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{"ops":[{"attributes":{"bold":true},"insert":"1.\u00a0\u00a0\u00a0\u00a0\u00a0"},{"insert":"Consider an individual who is concerned about monetary payoffs in the states of nature s= 1\u2026 S which may occur next period. Denote the dollar payoff in state by x, and the probability that states will occur by p, The individual is assumed to choose x = (x"},{"attributes":{"script":"sub"},"insert":"l"},{"insert":",...,x"},{"attributes":{"script":"sub"},"insert":"s"},{"insert":") so as to maximize the discounted expected value of the payoff. The discount factor is denoted by a; i.e., a = 1\/ (1+ r), where is the discount rate. The set of feasible payoffs is denoted by X, which we assume to be nonempty. \u00a0\n(a) Write down the individual's maximization problem. \n(b) Define v(p, a) to be the maximum discounted expected value that the individual can achieve if the probabilities are p = (p"},{"attributes":{"script":"sub"},"insert":"1"},{"insert":",, . . .p"},{"attributes":{"script":"sub"},"insert":"s"},{"insert":") and the discount factor is a. \nShow that v(p, a) is homogeneous of degree 1 in a.\n"}]}

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