Suppose 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 $112 and a 50% probability of lowering her wealth to $70 ?

risk premium = $4.39

Explanation:

given data

U (W) = W0.5

initial wealth = $100

wealth = $112

probability of raising = 50%

probability of lowering = 50%

wealth to = $70

to find out

risk premium

solution

we know here initial wealth = $100

so as given function

U (W) = W0.5 ... 1

expected utility will be

expected utility = 0.5 * √115 + 0.5*√78

expected utility = 5.362 + 4.416

expected utility is $9.9778

so amount give to utility to given certainty is

√w = $9.778

so w = $95.61

so here risk premium is difference so

difference is 100 - 95.61

risk premium = $4.39