Optimal Insurance and Generalized Deductibles

by Kenneth Arrow

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Develops the theory of demand for insurance where the marginal utility of income varies with the state of the world. It relaxes the assumption in the author's earlier work that the utility function is independent of the state of the world. If the utility function is independent of the state of the world, an optimal insurance policy makes income equal or exceed a critical level. Relaxing this assumption leads to a policy in which the marginal utility of income is no greater than a certain level. The following result is derived: at an optimal insurance policy, the ratio of the expected to the maximum marginal utility of postinsurance income is equal to the exogenously given benefit-premium ratio. If the insurance is fair, so that benefit-premium ratio equals one, all states are insured. The amount of insurance purchased is shown to be sensitive to loading charges.

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