A monopolist faces a constant elasticity demand curve Q = 100P^(-2). If its constant marginal cost is MC = 25, what is the profit-maximizing price level according to the Lerner Index of monopoly power?

First we find the price elasticity of demand. Q = 100P^(-2), so dQ/dP = -200P^(-3) e = (dQ/dP) × (P/Q) = (-200P^(-3)) × (P / 100P^(-2)) = -2 The elasticity is -2 at every price, which is what is meant by a constant elasticity demand curve. So |e| = 2. The Lerner Index for a profit-maximizing monopolist is L = (P - MC)/P = 1/|e| = 1/2 (P - 25)/P = 1/2 2P - 50 = P P = ₹50 The same result follows from the markup rule: P = MC × |e|/(|e| - 1) = 25 × 2/1 = ₹50. Equivalently, MR = P(1 - 1/|e|) = P/2, and MR = MC gives P/2 = 25. A monopolist always operates on the elastic part of the demand curve (|e| > 1), since MR would be negative otherwise. That is why this problem has a solution. The constant 100 in the demand function only scales the quantity and does not affect the optimal price. Hence the correct option is (C).