Using time-series data,the demand function for a profit-maximizing monopolist has been estimated as where is the amount sold,P is price,M is income,and is the price of a related good.The estimated values for M and in 2012 are $25,000 and $200,respectively.The short-run marginal cost curve for this firm has been estimated as: Total fixed cost is forecast to be $500,000 in 2016.What is the optimal price?

Question

Using time-series data,the demand function for a profit-maximizing monopolist has been estimated as  where  is the amount sold,P is price,M is income,and  is the price of a related good.The estimated values for M and  in 2012 are $25,000 and $200,respectively.The short-run marginal cost curve for this firm has been estimated as:  Total fixed cost is forecast to be $500,000 in 2016.What is the optimal price?

Quizplus · Accepted Answer

To find the optimal price, we need to maximize the profit function:
π = (P - MC)Q = [P - 100 - 0.02(25,000) + 0.5(200)]Q
where MC = 100 + 0.02M - 0.5N is the marginal cost function (based on the given data).
Taking the derivative of π with respect to Q and setting it equal to zero, we get:
P - 100 - 0.02(25,000) + 0.5(200) - 0.5(11eab534_6956_1fa8_9198_03a794d2ae39_TB2562_11) = 0
Solving for P, we get:
P = 408
Therefore, the optimal price is $408. Choice (D) is correct.

Using Time-Series Data,the Demand Function for a Profit-Maximizing Monopolist Has