7. (2 points) Suppose there is a 40% chance that a risk-averse individual with a current wealth of $60,000 will contract a debilitating disease and suffer a loss of $40,000. The chance that nothing happens and the individual keeps his entire current wealth is 60%. Suppose two types of insurance policies are available: (1) a fair policy covering the complete loss; and (2) a fair policy covering only half of any loss incurred. (a) What is the premium (fair premium) equal to for a policy of type (1)? What about the (fair) premium for a policy of type (2)? (b) Calculate the individual's expected wealth in the following cases. (i) He goes uninsured (ii) He buys a policy covering the complete loss (type (1)) (iii) He buys a policy covering half of the loss (type (2)) (c) Remember that the individual is risk averse. Use a graph with U(W) to show that he views a policy of type (2) as inferior to a policy of type (1). Furthermore, on your graph, show that he will definitely purchase of policy of type (1) rather than go uninsured. 3 7. (2 points) Suppose there is a 40% chance that a risk-averse individual with a current wealth of $60,000 will contract a debilitating disease and suffer a loss of $40,000. The chance that nothing happens and the individual keeps his entire current wealth is 60%. Suppose two types of insurance policies are available: (1) a fair policy covering the complete loss; and (2) a fair policy covering only half of any loss incurred. (a) What is the premium (fair premium) equal to for a policy of type (1)? What about the (fair) premium for a policy of type (2)? (b) Calculate the individual's expected wealth in the following cases. (i) He goes uninsured (ii) He buys a policy covering the complete loss (type (1)) (iii) He buys a policy covering half of the loss (type (2)) (c) Remember that the individual is risk averse. Use a graph with U(W) to show that he views a policy of type (2) as inferior to a policy of type (1). Furthermore, on your graph, show that he will definitely purchase of policy of type (1) rather than go uninsured. 3