Problem 2.1 (15 points) Andy looks at his account and notices that if the current monthly interest rate stays constant he is expected to have $54,000 in 6 years (i. e. once 6 years have elapsed) and $67,000 in 8 years. (15 points) a. How much money does he have now (at time 0)? (5 points) b. If his predictions are correct, except after 7 years, the nominal rate halves and then stays at that value, how much money will he have in 8 years? Assume the interest rate is compounded monthly. (10 points)

1. consider a two-firm industry. firm 1 (the incumbent) chooses a level of output qı. firm 2 (the potential entrant) observes qı and then chooses its level of output q2. the demand for the product is p 100 q, where q is the total output sold by the two firms which equals qi +q2. assume that the marginal cost of each firm is zero. a) find the subgame perfect equilibrium levels of qi and q2 keeping in mind that firm 1 chooses qi first and firm 2 observes qi and chooses its q2. find the profits of the two firms-n1 and t2- in the subgame perfect equilibrium. how do these numbers differ from the cournot equilibrium? b) for what level of qi would firm 2 be deterred from entering? would a rational firm 1 have an incentive to choose this level of qi? which entry condition does this market have: blockaded, deterred, or accommodated? now suppose that firm 2 has to incur a fixed cost of entry, f> 0. c) for what values of f will entry be blockaded? d) find out the entry deterring level of q, denoted by q1', a expression for firm l's profit, when entry is deterred, as a function of f. for what values of f would firm 1 use an entry deterring strategy?