Home | Business News | Browse by Publication | E | Economic Theory

The impact of prudence on optimal prevention.

Article Excerpt
Summary. What are the determinants of the optimal level of effort to reduce the probability of a loss to occur? Whereas most of the literature on this question focused on risk aversion, we show that the concept of prudence (i.e., a positive third derivative of the utility function) is essential to answer this question. We explain in this paper that prudence and prevention tend to be opponents rather than allies contrary to the intuition attached to everyday language.

Keywords and Phrases: Stochastic dominance, Prudence, Prevention.

JEL Classification Numbers: D61, D81.

1 Introduction

Prevention--or self protection in the terminology of Ehrlich and Becker (1972)--is an effort undertaken to reduce the probability of occurrence of an adverse effect. What is the level of effort that would maximize the expected utility u of the representative agent in the economy? In many instances, the cost-benefit analysis of prevention is examined under the assumption of risk neutrality. In reality, for most catastrophic risks like global warming, earthquakes or epidemic diseases, the assumption of risk neutrality is not acceptable. The question is thus to determine how to take into account the non linearity of the utility function in the cost-benefit analysis of preventive actions. One suspects that more prudence increases the willingness to engage into preventive activities.

When prudence is used in its colloquial sense, the relationship between prudence and the propensity to self-protect is almost tautological. However prudence has now in economics a very precise technical sense that makes its relationship with prevention less transparent. The notion of prudence was introduced by Kimball (1990) to measure the willingness to accumulate wealth in the face of a future risk. Namely, an agent is prudent if an increase in future risk in the sense of Rothschild-Stiglitz raises the marginal value of wealth. If the agent is an expected-utility-maximizer, the marginal value of wealth equals the expected marginal utility of future consumption. Using Jensen's inequality, this implies that an agent is prudent if and only if u'" is positive.

In this paper we analyze in details the link between prevention and prudence. This approach is rather new since most of the existing literature focused on the relationship between prevention and risk aversion. For instance, Dionne and Eeckhoudt (1985) showed that an increase in risk aversion has an ambiguous effect on the optimal level of effort. The intuition of this result is simple. Suppose that it is optimal for the risk-neutral agent not...

View this article FREE - Now for a Limited Time, try Goliath Business News
Free for 3 Days!