Jay has wealth (w) equal to $10,000, and a utility of wealth function given by U(w) = w^1/2 .

There is a 50% chance of an accident occurring today; if there is an accident, Jay will lose 75% of

his wealth.

a) (4) What is Jay's expected utility? How does this compare to the utility he actually

obtains?

b) (5) In a diagram, identify Jay's endowment point, and sketch his indifference curve

through this point. (Be sure to label all relevant curves and points.)

c) (4) On your diagram, indicate how much Jay would be willing to pay for full insurance

against this accident.

Suppose that Jay can decrease the probability of an accident by taking care. In particular, at a

cost of 5 utils, Jay could lower his probability of an accident to 30%. Then Jay's utility would be

U(w) =w^1/2-5, where the levels of wealth with and without an accident are the same as

above.

d) (4) Show that if no insurance is available, Jay would choose to exert the effort.

e) (4) In a new diagram, sketch Jay's indifference curve through his endowment point if

he chooses to exert effort.

f) (5) How does this indifference curve compare to the one you drew in c)? Briefly

explain why.

Recognizing that Jay is better off exerting effort when no insurance is available, a risk neutral

insurance company offers him full insurance against his possible loss at a fair premium based on

effort = 5.

g) (4) True or false: Jay would certainly choose to purchase the insurance, and the

insurance company would have negative expected profits. Explain your answer.