Bill's income is $50,000. There is a 30% chance Bill will get sick during the next year. If Bill gets sick, he will incur a loss of $20,000. His utility function is U(I)=I^1.1(that is, utility equals Income to the 1.1 power).

a) Calculate the actuarially fair insurance premium for Bill (5 points)

b) If the insurance company charges Bill an actuarially fair insurance premium, will Bill purchase Insurance? Explain why or why not. (5 points)

c) If the insurance company charges Bill a premium of $5,000, will Bill purchase Insurance?Explain why or why not. (5 points)

e) Show a-c using a diagram (5 points)