Question

The manager of a local monopoly estimates that the elasticity of demand for its product is constant and equal to -4 . The firm's marginal cost is constant at $25 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

Marginal revenue (MR) is expressed as MR = 0.75P for a monopoly with an elasticity of demand of -4. The profit-maximizing price is obtained by equating MR to the marginal cost (MC) of $25, resulting in a price of approximately $33.33.

Step-by-step explanation:

The student's question concerns a monopoly estimating that the elasticity of demand for its product is -4, with a marginal cost constant at $25 per unit. Firstly, we need to find the expression for marginal revenue (MR) as a function of price (P). Using the formula MR = P (1 + 1/E), where E is the elasticity of demand, we get MR = P (1 + 1/(-4)) = P (1 - 0.25) = 0.75P.

For the second part, the profit-maximizing price is found where MR equals MC. Given that MR = 0.75P and MC = $25, we can find the profit-maximizing price by setting MR = MC, which results in 0.75P = $25. Solving this equation, we find the profit-maximizing price P to be 25 / 0.75, which equals approximately $33.33.