The consumers in an economy own 1 unit of wealth each. They are subject to risk. If

a consumer is not careful, she may lose her wealth with probability p = 0.75. On the

other hand, if a consumer is careful, this probability is 0.25. The utility function of the

consumers is u = x e, where x is wealth and e takes the value 0.1 if the consumer

chooses to be careful and 0 otherwise. In the economy, there is perfect competition

among the insurance companies which, in addition, are risk neutral.

Find the best policy that offers partial coverage.

(b) Interpret the policy in (a) in terms of co-insurance (that is, the insured party pays

a percentage of the loss)

(c) Interpret the policy in (a) as an insurance with a deductible (the insured party

pays a fixed amount).