Question: You have just finished writing a program for a new and unique computer game. You are interested in selling the rights for this game to Alpha, a company that specializes in manufacturing and selling computer games. Assume that your costs of writing the program are all sunk. Your estimate of the demand that Alpha will face in selling this game is given by: P = 100 – Q, where Q is the quantity demanded when the price set by Alpha is P. You estimate Alpha’s marginal cost of producing this game at $20 a piece. You have no further costs and your objective is to maximize your profit. Alpha's objective is to maximize its profit.

Consider the contract between you and Alpha, according to which Alpha will pay you a fixed fee per unit that it sells in the market (denote this fee by f)

a. For a given fee (f) please calculate the price that maximizes Alpha's profit (call this price P(f)). Calculate Alpha's profit and your profit in this case.

b. On the basis of your calculations above, calculate the fee (f) that maximizes your profit. What is the price (P) that Alpha will charge its customers, and what will be Alpha’s profits and your profits in this case?

c. How would your answers to part a. and b. above change if Alpha’s marginal cost was only $10 per unit, but you also had to incur a cost of $10 per unit sold in the market? Can you provide an intuitive explanation for the results that you got here?