Recall that in chapter 9, we considered a large manufacturing monopolist selling to individual retailing monopolists. Recall that in one parameterization of the problem, there were ten retailers, three of whom faced demand of the form p = 12 - 9x, five of whom faced demand of the form p = 12 - 6x, and two who faced demand of the form p = 12 - 2x. Costs of production and sales were zero. The retailers are price-takers in their dealings with the manufacturing monopolist.
(a) Assume that the manufacturer can tailor a take-it-or-leave-it offer for each individual retailer, of any form desired. To maximize her profits, what should the manufacturer do?
(b) Suppose the manufacturer is compelled by law to make identical offers to all ten retailers, but she can otherwise make take-it-or-leave-it offers, offers with menus where retailers are restricted to taking only one item from the menu, and so on. What is the best the manufacturer can do in this instance?