3. 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 g = 38400 1001). (a) Express the protmaximizing re tail price }! set by R as a function of w. (b) Do the same for quantity. (c) Express P's prot as a function of w. (d) What is the protmaximizing wholesale price w? (e) What are the equilibrium retail price, the equilibrium quantity, and the equilibrium prots? Now suppose that R,P merge to become M. Nothing else changes. (f) What is the protmaximizing re- tail price, equilibrium quantity, and equilibrium prot for M? (g) Explain why everyone benets here. Now suppose that instead of merg- ing, R,P agree that P will sell R its product for w = 100 per unit in return for a one time franchise fee F, Le. a xed amount that R will pay P for the right to sell P's product. (h) (i) (i) (k) What would be the equilibrium retail price, equilibrium quantity, and equilibrium prots for P, R now? You will nd that compared to the rst situation described in this question, R's prot will be greater and P's prot will be less. For what range of values of F would both P and R be ok with this arrange- ment? What is the relevance of this last possibility for whether a merger should be allowed to go ahead? Can you think of a limitation of this last possibility in practice