Product Different And Performance in Insurance Markets

Insurance markets can be afflicted with several kinds of informational problems. One of the most common is that the expected cost of a policy to the insurer varies with the person to whom it is sold. The expected cost differences from one person to the next are not easily observed by the insurer.

If the differences are not observed, the prices cannot depend directly on differences in expected cost. The resulting market failure is commonly referred to as the adverse selection problem. A lucid discussion of its effects can be found in Akerlof (1970).

Not only may individuals differ in the expected cost they impose upon the insurer, they may also differ in their preferences with respect to insurance coverage. High risk people will generally place a higher value on insurance coverage than low risk people.

Moreover since insurance policies can vary in the amount of coverage, individuals can choose different amounts of coverage at any given price per dollar of coverage, because of the different preferences.

Thus individuaIs in an insurance market can differ in expected cost or risk to the insurer, and they can differ in their valuations of coverage.

These two dimensions are often correlated. For example, with attitudes toward risk held constant, high risk people will have a higher expected cost to the insurer and place a higher value on insurance coverage than low risk people.

We may then see a positive correlation between benefits and costs of coverage. Under conditions where people differ with respect to preferences, the issue of product differentiation arises.

In a market that is not afflicted with the problem of sellers not knowing expected costs for each individual, we would expect to see a menu of policies offered, and a selection from the menu made by consumers.

With impacted information, product differentiation does not disappear. But a competitive market is not able to provide the efficient menu of policies and to induce the consumers to make the correct choices.

The reason is that when the policies designed for the low risk people are priced at the expected cost for low risk people, the high risk people will tend to buy those policies because of the lower cost.

This forces the low risk people to consume less insurance and sometimes to pay more for it than its expected cost in order to be distinguished from high risk people.

Thus there are directional, informationally-based negative externalities running from high to low risk people, that damage the latter and impair the performance of the market. The market responds to this situation by implicitly maximizing the benefits to low risk people subject to the constraints imposed by the informational asymmetries.

This paper deals with the qualitative properties of such equilibria. This problem was first dealt with by Rothschild and Stiglitz (1976) and Wilson (1976). Both identified an equilibrium existence problem.

Wilson developed an alternative concept of equilibrium that I have employed here. Miyazaki (1977) extended Wilson’s analysis and showed in a two group model, that the equilibrium in the market is the solution to a constrained optimization problem.

This paper attempts to generalize Miyazaki’s work to an arbitrarily large number of groups, and to apply the results to the insurance market. A final word about the basic problem. The expected cost of an insurance policy to the insurer can vary from consumer to consumer for a number of reasons. Individuals may have different risks or probabilities of the adverse events.

But there are other reasons. For example, if medical insurance pays a fraction of the cost of care up to some limit, then two people may consume different amounts of medical care in each health state because they have different preferences with respect to health care.

Thus even if the underlying risks are the same the consumption of health care and hence the expected cost to the insurer may vary from individual to individual. Either differences in risks or differences in preferences can cause unobserved differences in expected cost to the insurer.

It is worth noting however, that in the medical care example just cited, the problem arises in part because the insurer does not directly observe the health state of the individual, and hence is forced to pay off to expenditures on care.

For a fuller analysis of this kind of moral hazard problem. see Zeckhauser (1970). To illustrate the qualitative problems encountered in insurance markets with unobserved cost differentials, I shall begin with the case of two groups, and then generalize to the case of n groups, where IZ can be arbitrarily large.

Section 2 deals with two group case. Section 3 describes the n-group problem and exhibits the optimizing problem, the solution to which is the equilibrium in the market. Section 4 argues that the solution is in fact an equilibrium.

It is somewhat technical, and can be skipped by those who are not interested. Section 5 summarizes the properties of the impacted information equilibrium. Section 6 discusses briefly the implications of introducing distributional considerations explicitly. Brief conclusions are contained in section 7.

The material in section 2 is not new. It summarizes the work of Wilson (1976) and, most directly, Miyazaki (1977). The latter was developed in the context of a labor market, but is formally directly applicable to insurance markets.

Location: Indonesia