Consider the single-dealership problem analyzed in section 14.3.1. Suppose that the manufacturer sells each unit to the dealer for d = c (unit manufacturing cost) but, in addition, requires the dealer to pay a fraction of
a) Formulate the dealer's profit-maximization problem under this contract and show that this contract maximizes the industry profit. That is, show that for any given φ, the sum of the manufacturers and the dealers profit is equal to the profit made by a monopoly manufacturer selling directly to the consumer.
(b) How would your answer change if φ is the fraction of the end-user price instead of the dealers profit. That is, suppose now that the dealer pays a fraction of φ of the end-user price to the manufacturer for each unit it sells.
(c) Explain why "share-in-profit" types of contract are not frequently observed.