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IO HW4 2019

Industrial Organization–Homework 4
Due date: Nov. 25, Monday (class time)
1. Consider the Chocolate War between Mars and Hershey. The game-tree is as follows.
What is game’s Subgame Perfect Nash equilibrium? (Hint: Use backward induction )
Firm 1
Firm 2
(-0.2, 0.1)
(0, 0)
(-0.1, -0.1)
2. There are two auto producers in Karmania, F1 and F2. The cars they produce are essentially
identical. The marker inverse demand curve is given by
p = a − bQ,
where p is the price (in thousands of dollars); Q market output (in thousands of units); and a
and b are parameters. It is estimated that a = 25 and b = 0.1. Both F1 and F2 have a marginal
cost of 10 thousand dollars per car.
Competition in the Karmania auto market works as follows. At the beginning of each year,
both firms simultaneously and independently decide how many cars to produce. Then the market
price adjusts to so that supply equals demand.
(1) What is firm F1’s best response mapping?
Hint: If firms F1’s profit is π1 = α0 + α1 q1 + α2 q12 + α3 q1 q2 , where α0 , α1 , α2 , α3 are parameters,
q1 is firm F1’s quantity supplied, and q2 is firm F2’s quantity supplied. Then firm F1’s best
response mapping is
q1 = −
q2 .
2α2 2α2
(2) What is the equilibrium of the game played between F1 and F2?
Hint: At equilibrium, the equilibrium output for firm F1 is the same as that for firm F2.
3. Consider a price-setting oligopoly with n firms, all with constant marginal cost c. Suppose
market demand is given by D(p) and the discount factor is 0.8.
(1) What is the maximum number of firms such that there exists an equilibrium with monopoly
pricing in a infinitely-period game?
Hint: Suppose the monopoly profit is πM . If there exists an equilibrium with monopoly pricing,
then each firm’s profit is πM /n in each period. However, if one firms deviates, he can obtain πM
in the first period, but always obtain zero profit afterwards. In addition, if one can obtain $a
profit in each period in a infinitely-period game with a discount factor δ, then his total profit is
a/(1 − δ).