Adverse selection and Pareto improvements through compulsory insurance

Abstract

Arrow (1963) and Akerlof (1970) have shown that competitive markets encounter difficulties when there is incomplete and asymmetrical information on product quality or riskiness. The problem of adverse selection arises in insurance markets when the purchaser of insurance has more information about the probability of a loss than the insurance company. If an insurance company is unable to distinguish a high-risk individual from a low-risk individual and each individual knows his probability of a loss, then an insurance policy giving full coverage to a low-risk individual at an actuarially fair premium will not be profitable because high-risk individuals will also purchase it. Thus the private insurance market will not provide insurance policies that offer complete coverage for low-risk individuals at an actuarially fair premium, and Akerlof (1970: 494) conjectured that compulsory health insurance may be justified on a cost-benefit basis.' Pauly (1974) argued that compulsory insurance may lead to a Pareto improvement if the low-risk individuals choose the level of compulsory insurance, and Johnson (1977, 1978) has claimed that compulsory insurance may result in a Pareto improvement even if high-risk individuals choose the level of compulsory insurance. In this paper, it will be shown that the Pauly-Johnson analysis of the case for compulsory insurance is correct given their model of a competitive insurance market in which firms only engage in price competition. Recently, Rothschild and Stiglitz (1976), Wilson (1977), and Spence (1978) have analyzed the equilibrium in a competitive insurance market in which firms can limit the amount of insurance that an individual may purchase. It is shown that if there is a Nash equilibrium with price and quantity competition among firms, then compulsory insurance which does not permit voluntary supplementary insurance will not lead to a Pareto improvement. With supplementary insurance, compulsory insurance may lead to a Pareto improvement in some cases. If a Wilson equilibrium exists with cross-subsidization of insur-