A firm with market power faces the following estimated demand and average variable cost functions: where is quantity demanded,P is price,M is income,and is the price of a related good.The firm expects income to be $40,000 and to be $2.Total fixed cost is $100,000.What is the estimated marginal revenue function for the firm?

Question

A firm with market power faces the following estimated demand and average variable cost functions:   where  is quantity demanded,P is price,M is income,and  is the price of a related good.The firm expects income to be $40,000 and  to be $2.Total fixed cost is $100,000.What is the estimated marginal revenue function for the firm?

Quizplus · Accepted Answer

The marginal revenue function can be derived from the total revenue (TR) function:
TR = P(Q) * Q = (78 - 0.002Q)Q = 78Q - 0.002Q^2
Then, the marginal revenue (MR) function can be found by taking the derivative of the TR function:
MR = d(TR)/d(Q) = 78 - 0.004Q
Therefore, the estimated marginal revenue function for the firm is MR = 78 - 0.004Q.

A Firm with Market Power Faces the Following Estimated Demand