Insurance Market and Adverse Selection:

We  repeat those results here  by  spelling out the problem explicitly, in principal-agent framework. You  know that the insurance company has less information about the  r.isks regarding illness of the insured than the insured individuals themselves.

Suppose that there are two groups of individuals, the high-risk group (H) and the low-risk group (L). Take their probabilities of illness or accident as P_H and P_L with  P_H >  P_L. Both groups  buy  insurance and the company cannot distinguish them.  The weighted average probability  of  illness for the whole group given by

In this formulation  P,  >  > 4,  .  If the cost of illness is C, then the insurance premium I for a full coverage will be

If individuals know their own risks, since P' >P_L, ,  the ones with low risk may not  be willing  to  buy  insurance whereas the high risk individuals would be willing  to  accept  the  offer. When low-risk agents drop out,  the  insurance company has to raise the premium, and only the high-risk individuals will buy the insurance. The low-risk individuals will go without any insurance.

To bye pass the problem, the insurance company can get the  low-risk people to reveal themselves  by  offering coinsurance or  some deductibility scheme. This process is known as "self-selection."  Such a move will help the insurance company to infer  the  risk characteristics of individuals.  However,  the information problem  in not completely solved. The information conveyed by the individual's  choice of a particular contract depends on the set of contracts available to the individual.

With  two groups  of  individuals with different probabilities  of  disaster (illness), there cannot, theoretically speaking, be  a single insurance policy. If at all, there have  to  be  two  insurance policies, and  it can be shown that the high-risk individual obtains complete insurance and the low-risk individual obtains only partial insurance.

We can incorporate other examples of adverse section as well. Try to consider the following: 

Labour Contract: A  firm may offer only  low wage without knowing the potential workers, which will give rise to recruiting least productive workers. These are the  types of workers who would be\willing  to accept the offer made.

Financial Markets:  A  bank  may  fail to observe  the  risk-return characteristics of a project. Consequently, it will extend credit facilities to bad projects while rationing credit to good projects. For  more instances  of  adverse selection  you may  also note  the  following contracts:

Landlord-Tenant  Case:  The  landlord delegates  the  cultivation of  his land  to  a  tenant who will  be  the  only  one  to  observe  the  exact local weather condition (i.e., the private information)

Legal Attorney-Client  Case:  A  client delegates  her  defence  to  an attorney who only has the private knowledge of the difficulty of the case.

Investor -  Broker Deals: An investor would delegate the management of her portfolio to a broker, who only knows the market conditions.