uppose that Mary's utility function is U(W) = W0.5, where W is wealth. She has an initial wealth of $100. How much of a risk premium would she want to participate in a gamble that has a 50% probability of raising her wealth to $115 and a 50% probability of lowering her wealth to $77? Mary's risk premium is $ nothing. (round your answer to two decimal places)

Note that

Mary's risk premium is $0.9375

Step-by-step explanation:

Mary's utility function,  

Mary's initial wealth = $100

The gamble has a 50% probability of  raising her wealth to $115 and a 50% probability of lowering it to $77

Expected wealth of Mary,

= (0.5 * $115) + (0.5 * $77)

= 57.5 + 38.5

= $96

The expected value of Mary's wealth is $96

Calculate the expected utility (EU) of Mary:-

The expected utility of Mary is $9.75

Mary will be willing to pay an amount P as risk premium to avoid taking the risk, where

U(EW - P) is equal to Mary's expected utility from the risky gamble.

U(EW - P) = EU

U(94 - P) = 9.63

Square root (94 - P) = 9.63

If Mary's risk premium is P, the expected utility will be given by the formula:

Mary's risk premium is $0.9375

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