Q2 faces a market demand function of A monopolist with total

Q2 faces a market demand function of A monopolist with total cost function c(Q) = 500 QD(P) = 150-2P. a) Calculate the monopolist\'s profit-maximizing price and quantity sold, and the monopolist\'s profits.

Solution

Marginal cost is the additional cost due to additional unit produced.

MC=dTC/dQ=50+3/2*2Q=50+3Q

And Q=150-2P. Then P=75-0.5Q. And TR=75Q-0.5Q²

MR=dTR/dQ=75-Q

Profit is maximised when MR=MC

50+3Q=75-Q

4Q=25. Then Q=25/4=6.25

Price=75-0.5(6.25)=71.875

Profit=TR-TC=71.875*6.25-50(6.25)-1.5(6.25)²=449.21875-312.5-58.6=78.12