Assume that a consumer's von Neumann-Morgenstern utility of wealth is u(w) = w, and her initial wealth is w0 = 100. Suppose that there are but two loss levels, l1 = 0 and l2 = 51. There are two effort levels, e = 0 and e = 1. The consumer's disutility of effort is given by the function d(e), where d(0) = 0 and d(1) = 1/3. Suppose that the loss probabilities, l(e), are given below: l1 (0) = 1/3, l2 (0) = 2/3; l1 (1) = 2/3, l2 (1) = 1/3.

(a) Verify that probabilities given above satisfy the monotone likelihood ratio property.

(b) Find the consumer's reservation utility assuming that there is only one insurance company and that the consumer's only other option is to self-insure.

(c) What effort level will the consumer exert if no insurance is available?

(d) Show that if information is symmetric, then it is optimal for the insurance company to offer a policy that induces high effort.

(e) Show that the policy in part (d) will not induce high effort if information is asymmetric.

(f) Compute the insurance policy (premium and coverage) that would induce high effort.