Suppose that in the repeated Bertrand model discussed in Section 19.5, Joe and Rebecca take only a week instead of a month to observe and respond to each other's prices. Derive the largest weekly interest rate for which the two producers have an incentive to follow this strategy: Charge the monopoly price of $70 if no one has yet undercut that price; otherwise, charge $40 (equal to marginal cost). What is the largest weekly interest rate when price changes take a month?