a. General Motors (GM) produces light trucks in several Michigan factories, where its annual fixed costs are $180 million, and its marginal cost per truck is approximately $20,000. Regional demand for the trucks is given by: P = 30,000 - 0.1Q, where P denotes price in dollars and Q denotes annual sales of trucks. Find GM’s profit-maximizing output level and price. Find the annual profit generated by light trucks.
b. GM is getting ready to export trucks to several markets in South America. Based on several marketing surveys, GM has found the elasticity of demand in these foreign markets to be EP = -9 for a wide range of prices (between $20,000 and $30,000). The additional cost of shipping (including paying some import fees) is about $800 per truck. One manager argues that the foreign price should be set at $800 above the domestic price (in part a) to cover the transportation cost. Do you agree that this is the optimal price for foreign sales? Justify your answer.
c. GM also produces an economy (“no frills”) version of its light truck at a marginal cost of $12,000 per vehicle. However, at the price set by GM, $20,000 per truck, customer demand has been very disappointing. GM has recently discontinued production of this model but still finds itself with an inventory of 18,000 unsold trucks. The best estimate of demand for the remaining trucks is:
P = 30,000 - Q.
One manager recommends keeping the price at $20,000; another favors cutting the price to sell the entire inventory. What price (one of these or some other price) should GM set and how many trucks should it sell? Justify your answer.