Question

Assume that the insurer can NOT distinguish between the two types of consumers, and can offer only one policy (the same policy to everyone). What will be the breakeven policy premium IF everyone buys the policy? With such a premium, will everyone actually buy the policy? Over long run, what will be the equilibrium policy premium in the market and who will get insurance?

Answer 1

The insurer will prefer to charge a high premium from the consumers who might default and will agree to charge a low premium from the consumers who have a lower chance of defaulting. Now, if the insurer doesn't know whether which type of customers are coming, then he will only agree to charge the premium, which is higher between two, so to reduce the chance of losses. The same thing applies to the consumers, the consumer who might default will agree to take the insurance even at a higher price, and the consumer who is not going to default will only be willing to buy at a lower premium price. Now, the breakeven point for such a situation will be at the position where the insurer agrees to charge his minimum premium. Now, this premium will be higher one, which is equal to what he is willing to give to a faulty consumer, as the insurer will not take a risk.
With such a premium, only the faulty consumers will buy the policies, and the non-default consumers will not but it. Now, in the long run, the equilibrium premium will be equal to the premium at which the insurer is agreed to sell the policy to the faulty consumer, and only the consumers who are going to default will buy this policy.