Please explain the steps taken in the answer below + Why do we count E(U(W)) when we aren't using the value in the calculations?

= You have a logarithmic utility function U(W) = ln(W) and your current level of wealth is 5,000 (a) Suppose you are exposed to a situation that results in a 50/50 chance of winning or loosing 1,000 . If you can buy insurance that com- pletely removes the risk for a fee of 125 , will you buy it or take the gamble? (b) Suppose you accept the gamble outlined in (a) and lose, so that your wealth is reduced to 4,000 . If you are faced with the same gamble and have the same offer of insurance as before, will you buy the insurance the second time around? = 1. E[U[W]] = (1 (1 P)ln(W loss) + Pln(W + win) = (1 P)ln(5,000 )) 1,000) + Pln(5,000 + 1,000) = {ln(4, 000) + { ln(6000) = 8.4967825 2. Notice that enW = W Hence to map from utility to certainty equivalent e8.4967825 = 4,898.98 3. Risk premium is W - CE = 5,000 4,898.98 = 101.02. 4. Because 101.02