Suppose Joe and Rebecca engage in a repeated Cournot competition in which they can change their quantity decisions only once a year. The yearly demand function and costs are the same as in Worked-Out Problem 19.1. Derive the largest yearly interest rate for which each has an incentive to adopt the following strategy: Produce half the monopoly output (1,500 cubic yards) if no one has yet deviated from that output level; otherwise, produce the Cournot output of 2,000 cubic yards. (Hint: You will need to figure out a firm's most profitable deviation from the monopoly output in order to see when deviating from it is profitable. The most profitable deviation involves the firm playing its best response to its rival's output of 1,500 cubic yards.)