A consumer has a utility mction of income Y of the form:

A consumer a utility -on of income Y of 50*Y Furthermore, her demand for medical care Q is:e-' 300- 6PP A healthy consumer is endowed with 150 units of medical care, the value of which is added to their income, and receives no additional value from consuming more care The dollar cost per unit of medical care is setat $25 Without insurance, the consumer faces a price of P S25_ The probability that she will become ill is 15. Her cument Income Ovithoutthehealth Z 'value' described above) is SIO,OOO_ Further, assume that it takes 150 units of medical care to restore an "ill" consumer to "healthy." In addition, once at the doctor, a sick person may elect more medical care than would just make them healthy, an opportunity that is not available to naturally healthy consumers. The value of all medical care is added to income when calculating utility Thus, the utility level in each state (sick or ill) depends on the income level aner medical expenses and premiums, supplemented by any consumer surplus from medical care (or its equivalent endowed value). (The sick consumer will always choose at least enough medical care to restore her health.) a. c. d. First, assume that the consumer has no opportunity to purchase medical care services. What is the consumer' s expected utility (numerical value)?e For all questions following assume that medical care services are available for purchase. what now IS the consumer' s expected utility uith no insurance?e-' What is the consumer' s expected utility if actuarially fair insurance is available that would allow the ill consumer to purchase up to 150 units, the level that would just restore them to health? The proposed premium would be 15 percent above the actuarially fair level for this consumer (to cover transaction costs). Political candidate A proposes that comprehensive health insurance be provided to everyone (no deductible, no co-pay). The proposed premium would be 15 percent above the actuarially fair level for this consumer (to cover transaction costs). What premium would be charged for this plan, and lvhat expected utility level would it yield?e-'