Question

You are the manager of a monopolistically competitive firm, and your demand and cost functions are estimated as Q=36−4P and qQ=4+4Q+Q

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a. Find the inverse demand function for your firm's product. P= b. Determine the profit-maximizing price and level of production. Instruction: Price should be rounded to the nearest penny (two decimal places) Price: 5 Quantity c. Calculate your firm's maximum profits. Instruction: Your response should appear to the nearest penny (two decimal places) d. What jong-run adjustments should you expect? Explain. Neither entry not exit will occur, Exit wall occur until profits rise sufficlently high. Entry wil occui unti profits are zero.

Answer 1

To find the inverse demand function, we solve for P in terms of Q; the function is P = 9 - 0.25Q. The profit-maximizing price and quantity require setting MR equal to MC and solving numerically. In the long run, entry will occur until profits are zero.

Step-by-step explanation:

To find the inverse demand function for your firm's product, we manipulate the demand function Q = 36 - 4P to express P in terms of Q. Solving for P yields P = 9 - 0.25Q, which is the inverse demand function.

The profit-maximizing price and level of production are found by setting marginal revenue (MR) equal to marginal cost (MC). Since the total cost function is given by C(Q) = 4 + 4Q + Q2, the marginal cost is the derivative of this function, which is MC = 4 + 2Q. Similarly, the marginal revenue can be found by taking the derivative of the total revenue function, which is P * Q. The profit-maximizing quantity and price can be calculated numerically from these equations.

To calculate maximum profits, we subtract total costs from total revenue at the profit-maximizing quantity and price.

In the long run, we expect that entry will occur until profits are zero in a monopolistically competitive market, as there are no significant barriers preventing new firms from entering the market and competing away profits.