A health insurance company knows that there are two types of customers (smokers

Question

A health insurance company knows that there are two types of customers (smokers and non-smokers), each facing different health risks. The probabilities of getting sick and the healthcare costs in the case of illness for the two customer types is given in the table below. Group Healthcare costs Probability of getting sick Smokers $1200 50% Non-smokers $1200 20% Assume that each customer has a monthly income of $1600 and has a utility function given by U(x)=sqrt(x), where x is the remaining income after medical/health insurance expenses have been paid. a. Explain the problem of “adverse selection” and the problem of “moral hazard.” Give one example of a market in which adverse selection occurs and one example of a market in which moral hazard can be observed. What is the difference between the two information problems? Explain the consequences of adverse selection and moral hazard for the principal – agent relationship. b. Discuss in detail the two ways (screening and signaling) in which the principal or the agent can try to resolve the problem of adverse selection. Give an example of screening and signaling and explain how the parties involved benefit from these strategies. c. For the numerical example above construct the lotteries associated with the income that remains after healthcare expenses have been paid for smokers and for non-smokers (assuming agents do not have health insurance). Calculate the expected utility associated with the lotteries for smokers and non-smokers. Calculate the certainty equivalent of the two lotteries. What is maximum amount that smokers and non-smokers are willing to pay for full insurance? Calculate the actuarially fair health insurance premium for the two groups of customers (i.e. the expected healthcare costs). d. Assume the company cannot distinguish between smokers and non-smokers and offers a full insurance contract to all customers. How much should the company charge for the full insurance contract? Which customer group will purchase full insurance?

Explanation / Answer

a) Asymmetric information may give rise to adverse selection. It is refers to a market process in which bad results occur due to information asymmeries between buyers and sellers. Example of insurance. As a result of private information, the insured are more likely to suffer a loss than the uninsured. Example: Suppose that there are two groups among the population, smokers and non-smokers. As the insurer selling life policies cannot distinguish between the two, the beneficiaries while smokers are likely to die younger than average. So the life policy is a better buy for the smokers. The insurance company anticipate or learns that the mortality rate of the combined policy holders exceeds that of the general population, and sets the premiums accordingly. The outcome is that the non-smokers are at disadvantage as they have to pay relatively higher premium. They may go uninsured though if they could buy a policy on terms that are actually fair given their characteristics, they would do so. So, market failure is involved.

Moral hazard refers to situation where one side of market cannot observe action of the other. For this reason, it is sometimes called hidden action problem. For example: If an individual buys an insurance of their car then he become careless towarrds his car and drive it rashly, keep key inside the car to purchase things because person knows that insurance company will bear the cost if anything happen to his car. This lead to market failure.

b. In order to overcome the problem of adverse selection signalling is used by which one side of market provide infromation to the other side of the market. For example: plum owners can offer warranty and by providing warranty they signal to the buyer that they are not purchasing lemon. Similarly, in labor market, a person may signal to the employer about higher productivity. For this purpose we provide information about level of education. In order to indicate better productivity, a person indicate about his education but acquiring education involves cost. So, a person will prefer to get education and incur a cost if by incurring a cost he is able to saperate himself from others. This type of signalling equilibrium is called saperating equilibrium. Because equilibrium involves each type of worker is making a choice that allow him to saperate himself from others.

Screening is an attempt to filter helpful from useless information. Plum car owners shows the test drives, metal of the car to ensure that their car is off good quality, etc.

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