= You have a logarithmic utility function U(W) = ln(W) and your current level of wealth is 5,000 (a) Suppose you are exp

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You Have A Logarithmic Utility Function U W Ln W And Your Current Level Of Wealth Is 5 000 A Suppose You Are Exp 1 (59.58 KiB) Viewed 172 times

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 Exp 2 (38.53 KiB) Viewed 172 times

= 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 < 125 you should not buy the insurance.