The demand functions for products 1 and 2 produced by firms 1 and 2 are: q1 = 12 - p1 + 0.6p2 q2 = 12 +0.6p1 - p2

(a) Find the differentiated Bertrand prices for goods 1 and 2. Find the profits of firms 1 and 2.

(b) Find the joint profit-maximizing (cartel) prices of goods 1 and 2 and the profits of firm 1 and 2.

(c) Find the price that would maximize the profit of either firm given that the other is charging the cartel price. Is undetected cheating on the cartel agreement profitable? Explain.

(d) Show that if producer 1 catches producer 2 cheating, it would be profitable for 1 to retaliate by reverting to its non-cooperative (differentiated Bertrand) price level.

(e) Suppose undetected cheating occurs for two periods in an infinitely repeated game. Upon discovery, competition reverts to differentiated Bertrand forever. Find the interest rate at which cheating becomes profitable.