Two farmers sell their product to a particular community. The inverse demand for the product in that community is

p=60-4q1 -5q2,

where qi is the amount produced by firm i = 1, 2. Both farmers produce at zero cost.

(a) Suppose this is a one-shot game. Find the Cournot-Nash equilibrium.

Suppose the farmers decide to work together forever. They agree that 5/9 of all customers are to be served by farmer 1 and the rest by farmer 2 in every period.

(b) Determine the per-period total quantity sold and the profits of each farmer when they maximize aggregate profits.

(c) What is the critical level of the discount factor ?, such that collusion is sustainable infinitely when farmers follow simple grim strategies (revert to Cournot-Nash strategy in case of deviation).

1. Two farmers sell their product to a particular community. The inverse demand for the product in that community is P = 50 - 4m - 5'12. where q. is the amount produced by firm i = 1, 2. Both farmers produce at zero cost. (a) Suppose this is a one-shot game. Find the Cournot-Nash equilibrium. Suppose the farmers decide to work together forever. They agree that 5/9 of all customers are to be served by farmer 1 and the rest by farmer 2 in every period. (b) Determine the per-period total quantity sold and the profits of each farmer when they maximize aggregate profits. (c) What is the critical level of the discount factor 5, such that collusion is sustainable infinitely when farmers follow simple grim strategies (revert to Cournot-Nash strategy in case of deviation)