Consider the following moral hazard insurance model.Consider an individual who has an initial wealthw0 = 100 who faces a possible loss of $51. The loss will occur with a probability that depends on the individual's choice of effort.

There are two possible levels of effort,e = 1 ande = 0. The individual's utility is a function of both wealth and effort, and is given byU(w,e) = w^1/2 - d(e),whered(e)is the disutility of effort, andd(0) = 0and d(1) = 1/3.

Finally, suppose that the loss probabilities are given by the following table:

no loss loss = 51

e = 1 1/3 2/3

e = 0 2/3 1/3

a)(5) Which effort level will the individual choose if no insurance is available?

Suppose now that this individual has access to actuarially fair insurance, andeffort is observable.

b) (3) What will be the cost of full insurance for each level of effort?

c) (5) Will the individual purchase insurance in this market? Why or why not?

d) (3) Which policy would the individual prefer? Explain briefly.

e) (6) Is the insurance market efficient? Explain briefly.

Suppose now that an insurance companycannotobserve the individual's effort choice. Insurance is still actuarially fair.

f) (5) Will the policy preferred by the individual when effort is observable be available when effort is not observable? Briefly explain why or why not.

g) (6) Explain how you would determine the optimal policy given this asymmetric information. How does it compare to the policy preferred by the individual when effort is observable?

h) (5) Compare the company's profits when effort is observable, and when it is not.

i)(6) Compare the individual's utility when effort is observable, and when it is not.

j)(6) What is the social cost of asymmetric information in this case, and who bears this cost?