interactions among deeisions Consider a setting in which Ralph is risk averse with utility function for total cashofU(totalcash) = [total casht. At present Ralph has 1,000 cashin hand, sowe have U(x) = [1,000 + x t, where x denotes cash flow from whatever decision must bernade.

a] First, eonsider an option to pay 1,000 up front in exchange for something we will call1ottery L. The holder of lottery L will receive 3,000 with probability .5 and o with probability.5. Verify that Ralph is not too interested in such a gamble, given its price of 1,000.

b] Second, suppose Ralph already owns (actually, inherits without having to pay the 1,000 for) such a lottery and is eontemplating the purchase of a seeond. Thus, ifthe additionallottery is not acquired, Ralph's cash will total1,000 + x = 1,000 +

3,000 if good luck prevails and 1,000 + Ootherwise. Verify that Ralph is not too interested in purchasing the seeond L lottery if its outeomes are independent ofthose of the originallottery, but is very interested if its outcomes are perfectly negatively eorrelated with those of the originallottery. (In the latter case the total cash will be 1,000 + x = 1,000 + 3,000 - 1,000.)

c] Finally, what does this teIl you about the importanee of Ralph' s current stock of lotteries in evaluating yet another lottery?

AppendixLO1