Question

b. My utility is U(w) with initial wealth W. There is a 50% chance I gain $x (so my wealth becomes W +x), and a 50% chance I lose $x so my wealth falls to W-x. Let c be my certainty equivalent for this gamble. Explain how the sign of the derivative dc/dx depends on my attitude towards risk.

Answer 1

nswer to question b. Your attitude towards risk determine whether you will take higher risk or lower risk. In the derivative dc/dx, dc is the change in the certainty equivalent and the dx is the change in the gain/loss. When the attitude towards risk is higher, the certainty equivalent for the gamble will be lower. Hence, when the numerator is lower, the sign of derivative will be negative. But when the attitude towards risk is lower, then the certainty equivalent will be higher and hence with higher numerator the derivative dc/dx will have positive sign.