Question

Consider a market with two firms selling homogenous goods. Let the inverse demand curve be ? =

1210 − 2(?1 + ?2) where p denotes market price and q1, q2 denotes output quantity from firm 1 and

2 respectively. The firms have identical constant marginal costs; c = 10.

Assume first that the firms compete ala Cournot:

a) Derive best response functions and illustrate equilibrium in a diagram

b) Derive equilibrium quantities and prices

c) Compute profit for each firm.

Assume now that the two firms form a cartel

d) Derive optimal price and quantity

e) Assume that the cartel output is shared equally between the two firms. Compute profit for

each firm. Compare the solution to what you found in question c.

Assume that firm 2 stays loyal to the cartel agreement, while firm 1 "cheat". Firm 1 maximize own profits, given that firm 2 produce half the cartel quantity.

f) Explain why the profit maximization problem for firm 1, the cheater, can be written :

"max [?1(1210 − 2(?1 + 150) − 10)]"

g) Solve the profit maximization problem for firm 1 and derive the corresponding optimal

quantity.

h) Compute the market price and derive profits for firm 1 (cheater) and firm 2 (noncheater).

Consider the choice of staying loyal to the cartel agreement as a single decision ("one shot game").

i) Use pay offs (profits) calculated in exercise c, e and h and write down this game in normal

form.

j) Derive equilibrium in this one shot game

k) If the game is to be repeated, are there any strategies that may lead to a reversal of the

conclusion from exercise j).

Answer 1