Question 4 An expected utility maximizing consumer with initial wealth W faces a loss of L with probability p. Her utility-of-wealth function for an arbitrary level of wealth Z is given by: VZ Suppose that the consumer can purchase insurance from a perfectly competitive insurance firm at a per unit of wealth insured, but that the firm charges an additive deductible: if C units of insurance is purchased, the firm pays out (C – d) if the loss occurs, where 0 < d< C. 4.1 Define the certainty equivalent of wealth mathematically, give a verbal explanation of what it means and find and expression for it for this consumer if she could not buy insurance. 4.2 Set up the consumer's problem and derive the first order condition that determines the optimal choice for insurance C*. 3 4.3 Show that the consumer fully insures in the case of actuarially fair pricing, p= r. 4.4 In the case of actuarially fair pricing, p = 7, find the expected profit of the firm, and argue whether the insurance industry is in the short or long run.
Question 4 An expected utility maximizing consumer with initial wealth W faces a loss of L with probability p. Her utility-of-wealth function for an arbitrary level of wealth Z is given by: VZ Suppose that the consumer can purchase insurance from a perfectly competitive insurance firm at a per unit of wealth insured, but that the firm charges an additive deductible: if C units of insurance is purchased, the firm pays out (C – d) if the loss occurs, where 0 < d< C. 4.1 Define the certainty equivalent of wealth mathematically, give a verbal explanation of what it means and find and expression for it for this consumer if she could not buy insurance. 4.2 Set up the consumer's problem and derive the first order condition that determines the optimal choice for insurance C*. 3 4.3 Show that the consumer fully insures in the case of actuarially fair pricing, p= r. 4.4 In the case of actuarially fair pricing, p = 7, find the expected profit of the firm, and argue whether the insurance industry is in the short or long run.
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Transcribed Image Text:Question 4
An expected utility maximizing consumer with initial wealth W faces a loss of L with probability
p. Her utility-of-wealth function for an arbitrary level of wealth Z is given by:
VZ
Suppose that the consumer can purchase insurance from a perfectly competitive insurance firm
at a per unit of wealth insured, but that the firm charges an additive deductible: if C units of
insurance is purchased, the firm pays out (C – d) if the loss occurs, where 0 < d< C.
4.1 Define the certainty equivalent of wealth mathematically, give a verbal explanation of what
it means and find and expression for it for this consumer if she could not buy insurance.
4.2 Set up the consumer's problem and derive the first order condition that determines the
optimal choice for insurance C*.
3
4.3 Show that the consumer fully insures in the case of actuarially fair pricing, p= r.
4.4 In the case of actuarially fair pricing, p = 7, find the expected profit of the firm, and argue
whether the insurance industry is in the short or long run.
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