Problem 1--Chapter 15 Horizontal merger There are 20 identical firms that provid

Question

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?

Explanation / Answer

Given P = 100 - Q and MC = 20

a. Now as there are 20 identical firms thus Q = q1 + q2 + q3 + ....... + q20 , therefore TR of firm1 is

TR1 = 100q1 - (q1^2 + q1q2 + q1q2 + q1q3 + ..... + q1q20)

MR1 = 100 - 2q1 - q2 - q3 - ...... - q20 -------------------- (1)

Similarly

MR2 = 100 - q1 - 2q2 - q3 - ...... - q20 --------------------(2)

MR3 = 100 - q1 - q2 - 2q3 - ....... - q20 ---------------------(3)

/

/

/

MR20 = 100 - q1 - q2 - q3 - ......... - 2q20 ----------------(20)

At equilibrium, MR = MC. Thus equating above equation with 20 and subtracting equation (2) from equation (1), we get

100 - 2q1 - q2 - q3 - ...... - q20 = 20

100 - q1 - 2q2 - q3 - ...... - q20 = 20

(-)_(+)_(+)___(+)_(+)____(+)___(-)__

q2 - q1 = 0

q1 = q2 ----------------------- (21)

Similarly solving rest of the equation, we get

q1 = q2 = q3 = ...... = q20 --------------------- (22)

Inserting the result from equation (22) in equation (1) with equating it with MC, we get

100 - 21q1 = 20

q1 = 80/21 = 3.81

Therefor the industry output would be

Q = 20 * 3.81 = 76.2

Now P = 100 - Q = 100 - 76.2 = 23.8

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