Consider a duopoly formed by firms 1 and 2, producing a homogeneous good.

The demand for this market is represented by the following function:

P = 30 - Q

And the cost of both firms is given by

C (q_i) = q_i, i = 1,2.

(i)Assume that firms compete in quantity.Calculate the Cournot balance: quantity produced and profit for each firm and the market price.

In the following items, firms compete on price.

(ii)Calculate the balance of Bertrand: quantity produced and profit of each firm and the market price.

(iii)Now the firms decide to form a cartel.Find the quantity produced and profit of each firm and the market price of the cartel.

(iv)Consider now the infinite repeated game of these firms, and that they adopt the trigger strategy.Find the discount rate that allows the cartel price to be sustained in a balance of repeated play.