Vertical Mergers 1. Suppose a dealer has a local monopoly in selling Toyotas. It
ID: 1115012 • Letter: V
Question
Vertical Mergers 1. Suppose a dealer has a local monopoly in selling Toyotas. It pays W to Toyota for each car it sells and charges each customer P. It incurs no costs beyond the price it pays to Toyota. The inverse demand for Toyotas is given by P=10-Q where Q denotes the number of Toyotas. It costs Toyota C- 2 to produce each car. a. Formulate the dealer's optimization problem and derive the dealer's optimal purchase b. Formulate Toyota's optimization problem given the purchase decision rule of the c. Staff economists at Toyota convince the company to charge its dealers a franchise fee decision rule as a function of the purchase price w dealer and determine the profit maximizing choice of w. What are Toyota's profits? What price will the dealer charge? F for selling its cars in addition to w for each car. Compute the values of F and w that maximizes Toyota's profits Does franchising increase or decrease consumer surplus? Briefly explain the intuition for your answer d.Explanation / Answer
b. Profit= P(Q)= R(Q) - C(Q)
where R(Q) is the revenue function and C(Q) is the cost function
Revenue = Quantity X Price
Here Quantity = Number of Toyotas = Q (given)
Price = 10 - Q, So, Revenue = Q* (10 - Q) = 10Q - Q2 , So, Marginal Revenue = MR = 10 - 2Q
Cost function = C(Q) = W*Q, Marginal cost = MC = W
Profit Maximizing rule in a Monopoly = MR = MC
10 - 2 Q = W, Q = 5 - W/2
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