1. There are two players, 1 and 2. Each player owns a firm in a Cournot duopoly. The inverse demand function is P =

60 Q and both firms have the same cost function characterized by a constant marginal cost equal to 12

and zero fixed cost. The firms are run by managers who make all the relevant decisions. The objective of a

manager is to maximize his own income. In the following assume that (0,1). Consider the following

game. First the owner of firm 1 (player 1) decides whether to appoint a manager with a profit-sharing contract

(the manager of firm 1 gets the fraction of the profit of firm 1) or a revenue-sharing contract (the manager

of firm 1 gets the fraction of the revenue of firm 1). Then player 1's decision is made public and the owner

of firm 2 (player 2) makes a similar decision. Then player 2's decision is made public and, afterwards, the

managers simultaneously and independently compete in output levels. Note that the value of is fixed and is

not subject to choice. The only choice each player has is between a profit-sharing and a revenue-sharing

contract.

(a) Sketch the extensive-from game.

(b) Find the pure-strategy subgame-perfect equilibria of this game. [Hint: your answer will have to

distinguish between different values of .]

(c) For the case where

1

20

= find the payoffs of the two players at the subgame-perfect equilibrium.

(d) For the case where

1

20

= give an intuitive explanation for the equilibrium: why do the players make

those choices at the subgame-perfect equilibrium?

2. HAL and JCN are the only producers of personal computers. Their computers are considered

to be perfect substitutes by consumers. The demand function for computers is given by

(Q denotes industry output and P price):

Q = 500 P

2 .

HAL and JCN compete in output levels (Cournot competition). JCN is a fully

integrated firm (it produces all its inputs) and has a constant unit cost of production equal to 3.

HAL, on the other hand, buys the CPUs from Entil (each computer requires one CPU). Entil

publicly announces the (unit) price of CPUs and HAL takes that price as given and decides

how many CPUs to buy. Besides the CPU, each computer requires a bundle of inputs that HAL

produces internally at a (constant) cost of 1. Entil's (constant) cost of producing one CPU is 2.

After many years of operation as separate firms, Entil and HAL apply to the government for

permission to merge. Assume that the government is exclusively concerned with the welfare of

consumers. Should the government allow the merger to take place? (give a detailed proof of

your claim).