12.1 Adverse Selection in the Insurance Market
A key assumption of the theory presented in the previous chapters is that all agents have access to the same information relevant to their decisions. As we have seen, this assumption allows us to demonstrate the efficiency of competitive markets, where prices fully reflect preferences, costs, and event probabilities. However, in many markets, information is often distributed unequally between the parties. An informational asymmetry arises when one party involved in an economic transaction possesses information that the other does not. This can impair the proper functioning of the market.
Informational asymmetry can take two forms: adverse selection, which we discuss in this chapter, and moral hazard, which we will cover in Chapter 13. Both phenomena were originally observed in insurance markets, where companies recognized the difficulties arising from unequal distribution of information. In particular, before signing the contract, the insurer may be unable to distinguish between high-risk and low-risk clients, and may end up attracting mostly those more prone to claims: this is the problem of adverse selection. After the contract is signed, the insurer cannot observe the behavior of the insured, who may be incentivized to take greater risks relying on the coverage: this is the problem of moral hazard.
In this chapter, we focus on the problem of adverse selection, analyzing it first in the context of the insurance market. In the next section, we will extend the analysis to the labor market, where firms face similar challenges when selecting workers whose productivity is unknown.
Observable Heterogeneous Risks
In Chapter 11, we analyzed a competitive insurance market in which all individuals face the same risk of loss. In that context, the contract offered by the insurance company included a premium equal to the expected value of the claim, and each individual decided whether to purchase coverage based on their degree of risk aversion. The resulting equilibrium was efficient: all transactions that generated a net surplus were realized, and the area between the demand curve and the horizontal supply line represented the maximized social surplus.
Let us now suppose that the population consists of two groups of individuals, $A$ and $B$. The two groups are equal in size and identical in the distribution of risk attitudes: each group contains exactly 500 risk-averse individuals, that is, with $\pi < 1$. All individuals have an initial wealth of $10000$ euros, which they may completely lose. The difference between the groups lies in the probability that the loss occurs: for group $A$ it is $0.25$, while for group $B$ it is higher, at $0.75$.
As in the previous chapter, within each group the variation in risk aversion results in a downward-sloping demand curve for insurance. For simplicity, we again assume that this curve is linear. Since an individual with $\pi \approx 0$ is willing to pay up to $10000$ to insure themselves, and one with $\pi \approx 1$ is willing to pay the fair premium, the demand curve for each group must pass through two points: $(0, 10000)$ and $(500, 10000p)$, where $p$ is the loss probability of the group. From these conditions, it follows that the demand curve for the low-risk group is:
\(\begin{gathered} P = 10000 - 20 \times (1 - 0.25) \times Q_A \end{gathered}\)
and the demand curve for the high-risk group is
\(\begin{gathered} P = 10000 - 20 \times (1 - 0.75) \times Q_B \end{gathered}\)
where $Q_A$ and $Q_B$ represent the number of individuals in each group willing to purchase a policy at a given price $P$. As illustrated in Figure 11.4, for a given level of risk aversion, those facing a higher probability of loss assign greater value to insurance coverage. As a result, the demand curve of the high-risk group lies above that of the low-risk group: for any given price level, this group demands more insurance.
If insurance companies can observe the risk level of their clients, then two separate markets effectively form — one for low-risk and one for high-risk individuals. In both, companies will offer contracts with premiums corresponding to the expected value of the loss: $2500$ for the low-risk group, and $7500$ for the high-risk group.
As in the homogeneous-risk case, each individual decides whether to purchase the policy by comparing the price to their willingness to pay. Risk-averse individuals buy the policy, others do not. Since the price matches the expected cost, insurance companies make no profits. A transaction takes place only if it generates a net gain for the insured. In equilibrium, social surplus is therefore maximized within each group — and thus in the population as a whole.
This result shows that the presence of heterogeneous risks does not compromise market efficiency, provided that information is symmetric. The market carries out all efficient transactions, and the area between each demand curve and the corresponding fair premium represents the total surplus achieved, which is maximized. This situation serves as a useful benchmark to assess what happens when risk information is no longer observable — that is, in the case of asymmetric information, which we now turn to.
Heterogeneous and Unobservable Risks
Let us now assume that the insurance company cannot distinguish between individuals of the two groups. Unable to offer differentiated premiums, the company must propose a single contract, valid for all. In this case, the premium must reflect the average risk among the insured, which in turn depends on the number of individuals from each group who choose to buy a policy at that price. Let us return to the demand curves given above:
\(\begin{gathered} P = 10000 - 20 \times (1 - 0.25) \times Q_A \\ P = 10000 - 20 \times (1 - 0.75) \times Q_B \end{gathered}\)
From these two equations, we see that for any price $P$, the quantity of policies demanded by group $B$ is exactly three times that demanded by group $A$. In other words, at any given price $P$, among the individuals willing to buy insurance, one in four is low-risk and three in four are high-risk. The average risk among the insured is therefore \(\frac{1}{4}\times 0.25 + \frac{3}{4} \times 0.75 = 0.625\) which implies that the premium that leaves zero profits for the insurance company is $10000 \times 0.625 = 6250$. This is the equilibrium price when risks are not observable.
This equilibrium is distorted relative to the case of symmetric information. Some risk-averse individuals from group $A$ who previously found it worthwhile to buy insurance now withdraw from the market. Meanwhile, some risk-loving individuals from group $B$ who previously found it unprofitable now choose to buy. The composition of demand shifts toward riskier individuals, and the total surplus in the market is reduced. In equilibrium, not all efficient transactions occur, and some inefficient transactions take place.
This is the phenomenon of adverse selection: private information induces higher-risk individuals to be overrepresented among the insured, driving lower-risk individuals out of the market. In extreme cases, this mechanism can trigger a downward spiral that leads to the collapse of the market altogether.