Suppose a monopolist faces the following demand curve: P = 88 – 3Q. The long run

Question

Suppose a monopolist faces the following demand curve: P = 88 – 3Q. The long run marginal cost of production is constant and equal to $4, and there are no fixed costs.

A) What is the monopolist’s profit maximizing level of output?

B) What price will the profit maximizing monopolist produce?

C) How much profit will the monopolist make if she maximizes her profit?

D) What would be the value of consumer surplus if the market were perfectly competitive?

E) What is the value of the deadweight loss when the market is a monopoly?

Explanation / Answer

Answer :-

A.) P= 88-3Q

MC =$4

TR = 88Q - 3Q2

MR = 88 - 6Q

for equilibrium quantity

MR = MC, therefore, Q = 14 units.

B.) we have Q = 14 units

putting this value in P = 88 - 3Q, we get , P = $46.

C.) profit = TR -TC. => [88(14) -3(14)2] - [ 4*14 ] THUS

profit = $588.

D.) in case of perfect competition, price = MC= $4.

thus , Q = 28 unitrs.

CS = 1/2*28*84 = $1176.

E.) DeadWeight Loss = its the loss in total surplus due to moving from perfect competition to monopoly.

so, we have DWL =1/2*42*14 = $294.

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