Suppose that a consumer has a utility function that satisfies CRRA U ( Y ) = with y>0, y#1 1-y = In(Y) with y =1 Suppose initial consumption or income of the consumer is $200,000. a) Suppose that the payoffs from an investment in normal economic times are a 50% chance of $2,000 or a 50% chance of -$2,000. Derive expressions for the risk premium using the exact expression and the approximation (see Chapter 4 of Danthine and Donaldson). Compute the risk premium using the exact expression and the approximation for values y equal to 0, 0.5, 1, 2, 5 and 10. What happens to the difference between these two estimates of the risk premium as y increases? Comment on your results. b) Suppose that the payoffs from an investment in a recession are a 10% chance of $1,000 or a 90% chance of -$10,000. Compute the risk premium using the exact expression and the approximation for with values y equal to 0, 0.5, 1, 2, 5 and 10. What happens to the difference between these two estimates of the risk premium as y increases? Comment on your results