The Sterling Corporation makes and sells motorcycles. The total cost of each cycle is the sum of the costs of frames, assembly, and engine. The firm produces its own engines according to the following cost equation: CE = 250,000 + 1,000 q. The cost of frames and assembly is $2,000 per cycle. Monthly demand for cycles is given by the demand equation P = 10,000 – 25 q.

a) What is the marginal cost of producing an additional engine?

What is the marginal cost of producing an additional cycle ?

Explain.

b) Find the firm’s profit-maximizing quantity and price of cycles using marginal decision analysis? Show work.

What are the firm’s monthly profits? Show work.

c) Suppose instead the firm has the chance to buy an unlimited number of engines from another company at a price of $2,000 per engine and it can completely avoid the $250,000 fixed cost of producing engines.

Find the profit-maximizing quantity and price of cycles using marginal decision analysis? Show work.

What are the firm’s monthly profits? Show work.