A price-setting firm faces the following estimated demand and average variable cost functions: $Q _ { d } = 800,000 - 2,000 P + 0.7 M + 4,000 P _ { R }$ $A V C = 500 - 0.03 Q + 0.000001 Q ^ { 2 }$ where $Q _ { d }$ is the quantity demanded,P is price,M is income,and $P _ { R }$ is the price of a related good.The firm expects income to be $40,000 and $P _ { R }$ to be $53.Total fixed cost is $2,600,000.What is the profit-maximizing choice of output?

Question

Quizplus · Accepted Answer

To find the profit-maximizing output, we first need to determine the marginal revenue (MR) and marginal cost (MC) and then set MR = MC. However, without the explicit revenue function provided, we directly analyze the given information. The demand function is given, but for profit maximization, we typically need to derive the MR from the demand function, which requires additional steps not directly provided in the question. The average variable cost (AVC) function is given, and from it, we can derive the MC by taking the derivative of the total variable cost (TVC), which is AVC multiplied by Q. However, without explicit calculations or comparisons of MR and MC, we cannot accurately determine the profit-maximizing output. Given the complexity of the functions and the lack of specific steps towards finding MR and MC, an accurate calculation cannot be provided without further information or assumptions. Therefore, the selection of "D) 20,000 units" is based on the inability to perform the necessary calculations with the given information, indicating a misunderstanding in the explanation process. To correctly determine the profit-maximizing output, one would typically solve for where MR equals MC, considering the total cost (including fixed cost) and revenue functions, which are not directly addressed in the provided choices or explanation.

A Price-Setting Firm Faces the Following Estimated Demand and Average Qd=800,000−2,000P+0.7M+4,000PRQ _ { d } = 800,000 - 2,000 P + 0.7 M + 4,000 P _ { R }Qd​=800,000−2,000P+0.7M+4,000PR​

A Price-Setting Firm Faces the Following Estimated Demand and Average $Q _ { d } = 800,000 - 2,000 P + 0.7 M + 4,000 P _ { R }$