(Trigger Prices in Games withUncertainty) Suppose a duopoly is characterized by the following profits: if the two firms collude and charge the joint profit-maximizing price, they each earn a profit equal to 2000 in each period; if the two firms charge theCournot-Nashprice, they each earn a profit equal to 1200 in each period; and if one firm defects while the other charges the joint profit-maximizing price, the firm that defects earns 4000. Now suppose both firms adopt the following strategies:

1. Start by cooperating with each firm charging the joint profit-maximizing collusive price;
2. Continue to sell at the joint profit-maximizing outputs and price unless the other firm increases its output and lowers its price, in which case producetheCournot-Nashquantityand chargetheCournot-Nashpriceforever.

a. If the probability that the game is played in the next period is 0.99, what discount rates will sustain collusion?

b. If the profit under collusionincreases, is it easier or harder tosustain collusion?