3. In the second example, we will consider the case where the insurance contract involves a deductible this is an amount which is deducted from the final pay-out of the insurance firm in the case of a loss. In other words, the consumer bears this part of the loss herself. For this problem, assume a risk-averse, expected utility maximizing consumer with initial wealth wo who faces a potential loss of size L which will occur with probability p. Her utility-of-final-wealth function is denoted by u(.). Suppose that the consumer can purchase insurance coverage of C > 0 units of wealth from a perfectly competitive insurance firm at a premium of T per unit of coverage, but that the firm charges an additive deductible: if C units of insurance is purchased, the insurance firm pays out (C – d) if the loss occurs, where d >0 is a fixed amount independent of C. (a). For this problem, state the consumer's expected utility function. (b). Set up the consumer's utility maximization problem and find the optimal choice of C*. (c). If the price per unit of insurance is actuarially fair, i.e. if 7 = p, will the consumer choose to fully insure or under-insure? Provide reasons for your answer

3. In the second example, we will consider the case where the insurance contract involves a deductible this is an amount which is deducted from the final pay-out of the insurance firm in the case of a loss. In other words, the consumer bears this part of the loss herself. For this problem, assume a risk-averse, expected utility maximizing consumer with initial wealth wo who faces a potential loss of size L which will occur with probability p. Her utility-of-final-wealth function is denoted by u(.). Suppose that the consumer can purchase insurance coverage of C > 0 units of wealth from a perfectly competitive insurance firm at a premium of T per unit of coverage, but that the firm charges an additive deductible: if C units of insurance is purchased, the insurance firm pays out (C – d) if the loss occurs, where d >0 is a fixed amount independent of C. (a). For this problem, state the consumer's expected utility function. (b). Set up the consumer's utility maximization problem and find the optimal choice of C*. (c). If the price per unit of insurance is actuarially fair, i.e. if 7 = p, will the consumer choose to fully insure or under-insure? Provide reasons for your answer

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.5P

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