Department of Economics Rutgers University Spring 2021 Jennifer Hunt jennifer.hunt@rutgers.edu Econ 320 Intermediate Microeconomic Analysis Practice Question on Insurance Make sure you try to answer the questions, especially the graph, before turning over to the solutions. Suppose there is a 50–50 chance that a risk–averse individual with a current wealth of $20,000 will contract a debiliatating disease and su↵er a loss of $10,000. a) Calculate expected wealth without insurance. b) Calculate the cost of actuarially fair insurance in this situation. c) Calculate wealth with insurance. d) On a utility–of–wealth graph show an individual’s expected utility without insurance, and utility with insurance. Which is higher? (Since I didn’t give you a precise utility function, you will not have precise numbers for utility, but you should label the relevant wealth numbers.) In addition to this full insurance policy, there is a fair policy covering only half of any loss incurred. e) Calculate the cost of the premium for this partial insurance. f) Calculate wealth with insurance if the person stays health, and if the person does become ill. g) On the diagram from a), show an individual’s expected utility with partial insurance. How does the individual rank full insurance versus partial insurance versus no insurance? Solutions a) Wealth is $10,000 with illness and $20,000 without, so expected wealth is (.5)(10,000)+(.5)(20,000)=15,000. b) The fair premium is the expected loss: E(loss) = (0.5)(10, 000) = 5000. (1) c) Wealth with insurance is 20,000-5000=15,000. d) The certain utility with insurance is higher. See below. e) The fair premium for the partial insurance is the expected loss per person to the insurance company: E(loss) = (0.5)(5, 000) = 2500. (2) f) Health is $17,500 with no illness and $12,500 with illness. g) Partial insurance shows up on the diagram qualitatively like the no insurance case, because there is still a risk involved. The expected utility of partial insurance is lower than the certain utility with full insurance, but higher than the expected utility without any insurance. See below. ' Vfw ¥¥¥¥ ¥=§÷i; Elulnoins)) i I 1 I Eamonn . 2