1. A consumer has the following utility function U= ln(5I) whereIis the income. She works for a store and earns a regular income of $12,000 per month. However, there is a chance that she gets fired and in that case she has to go on unemployment insurance, which only pays $4,000 a month. The probability of getting fired is 25%.

a) Depict the utility of this consumer on the following diagram. Calculate the expected utility for this consumer and identify it on the graph. Demonstrate that his utility of expected is higher than his expected utility. (round to three digits)

b) Now suppose that the insurance company is offering a partial insurance of $1,000 (in the case of lost job $1,000 will be paid to the consumer) at a premium of $150. Would the consumer insure herself?

c) So far we have assumed that the probability of losing the job is 25%. Now suppose that is not necessarily the case. What would be the maximum probability such that she is indifferent between insuring and not insuring herself if she is offered the insurance as described in part (b).