Lawrence invests his money in a special fund for n years. At the end of n years, he has three payout options from which to choose: One-time $11,874.09 cash payment at the end of year n. A perpetuity-immediate with $465.83 level semiannual payments. A 2n-year annuity-immediate with $593.07 level semiannual payments. The annual effective interest rate, i, earned by the fund is constant. Calculate Lawrence’s initial fund value.

Suppose that fixed costs for a firm in the automobile industry (start-up costs of factories, capital equipment, and so on) are $5 billion and that variable costs are equal to $17,000 per finished automobile. because more firms increase competition in the market, the market price falls as more firms enter an automobile market, or specifically, , where n represents the number of firms in a market. assume that the initial size of the u. s. and the european automobile markets are 300 million and 533 million people, respectively. a. calculate the equilibrium number of firms in the u. s. and european automobile markets without trade. b. what is the equilibrium price of automobiles in the united states and europe if the automobile industry is closed to foreign trade? c. now suppose that the united states decides on free trade in automobiles with europe. the trade agreement with the europeans adds 533 million consumers to the automobile market, in addition to the 300 million in the united states. how many automobile firms will there be in the united states and europe combined? what will be the new equilibrium price of automobiles? d. why are prices in the united states different in (c) and (b)? are consumers better off with free trade? in what ways?