A monopolist\'s total costs are The monopolist operates in a market in which the

Question

A monopolist's total costs are The monopolist operates in a market in which the demand curve a) Find the monopolist's profit-maximizing price and outpu 1. c = 15 + 124 p=20-q monopolist so as to maxi. output should the governmen b) Suppose that the government decides to regulate the mo mize the net benefis to society, What price and output should the set? c) Suppose that the government takes over the firm and operates it to m o maximi net social benefits. What should the price and output be? What will losses be?

Explanation / Answer

P=20-q

TR=Pq= 20q-q2

differentiate TR with respect to q

MR= 20-2q

C= 15+12q

differentiate C with respect to q

MC= 12

1) Monopolist produce that level of output at which marginal revenue=marginal cost i.e MR=MC to maximise his profit.

MR=MC

20-2q=12

8=2q

q=4

p=20-q= 20-4= 16

2) if government decides to regulate the monopolist then they will charge price=marhinal cost i.e P=MC

Now P=MC

20-q=12

q=8

p=12

3) if goverment takes over the firm then they will charge price=12 and produces output=8

profit of monopolist in the case of non goverment regulation = TR-TC

Profit = (16)(4)-15-12(4)

profit= 64-15-48= 1

profit of monopolist in the case of goverment regulation= TR-TC

Profit= (12)(8)-15-12(8)

profit=96-15-96= -15

so, losses for monopolist in the case of government regulation=1-(-15)= 16.

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