Question

Assume that Julia is playing a gamble that pays $150 if whe wins and $50 if she loses. The probabiltiy of winning and losing are equal to 1/2. Assume that her utility function is given as below.

U(W)=W^(1/2)

Calculate the risk premium for this individual. Describe your steps and draw a graph that shows risk premium.

Answer 1

Payoff if wins=$150

Payoff if loses=$50

Probability of win=0.5 and Probablity of Loss=0.5

U(W)=W^0.5

Risk Premium=Expected Payoff-Certainy Equivalent

Expected Payoff=Prob.of WIn*Payoff if wins+(1-Prob.of loss)*Payoff if loses

=0.5(150)+0.5(50)=100

Certainty Equivalent=Inverse of Expected Utility

Expected Utility=Prob.of WIn*Utility if wins+(1-Prob.of loss)*Utility if loses

=0.5*(150)^1/2+0.5*(50)^1/2=9.6592

Certainty Equivalent=U(-1)(EU)=9.6592^2=93.30

Risk Premium=100-93=7