Question: DP, Inc. is a U.S. based firm that sells farm equipment and faces demand given by P = 4,000 - Q, where P denotes price in dollars and Q is quantity of units sold per month. In its East coast factory, the firm's fixed costs are $500,000 per month, and its marginal cost of manufacturing the equipment is $1,500 per unit.
(a) Find the firm's profit-maximizing output and price. What is its profit?
(b) Over the last year, the US dollar has appreciated (gained value) versus the Korean won with the result that Korean imports of farm equipment to the US have increased. Firm DP's marketing department judges that it now would have to cut price by $1,000 per unit in order to sell the same profit-maximizing quantity as estimated earlier (The new demand is given by P = 4,500 - Q and MR = 4,500 - 2Q). Is the price-cut consistent with a profit-maximizing strategy? Explain.
(c) Suppose that the firm has produced the optimal level of output in part (a). But before this quantity is sold, demand unexpectedly falls to: P = 4,500 - 2Q, and the marginal revenue is MR = 4,500 - 4Q. One manager recommends cutting price to sell the entire inventory; another favors maintaining the price in part (a) (selling less than the total inventory). Do you agree with either manager? What optimal price would you set?