A producer of agricultural equipment operating in the U.S. faces demand given by: P = 4,200 - 2Q, where P denotes price in dollars and Q is quantity of units sold per month. The firm's fixed costs are $320,000 per month, and its marginal cost of manufacturing the equipment is $1,400 per unit.

a) Find the firm's profit-maximizing output and price. What is its profit? (20 points)

b) Suppose that a new market for the firm's product emerges in South America. The firm has begun selling the equipment in several test markets there and has found the elasticity of demand to be EP= -3.5 for a wide range of prices (between $1,500 and $3,000). The cost of shipping to South America is $200 per unit. One manager argues that the foreign price should be set at $200 above the domestic price (in part a) to cover the transportation cost. Do you agree that this is the optimal foreign price? Justify your answer. (10 points)

c) Suppose that the firm has produced the optimal level of domestic output as calculated in part a. But before this quantity is sold, demand unexpectedly falls to: P = 2,500 - 2Q, (equivalently Q = 1,250 - .5P). One manager recommends cutting price to sell the entire inventory; another favors maintaining the domestic price as calculated in part a (selling less than the total inventory). Do you agree with either manager? What optimal price would you set?