Suppose that there is a single producer P producing a single product which it sells at a wholesale price w chosen by P to a retailer R. R chooses a retail price p to sell it to consumers. The unit cost of production is $100, there are no retail costs, and retail demand is q = 38400 100p. (a) Express the profit-maximizing retail price p set by R as a function of w. (b) Do the same for quantity. (c) Express P's profit as a function of w. (d) What is the profit-maximizing wholesale price w? (e) What are the equilibrium retail price, the equilibrium quantity, and the equilibrium profits?

Now suppose that R,P merge to become M. Nothing else changes. (f) What is the profit-maximizing retail price, equilibrium quantity, and equilibrium profit for M? (g) Explain why everyone benefits here. Now suppose that instead of merging, R,P agree that P will sell R its product for w = 100 per unit in return for a one time franchise fee F , i.e. a fixed amount that R will pay P for the right to sell P's product. What would be the equilibrium retail price, equilibrium quantity, and equilibrium profits for P, R now? (i) You will find that compared to the first situation described in this question, R's profit will be greater and P's profit will be less. For what range of values of F would both P and R be ok with this arrangement? (j) What is the relevance of this last possibility for whether a merger should be allowed to go ahead? (k) Can you think of a limitation of this last possibility in practice?