Consider a consumer who buys insurance. The consumer will have an income of = 100. She can consume all of her income in case of no accident, while she can consume $36 in case of accident. The probability of accident is 50%. At the price (premium) of , the consumer can buy an insurance in which she can get in case of accident. Let define 1 as the final consumption in case of accident and 2 in case of no accident.

A. The consumers utility from final consumption is ( ) = , where = 1, 2. Suppose that the consumer can buy an insurance with = 64. What is the maximum amount the consumer is willing to pay for this insurance? Illustrate your answer using a graph. If the consumers utility from final consumption is now ( ) = , what is the maximum amount the consumer is willing to pay for the insurance with = 64? Compare to the case where ( ) = , does the consumers willingness to pay for the insurance increase or decrease? Explain your answer.

B. The consumers utility from final consumption is ( ) = 2 . Suppose that an insurance company sells an insurance in which the company gets $4 profit. Would the consumer buy this insurance? If so, solve and for this insurance, and explain why the consumer buys such an insurance. Illustrate it using a graph.

I am trying to understand the effects of risk averse individuals and insurance--a unit covered in class.I am stuck on this problem in my problem set and I am having a difficulty understanding how to solve it, particularly with a graph. Can someone please help and explain? :)