A monopolist has a constant marginal and average cost of $10 and faces a demand

Question

A monopolist has a constant marginal and average cost of $10 and faces a demand curve of:

Qd=1000-10P

The firm's marginal revenue curve is equal to

MR= 100-0.2Q

What is the monopolist's profit-maximizing rate of production? What is the monopolists's profit-maximizing price? What is the monopolist's profit-maximizing price assuminf fixed costs are 0. What is the monopolist's profit-maximizing rate of production? What is the monopolists's profit-maximizing price? What is the monopolist's profit-maximizing price assuminf fixed costs are 0.

Explanation / Answer

Hi I' have seen this problem before: Assuming there is no price discrimination MC=MR MC=10 MR=100-0.2Q 10=100-0.2Q 90=0.2Q Q = 90/0.2 = 450 Q=1000-10P P = 100-0.1Q = 100-450*0.1 = 100-45 = 55 Profit=TR-TC= (P*Q)-(ATC*Q) =Q*(P-ATC)= 450*(55-10) = 450*45 = 20'250 Answ: Q=450 P=55 Profit=20'250

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