2. Suppose that there are two single product firms P1, P2 selling to dedicated retailers (one each) R1, R2, which then sell their product on to consumers. Use the symbols w1, w2 for the wholesale prices and p1, p2 for the retail prices. Marginal production costs are 20; there are no marginal retail costs nor fixed costs, though retailers do have to pay the wholesale prices. The consumer demand equations are given by+91 = 776 - 8p1 + 4p2 192 = 776 + 4p1 - 8p2. Assume Bertrand competition and Nash. Producers set wholesale prices and retailers set retail prices after see- ing the wholesale prices. (a) Determine equilibrium retail prices as a function of wholesale prices by looking at the retailers' profit maximization problem. (b) Determine equilibrium volumes as a function of wholesale prices. (c) Express the producers' profit func- tion as a function of wholesale prices. (d) What are the equilibrium whole- sale prices and volumes? (e) What are the equilibrium retail prices? (f) What are the equilibrium profits of retailers and producers sepa- rately? Now suppose that Pl merged with R1 and P2 merged with R2 to form M1, M2 respectively. Now, M1 and M2 sell directly to end con- Sumers, charging prices palspm2, respectively. (g) What are the equilibrium retail prices and volumes now?{h} What are the prots of M1 and M2? (i) What is the range of franchise fees for which P1 and R1 plus P2 and 13.2 are better n" having a re tail channel than both being inte- grated companies? Consider the following two alter- native scenarios: 1 2 Drill "' I\" ] + '1 2+ {5' W P 3" {A} 5:3 = \"11+ c1111 H HUI-2+ with marginal production costs equal to 2G, and {m = Tl .. 31E\" + lift-2f .7\" 1 {Bl Q: = a It} +[1p1 " 3102+ with marginal costs 48. In one of these two cases, it is more protable not to have a re tail channel at all and in one of these cases it is protable to have a retail channel even absent a fran chise fee. Argue which is which; do as: compute anything