Question

The manager of a local monopoly estimates that the elasticity of demand for its product is constant and equal to -3. The firm’s marginal cost is constant at $35 per unit. a. Express the firm’s marginal revenue as a function of its price. Instruction: Enter your response rounded to two decimal places. MR = × P b. Determine the profit-maximizing price. Instruction: Use the rounded value calculated above and round your response to two decimal places. $

Answer 1

Answer

Marginal revenue(MR) = dTR/dQ where TR = Total revenue = PQ

MR = d(TR)/dQ = P + Q(dP/dQ) = P(1 + (Q/P)(dP/dQ)) = P(1 +1/e)

Given elasticity of demand = e = (P/Q)(dQ/dP) = -3

=> MR = P(1 + (Q/P)(dP/dQ)) = P(1 +1/e) = P(1 - 1/3) = 2P/3

=> MR = 2P/3

In order to maximize profit MR must equals MC

Here, MR = 2P/3 and MC = 35

=> 2P/3 = 35

=> P = 52.5

Hence, Profit maximizing price = $52.5