Question THREE (20 Marks)

Suppose two firms produce an identical good. The (inverse) demand function for the good is

given as P = 130 - Q, where Q is the total quantity produced by the two firms. Each firm had a

constant marginal cost 10 of producing the good and zero fixed cost.

a) Suppose firms compete as quantity setting duopolists. Find the Cournot Nash equilibrium

of this game. What quantities will they produce, what is the market price and how much

profit does each firm earn? (4 Marks)

b) What happens if firm 2's marginal cost becomes private information and takes either 0 or

10 with probability 1/2? Note that only firm 2 knows the true cost while firm 1 cannot

observe it. Assume firm 1's cost remains to be 10 and this information is common

knowledge. Find a Bayesian Nash equilibrium at this game. What quantities will they

produce? {Note that firm 2's strategy is a function (or, a complete plan of actions

depending on realized costs) from each possible cost to its output} (4 Marks)

c) Now, suppose firm 1 decides how much to produce first; firm 2 chooses only after

observing firm 1's choice. Find the sub-game perfect Nash equilibrium (Stackelberg

equilibrium) of this game. What quantities will they produce, what is the market price and

how much profit does each firm earn? (4 Marks)

d) Suppose the firms form a cartel: each firm produced the same output and maximizes their

joint profit. What quantity would each firm produce? What would be the market price?

What would be the profit of each firm? (4 Marks)

e) Now suppose the firms play this Cournot game infinitely many times, and discount future

profits at a discount factor . For what value of is there an equilibrium where firms

follow the "trigger strategies". {Note in trigger strategies, each firm produces the cartel

output in (your answer in (d) as long as no firm has deviated before, and starts producing

the Cournot output forever after someone deviates} (7 Marks)