Suppose the demand curve for a monopolist is Qd=500-P, and the marginal revenue

Question

Suppose the demand curve for a monopolist is Qd=500-P, and the marginal revenue function is MR=500-2Q. The monopolist has a constant marginal and average total cost of $50 per unit.

a) Find the monopolist's profit-maximizing output and price.
b) Calculate the monopolist's profit.
c) What is the Lerner Index for this industry?

Explanation / Answer

Q = 500-P MR=500-2Q d(TR)/dQ = MR TR=500Q-Q^2 MC=AC=50 => TC=50Q MR=MC(PROFIT MAXIMIZATION CONDITION) 500-2Q=50 Q=225 no of units...... P=500-225=$275.... PROFIT=TR-TC TR=500Q-Q^2 TC=50Q PROFIT= 500Q-Q^2-50Q = 450Q-Q^2 =Q(450-Q) =225(225) =$50625........ lerner index= (P-MC)/P = (275-50)/275 225/275=0.8181

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