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 estimated marginal revenue function for the firm?

Question

Quizplus · Accepted Answer

To derive the marginal revenue function, we need to first find the total revenue function. Total revenue is simply price multiplied by quantity, or TR = PQ. Using the demand function, we can rewrite it as P = 400 - 0.0005Q + 0.875M + 2PR. Then, substituting this back into the total revenue equation, we get TR = (400Q - 0.0005Q^2 + 875M*Q + 2PR*Q). Now, taking the derivative of this with respect to Q, we get MR = 400 - 0.001Q + 875M + 2PR. Plugging in the given values of M and PR, we get MR = 520 - 0.001Q. Therefore, the correct answer is D.

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 $Q _ { d } = 800,000 - 2,000 P + 0.7 M + 4,000 P _ { R }$