Firm A makes and sells motor cycles. 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) Calculate the MC of producing an additional engine. Calculate the MC of producing an additional cycle. Find the firm’s profit maximizing quantity and price.

(b) Now, suppose the firm has the opportunity to buy an unlimited number of engines from another company at a price of $1,400 per engine. How many cycles should the profit maximizing firm produce now? What price should it charge? Will the firm continue to produce engines itself? If so, how many? If not, why not?

Show all your calculations.