Suppose that an insurance company wants to offer insurance for bicycle theft. They do a careful market survey and find that the incident of theft varies widely across communities. In some areas there is a high probability that a bicycle will be stolen, and in other areas thefts are quite rare. Suppose that the insurance company decides to offer the insurance based on the average theft rate. What do you think will happen? Answer: the insurance company is likely to go broke quickly! Think about it. Who is going to buy the insurance at the average rate? Not the people in the safe communities they dont need much insurance anyway. Instead the people in the communities with a high incidence of theft will want the insurance theyre the ones who need it. But this means that the insurance claims will mostly be made by the consumers who live in the high-risk areas. Rates based on the average probability of theft will be a misleading indication of the actual experience of claims filed with the insurance company. The insurance company will not get an unbiased selection of customers; rather they will get an adverse selection. In fact the term adverse selection was first used in the insurance industry to describe just this sort of problem. It follows that in order to break even the insurance company must base their rates on the worst-case forecasts and that consumers with a low, but not negligible, risk of bicycle theft will be unwilling to purchase the resulting high-priced insurance. A similar problem arises with health insuranceinsurance companies cant base their rates on the average incidence of health problems in the population. They can only base their rates on the average incidence of health problems in the group of potential purchasers. But the people who want to purchase health insurance the most are the ones who are likely to need it the most and thus the rates must reflect this disparity. In such a situation it is possible that everyone can be made better off by requiring the purchase of insurance that reflects the average risk in the population. The high-risk people are better off because they can purchase insurance at rates that are lower than the actual risk they face and the low- risk people can purchase insurance that is more favorable to them than the insurance offered if only high-risk people purchased it.

Consider the bicycle example. Suppose that the insurance company must not differentiate by the districts where theft happens. What will be the equilibrium? Why?