Suppose that, for prices below 200, demand for quantity q of a monopoly firm's output good...

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Suppose that, for prices below 200, demand for quantity q of a monopoly firm's output good is described by the function PP = 200 - 2q, where PP is the price of the output good. The firm has a fixed cost of S1400. Its marginal cost and average variable cost are 40 at all levels of output (i.e., for all q). (a) Find the monopoly firm's marginal revenue, as a function of output q. (b) Find the monopoly firm's profit-maximizing choice of output qqr, the price it charges to sell qq, and the firm's profit when it produces qq*. (C) Find the deadweight loss caused by the firm's choice of qq+. (d) Suppose that the government decides to regulate the monopoly firm, by not allowing it to charge any price higher than the lowest price that would make the firm's profit zero. Find that lowest price. Hint: the firm's profit as a function of quantity q is quadratic, i.e, it has qq2 in it. I have chosen the numbers for this problem so that you can find the quantities that make the firm's profit zero without using the quadratic formula, though you can use it if you want. You will find that there are two quantities that would make the firm's profit zero; if the government wants the lowest possible price that makes the firm's profit zero, should it choose the larger or smaller of these two quantities? (e) When the government regulates the monopoly firm as in part (d), is the resulting deadweight loss greater or smaller than when the monopoly maximizes its profit? You could do this by calculating the deadweight loss under regulation, and comparing it to your answer to (C), but you can also make a direct argument without that calculation, based on the quantities you found in (b) and (d), and what they imply about the areas that represent a deadweight loss. Suppose that, for prices below 200, demand for quantity q of a monopoly firm's output good is described by the function PP = 200 - 2q, where PP is the price of the output good. The firm has a fixed cost of S1400. Its marginal cost and average variable cost are 40 at all levels of output (i.e., for all q). (a) Find the monopoly firm's marginal revenue, as a function of output q. (b) Find the monopoly firm's profit-maximizing choice of output qqr, the price it charges to sell qq, and the firm's profit when it produces qq*. (C) Find the deadweight loss caused by the firm's choice of qq+. (d) Suppose that the government decides to regulate the monopoly firm, by not allowing it to charge any price higher than the lowest price that would make the firm's profit zero. Find that lowest price. Hint: the firm's profit as a function of quantity q is quadratic, i.e, it has qq2 in it. I have chosen the numbers for this problem so that you can find the quantities that make the firm's profit zero without using the quadratic formula, though you can use it if you want. You will find that there are two quantities that would make the firm's profit zero; if the government wants the lowest possible price that makes the firm's profit zero, should it choose the larger or smaller of these two quantities? (e) When the government regulates the monopoly firm as in part (d), is the resulting deadweight loss greater or smaller than when the monopoly maximizes its profit? You could do this by calculating the deadweight loss under regulation, and comparing it to your answer to (C), but you can also make a direct argument without that calculation, based on the quantities you found in (b) and (d), and what they imply about the areas that represent a deadweight loss.

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a P 200 2q TR P x q 200q 2q 2 MR dTRdq 200 4q b Setting MR MC 200 4q 40 4q ... View the full answer