Your utility function is given by U = M^1/2.You have a choice: take $100 in cash or flip a coin.If you flip a coin, the outcomes are as follows: heads, you win $225; tails, you win $49.You will

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Quizplus · Accepted Answer

To make the decision, we need to compare the expected utility of each option. If we choose the $100 in cash, our utility would be:

U(cash) = M*S1*U1*P1^1/2*S1*S1*P0 = M*1*U1*1*1*1 = M*U1

If we choose to take the gamble, our expected utility would be:

U(gamble) = 1/2*(M*S1*U1*(225/100)^1/2*S1*S1*P0) + 1/2*(M*S1*U1*(49/100)^1/2*S1*S1*P0)
= 1/2*(M*U1*(15/10)*(1/2)) + 1/2*(M*U1*(7/10)*(1/2))
= M*U1*0.55

Since the expected utility of the gamble (0.55*M*U1) is greater than the utility of taking the cash (M*U1), we should choose to take the gamble.

Your Utility Function Is Given by U = M1/2

Your Utility Function Is Given by U = M^1/2