Question: 1.Vertical Integration and Franchising Fees. Suppose an upstreammanufacturer sells a product A which he can produce for a marginal cost of4 dollars to two downstream distributors who compete in a Cournot game.The distributors face the following demand,marginal revenues and marginalcosts
Px = 260 - 5Q
MR1 = 260 - 10q1 - 5q2
MR2 = 260 - 10q2 - 5q1
MC = 6 + PA
Where PA is the price the manufacturer charges for A. Since the distrib-utors have market power the manufacturer is thinking of using a one timefranchising fee to maximize its pro?t.
i) What would are the prices, quantities and pro?ts when the distributorsface a perfectly competitive market?
ii) What is the franchising fee and PA the manufacturer should choose tomaximize pro?t if this situation is repeated? Assume collusion is impossibleand the discount rate is 6 percent. (HINT: This does not require calculus. )
iii) How much do the distributors produce under this franchising system?What is the price? How does it compare to part i?