Question

A monopolist faces a demand curve of P = 120 – Q, and has costs of C = 50 + 20Q. The monopolist sets a uniform price to maximize profits.

Group of answer choices

a) All of the answers are correct.

b)The profit-maximizing price is 70.

c)Deadweight loss is 1250.

d) Producer surplus is 2500.

Answer 1

a) all of these are correct.

Explanation:

The profit maximising output of a monopoly is found using the condition: MR=MC

Here, TR= P*Q = 120Q-Q² and TC = 50+20Q

So, MR = 120-2Q and MC= 20

Equating MR and MC; 120-2Q=20

or, 100 = 2Q

or, Q = 50

Substituting this value of Q in the demand curve: P = 120-50

P = 70

So, the profit maximising price is 70.

The deadweight loss in a monopoly is the area between the perfectly competitive output and price with that of the monopoly firm.

Perfectly competitive firm's equilibrium is found by the condition: P=MC

i.e., 120-Q= 20

or, Q = 100

Substituting this value of Q in the demand curve: P = 120-100

P = 20

So, the deadweight loss is the triangle , area of which = (1/2)*50*50

= (1/2)*2500

= 1250

Producer surplus is the area between the price and the supply curve. The supply curve for monopoly is the MC curve itself. So, here supply is constant at 20 at every level of output-

So, the shaded region seen here is the producer surplus, area of which = length*breadth

= (70-20)*50

= 50*50

= 2500