Question

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​?

Answer 1

risk premium = $4.39

Step-by-step 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