Vertical Contracting Relationship Consider the problem of vertical contracting between a monopoly upstream manufacturer and a monopoly downstream retailer. The upstream manu- facturer can produce an intermediate goods at zero cost. The downstream retailer can turn an intermediate goods into a nal goods, again at zero cost. The demand for the nal goods is given by D (p) = 9 p, where p is the price charged by the retailer, and 9 is a demand parameter that takes a value of either 1 or 2. Assume that only franchise fee contracts are feasible. A franchise fee contract consists of a lump-sum franchise fee A, and a per-unit price pm for each unit of intermediate goods procured. The timing of the game is as follows. First, the manufacturer offers a franchise fee contract. Second, the retailer decides whether to accept it or not. If it does not, the game is over; if it does, then it decides the price for the nal goods p. In this case, it is going to sell 9 p units of nal goods. This means it has to buy 6' p units of intermediate goods and pay the manufacturer (a) Suppose the demand parameter 6 is commonly known to both the manufacturer and the retailer. For each case of 9 E {1, 2}, what is the optimal franchise fee contract for the manufacturer? (b) Now suppose the demand parameter is private information to the retailer. The manufacturer only knows that 9 : 2 with probability 1 f 4, and 9 : 1 with probability 3/ 4. The precise timing of the game is as follows. First, Nature decides the realized value of 9' according to the probability function above, and shows it to the retailer (but NOT the manufacturer). Second, the manufacturer offers a menu of franchise fee contracts. Third, the retailer decides which contract to pick from the menu (or not picking anyone at all). If it does not pick any contract, the game is over. If it picks any contract, say (A', pin), then it decides the price for the nal goods 19. In this case, it is going to sell 9 p units of nal goods. This means it has to buy 6' p units of intermediate goods and pay the manufacturer A' + (9 P) pin- As usual, you may assume that the menu consists of only two contracts, each of which is designed for a particular value of 9. You may think that there are two types of retailer corresponding to 9' = 1 and 9 = 2 respectively. Denote the contract designed for type 6' = 1 by (A1,p1) and that for type 9 = 2 by (A2492). For the sake of simplifying the calculation, you may assume throughout that 191,192