Problem 1--Chapter 15 Horizontal merger
There are 20 identical firms that provide car wash services in the town of Dartmouth. Inverse demand for this service is P = 100 – Q. Unit cost is constant and equal to $20. Firms in this industry compete in quantities of cars washed.
(a)Show that in a Cournot equilibrium, the aggregate number of cars washed is Q=76.2, And equilibrium price is P=23.8
(b)Suppose that 5 two-firm mergers occur, and these 5 merged firms become Stackelberg leaders post-merger, and the remaining 10 non-merged firms are followers. Show that in the two-stage game a leader firm washes 13.38 cars and each follower firm washes only 1.18 cars. Show that total industry output will be Q=78.8 and price will be P=21.2
Problem 2 --Chapter 16 Vertical Merger
Suppose the smart-phone market is monopolized by iPhone. The manufacturing of each iPhone requires exactly one unit of smart-phone chip as an input, and incurs other variable costs of $4 per unit. The smart-phone chips market is also monopolistic; the unit cost of manufacturing each chip is $5. Assume the inverse demand for iPhone is, where i represents iPhone.
(a) If both Chip and iPhone act as independent profit-maximizing companies, what would be the quantity, price and profit for each firm?
(b) If Chip and iPhone merge, what would be the profit-maximizing quantity, price and profit for the merged firm?
Problem 3 --Chapter 17 Vertical price restraint
Suppose that a car dealer has a local monopoly in selling Volvos. It pays to Volvo for each car that it sells, and charges each customer . The demand curve is best described by the linear function , where Q is the number of cars sold.
(a) What is the profit-maximizing price for the dealer to set? At this price, how many Volvos will the dealer sell and what will the dealer's profit be? (Hint: the results won't be exact numbers, but will be functions of the wholesale price )
(b) Now let's think about how the situation looks from the car manufacturer's point of view. What is the demand curve facing Volvo? Suppose that it costs Volvo $5 to produce each car. What is the profit-maximizing choice of ? What will Volvo's profit be? What would be the retail price ? What profit will the dealer earn at Volvo's profit-maximizing choice of wholesale price ?
(c) Suppose that Volvo operates the dealership itself and sells directly to its customers. What would be the profit-maximizing price ? What is Volvo's profit?
(d) Suppose instead that Volvo can impose an RPM agreement on its independent retailers. What price will Volvo actually set?