= = = = = = = 2. (10 points) Assume that a consumer's von Neumann-Morgenstern utility of wealth is u(w) Vw, and her init

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2 10 Points Assume That A Consumer S Von Neumann Morgenstern Utility Of Wealth Is U W Vw And Her Init 1 (87.71 KiB) Viewed 38 times

2 10 Points Assume That A Consumer S Von Neumann Morgenstern Utility Of Wealth Is U W Vw And Her Init 2 (19.82 KiB) Viewed 38 times

= = = = = = = 2. (10 points) Assume that a consumer's von Neumann-Morgenstern utility of wealth is u(w) Vw, and her initial wealth is wo = 100. Suppose that there are but two loss levels, l1 = 0 and 12 = 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, 7(e), are given below: TT1,0) = 1/3, 412 (0) = 2/3; 71 (1) = 2/3, T12 (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 th consumer exert if no insurance is available? (d) Show that if information is symmetric, then it is optimal for the insur- ance company to offer a policy that induces high effort.
(e) Show that the policy in part (d) will not induce high effort if informa- tion is asymmetric. (f) Compute the insurance policy (premium and coverage) that would in- duce high effort.