Retirement planning hal thomas, a 25-year-old college graduate, wishes to retire at age 65. to supplement other sources of retirement income, he can deposit $2,000 each year into a tax-deferred individual retirement arrangement (ira). the ira will earn a 10% return over the next 40 years. a. if hal makes annual end-of-year $2,000 deposits into the ira, how much will he have accumulated by the end of his sixty-fifth year? b. if hal decides to wait until age 35 to begin making annual end-of-year $2,000 deposits into the ira, how much will he have accumulated by the end of his sixty-fifth year? c. using your findings in parts a and b, discuss the impact of delaying making de- posits into the ira for 10 years (age 25 to age 35) on the amount accumulated by the end of hal’s sixty-fifth year. d. rework parts a, b, and c, assuming that hal makes all deposits at the beginning, rather than the end, of each year. discuss the effect of beginning-of-year deposits on the future value accumulated by the end of hal’s sixty-fifth year.

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?