Monopoly Profits for Contingent-Claims Contracts When Preferences Are State Dependent

Abstract

This paper considers the expected profit obtainable by a monopoly seller of state-claims contracts confronted by a risk-averse individual with statedependent preferences. This profit is illustrated using Karni's extension of Arrow-Pratt risk premiums (1983). We show that while this is expected profit is unique, the risk premium, when interpreted as a state-contingent willingness to pay, is not. When preferences are state independent and there are no costs except for actuarial costs, the highest expected monopoly profit derives from selling a full-coverage insurance contract at a price leaving the individual just indifferent between full coverage and no coverage (cf. Schlesinger (1983)). Of course, this assumes that the monopolist has complete information about individual tastes and loss characteristics, which in turn mitigates any moral-hazard and adverse selection problems. If the individual must be allowed to choose a level of coverage, the monopolist can set a price (insurance premium) equalling actuarial value (i.e., expected loss) plus a fixed loading for any level of coverage the individual desires. Setting this fixed loading equal to the individual's Arrow-Pratt risk-premium, as defined by Pratt (1964), the individual will choose full coverage and the monopoly's expected profit will equal the risk premium. 1 Before turning to the case of state-dependent preferences, we wish to slightly reinterpret the risk premium. Since the individual would choose full coverage at actuarially-fair insurance prices, the risk premium is the maximum