4. Consider a market in which there are two single product producers, P1 and P2, and a single retailer R. P1 and P2 sell their product to R at wholesale prices w1,w2 respectively, which P1 and P2 choose simultaneously and indepen- dently. Marginal production costs are zero and there are no retail costs. The producers do however face a. xed cost F 2 0 of operating in the market: F does not depend on volume. R then sells the products on to consumers at prices 191,192, respectively. Demand is given by {91 = 2160 10191 + 5,02, _ (1) QQ _ 2160 + 5p, 10,02. (a) First consider R's problem. What are the optimal retail prices p1, p2 as a function of the wholesale prices 3501,2502? (b) What are the corresponding quan- tities 91,92, again expressed in terms of 201,302? (c) Express P2's prot as a function of 2501,2302. (d) What are the equilibrium whole- sale prices w1,w2? (e) What are the equilibrium quanti- ties 91,92? (f) What are the equilibrium retail prices 111, 132? (g) What are the equilibrium prots 717,711,712 for the retailer and each of the two producers? Now suppose that R merges with P1 to become the merged entity M. So M now produces product 1 and sells both products 1 and 2 in the retail market. You can think of the situation as 101 = O with 102 being set by P2. (h) Express P2's prot as a function of 102. (i) What is the equilibrium wholesale price 1192 of product 2? (i) What are the equilibrium prots of M, P2? (k) Explain why it is still protable for M to continue selling product 2. (1) Who benets and who is harmed by this merger? Now suppose that F is so high that it is no longer protable for P2 to stay in the market. (m) For what values of F would P2 want to be in the market absent a merger but not with a merger? Suppose further that this situation is equivalent to one in which [)1 = 216 and p2 = 270. (n) What is the expected prot of M in this case? (o) Who benefits and who is harmed by this merger? (p) What is the term used for the prob- lem described here