An individual invests in a project. He is risk averse, with a utility index v(m) = m , where m is the money he earns from the project. If the project succeeds, he will earn an income of m=m0> 0, but if it fails, he gets m=0. Suppose the probability of the project succeeding is p, which is between zero and one.

-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^ = p(1-p)m0