You have a logarithmic utility function U(W) = In 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 losing $1,000. If you can buy insurance that completely 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?