Mark receives 500,000 at his retirement. He invests 500,000−X in an annual payment 10 year annuity-immediate and X in an annual payment perpetuity-immediate. His total payments received per year during the first 10 years are twice as large as those received thereafter. The annual effective rate of interest is 6%. Calculate X.

Consider a two-firm industry. firm 1 (the incumbent) chooses a level of output q1. firm 2 (the potential entrant) observes q1 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 q1 +q2. assume that the marginal cost of each firm is zero. a) find the subgame perfect equilibrium levels of q1 and q2 keeping in mind that firm 1 chooses q1 first and firm 2 observes q1 and chooses its q2. find the profits of the two firms-? 1 and ? 2- in the subgame perfect equilibrium. how do these numbers differ from the cournot equilibrium? b) for what level of q1 would firm 2 be deterred from entering? would a rational firm 1 have an incentive to choose this level of q1? 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 q1, denoted by q1b, as a function of f. next, derive the expression for firm 1

Awidower devised his fee simple interest in his residence as follows: “to my daughter for life, then to my oldest grandchild who survives her.” at the time of the widower’s death, he was survived by his only two children, a son and a daughter, and by one grandchild, his daughter’s son. a short time later, the daughter together with her son entered into a contract to sell the residence in fee simple to a buyer. the applicable jurisdiction continues to follow the common law rule against perpetuities, but has abrogated the rule in shelley’s case. at the closing, the buyer refused to purchase the residence. can the sellers compel the buyer to do so?

At cooly cola, we are testing the appeal of our new diet one cola. in a taste test of 250 randomly chosen cola drinkers, 200 consumers preferred diet one cola to the leading brand. assuming that the sample were large enough, the large-sample 95% confidence interval for the population proportion of cola drinkers that prefer diet one cola would be: