only (iv)

An individual invests in a project. He is risk averse, with a utility index v(m) = Vm, where m is the money he earns from the project. If the project succeeds, he will earn an income of m = mo > 0, but if it fails, he gets m = 0. Suppose the probability of the project succeeding is p, which is between zero and one. (i) What is the individual's expect income from the project? Denote this value by m. (ii) Write down an expression for the individual's expected utility from the project. (Hint: it should be a function of p and mo.) (iii) If the individual got the expected income of the project, m, for sure, what would his expected utility be? How does this compare with the expected utility of the project that you calculated in part (ii)? (iv) Suppose the individual could purchase insurance on the market. This insurance contract guarantees the individual a fixed level of income, no matter what happens with the project. Let m be the smallest fixed level of income that the individual would accept from the insurance company. Show that the risk premium, m - m, is m - m = p(1 - p)mo