Y5

Professor Dyvbyg has the opportunity to engage in a gamble that will net him either a gain of $50,000 or a loss of $25,000, each with the probability of . Prof. Dvybyg is an expected utility maximizer with the underlying utility function defined over income (y): U(y) = 12.5859 - 7.4267exp(-0.0000211y) Would Dyvbyg want to undertake this gamble if his current income is $200,000? [NOTE: in both parts of this question, you should carry out your calculations with the same exacting precision as would Prof. Dyvbyg, i.e., to at least five significant digits past the decimal point!] Suppose he could securitize this gamble, which means he prints up 100 shares in the gamble, each of which gives a chance of a gain of $500 and chance of a loss of $250. Suppose Dyvbyg has 99 friends who are his clone, each of whom therefore has precisely the same utility function as Dyvbyg as well as identical incomes. Would his friends be willing to pay Dyvbyg $100 for a 1% share of the gamble? If so, in what position would Dyvbyg find himself in terms of his expected utility?