Statement of a problem № m40198


A person is given m dollars, which he must allocate between an event A and its complement Ac. Suppose that he allocates a dollars to A and m − a dollars to Ac. The person’s gain is then determined as follows: If A occurs, his gain is g1a; if Ac occurs, his gain is g2(m − a). Here, g1 and g2 are given positive constants. Suppose also that Pr(A) = p and the person’s utility function is U(x) = log x for x > 0. Determine the amount a that will maximize the person’s expected utility, and show that this amount does not depend on the values of g1 and g2.

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