Suppose a consumer has a wealth of W. There is a probability p of a loss...

 

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Suppose a consumer has a wealth of W. There is a probability p of a loss of L if an adverse event happens. The consumer can buy insurance that will pay him Q in case that the loss happens. The consumer has to pay per dollar insured as the premium. The consumer's problem can be formulated as pU(WLQ)+(1 p)U(WQ) maxQ i) Find the first order condition. ii) iii) Note that the expected profit for the insurance company is (1-p)Q-p(1-)Q. Suppose that the market is competitive which forces the expected profit to be zero. In this case, find 7. If the consumer is strictly risk-averse i.e. dU/dW <0, show that under (ii) the consumer fully insure against the lost i.e. Q* = L Suppose a consumer has a wealth of W. There is a probability p of a loss of L if an adverse event happens. The consumer can buy insurance that will pay him Q in case that the loss happens. The consumer has to pay per dollar insured as the premium. The consumer's problem can be formulated as pU(WLQ)+(1 p)U(WQ) maxQ i) Find the first order condition. ii) iii) Note that the expected profit for the insurance company is (1-p)Q-p(1-)Q. Suppose that the market is competitive which forces the expected profit to be zero. In this case, find 7. If the consumer is strictly risk-averse i.e. dU/dW <0, show that under (ii) the consumer fully insure against the lost i.e. Q* = L