Firm A 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 cost equation:
CE = 250,000 + 1,000Q + 5Q2.
The cost of frames and assembly is $2,000 per cycle. Monthly demand for cycles is given by the inverse demand equation:
P = 10,000 - 30Q.
a. What is the MC of producing an additional engine? What is the MC of producing an additional cycle? Find the firm’s profit-maximizing quantity and price.
b. Now suppose the firm has the chance to buy an unlimited number of engines from another company at a price of $1,400 per engine. Will this option affect the number of cycles it plans to produce? Its price? Will the firm continue to produce engines itself? If so, how many?