Question Two Consider a consumer facing a utility function given as U, where utility is a function of income, y Suppose an individual faces a 0.5 probability that they will fall sick and will need surgery which will cost of $20,000 (the 0.5 is the probability that the consumer stays healthy and enjoys utility from his/her full income). Assume that the individual's initial income is $40,000. (a) Calculate the consumer's expected income bearing in mind the probability that he/she could face an illness or he/she could stay healthy. [5 marks] (b) Now, suppose that the individual is offered a health insurance policy that will cover all of his/her medical expenses in the event of illness and this insurance will cost $10,000. Calculate the expected utility with insurance. [5 marks] (c) Determine whether it would make economic sense for the individual buy this insurance policy. Hint. Compare expected utility with and without health insurance. [5 marks] (1) What is the maximum the individual be willing to pay for insurance cover? Hint: Work out the certainty equivalent, i.e. the level of income that would make the individual be just indifferent to having no insurance. So we need to find the Y (certain inconue) that corresponds to the expected utility without insurance. [10 marks] Question Two Consider a consumer facing a utility function given as U, where utility is a function of income, y Suppose an individual faces a 0.5 probability that they will fall sick and will need surgery which will cost of $20,000 (the 0.5 is the probability that the consumer stays healthy and enjoys utility from his/her full income). Assume that the individual's initial income is $40,000. (a) Calculate the consumer's expected income bearing in mind the probability that he/she could face an illness or he/she could stay healthy. [5 marks] (b) Now, suppose that the individual is offered a health insurance policy that will cover all of his/her medical expenses in the event of illness and this insurance will cost $10,000. Calculate the expected utility with insurance. [5 marks] (c) Determine whether it would make economic sense for the individual buy this insurance policy. Hint. Compare expected utility with and without health insurance. [5 marks] (1) What is the maximum the individual be willing to pay for insurance cover? Hint: Work out the certainty equivalent, i.e. the level of income that would make the individual be just indifferent to having no insurance. So we need to find the Y (certain inconue) that corresponds to the expected utility without insurance. [10 marks]