.5

Yes the consumer suplus under perfect compeitition is greater than total surplus of monopoly

D) Dead weight loss under monopoly :

DWL = 0.5 ( Quanity under perfect compeitition - Quantity under monopoly) ( Price of monopoly - Marginal cost)

= 0.5 ( 42 - 21 ) ( 31 - 10) = 0.5 x 21 x 21 = 220.5