As noted in Problem 5 of Chapter 3, General Motors (GM) produces light trucks in its Michigan factories. Currently, its Michigan production is 50,000 trucks per month, and its marginal cost is $20,000 per truck. With regional demand given by: P = 30,000 - 0.1Q, GM sets a price of $25,000 per truck.
a. Confirm that setting Q = 50,000 and P = $25,000 is profit maximizing.
b. General Motors produces the engines that power its light trucks and finds that it has some unused production capacity, enough capacity to build an additional 10,000 engines per year. A manufacturer of sports utility vehicles (SUVs) has offered to purchase as many as 25,000 engines from GM at a price of $10,000 per engine. GM’s contribution is estimated to be about $2,000 per engine sold (based on a marginal cost of $8,000 per engine). Should GM devote some of its engine capacity to produce engines to sell to the SUV manufacturer? Does this outside opportunity change GM’s optimal output of light vehicles in part (a)?
c. GM also assembles light trucks in a West Coast facility, which is currently manufacturing 40,000 units per month. Because it produces multiple vehicle types at this mega-plant, the firm’s standard practice is to allocate $160 million of factorywide fixed costs to light trucks. Based on this allocation, the California production manager reports that the average total cost per light truck is $22,000 per unit. Given this report, what conclusion (if any) can you draw concerning the marginal cost per truck? If West Coast demand is similar to demand in Michigan, could the West Coast factory profit by changing its output from 40,000 units?