Assume that you have two types of customers in an insurance market.

Assume that you have two types of customers in an insurance market. Both types have the same utility function U(W) = W½ where W denotes wealth. The probability of a bad outcome is pA = ½ for type A customers and qB = ¼ for type B customers. Assume that the level of wealth in the bad outcome is 10000 and that the level of wealth in the good outcome is 50000.

a) Derive the optimal insurance solution assuming that the insurance company acts in a perfectly competitive market under the condition that the risk neutral insurance company can observe the type of each customer. For how much will the customers insure and what will the insurance premium be for each group?

b) Calculate the insurance premium in a competetive market if the insurance company cannot distinguish between the two groups. Assume that each group consists of half of all customers in this market. Is there a problem with this solution? Explain what will happen in this market. (Hint : √10000=100 , √35000 ≈ 187 , √50000 ≈ 224 )

Solutions

Expert Solution

A.) Insurance preium=Premium rates+Bonus coverage=pa*Bad outcome +good outcome=1/2*50000+10000

=1/2*60000=30000

B.) Insurance premium=Estimated preimum/100+187+224(Market rates)

=30000/224=Rs 133 per month

Rahul Sunny answered 1 year ago

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