9.a. General Motors (GM) produces trucks with annual fixed costs are $180 million, and its

9.
a. General Motors (GM) produces trucks with annual fixed costs are $180 million, and its
marginal cost per truck is approximately $20,000. Regional demand for the trucks is written as: P = 30,000 − .1Q, where P =price in dollars and Q =annual sales of trucks.
What is GM’s profit- maximizing output level and price, and what is the annual profit generated by the trucks.
b. GM has found the elasticity of demand in 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 $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. Is setting it above $800 an optimal price for foreign sales?
c. GM also produces an economy version of its truck at a marginal cost of $12,000 per vehicle. But at the price set by GM of $20,000 per truck, customer demand has been very disappointing. GM discontinued production of this model but has an inventory of 18,000 unsold trucks. The best estimate of demand for the remaining trucks is:
P = 30,000−Q.
Should the price be kept at $20,000 or should it be cut to sell the inventory? If the price is reduced, what price would be good and how many should be sold?