AFP equation Expected Value Expected Value Equation Risk Aversion Expected Income Insurance Example Expected value is the average value associated with the outcome of a risky situation: Graphically, EU of a gamble with 2 possible outcomes can be determined in 3 steps: EV = 40 (1) Find the 2 outcomes on the U(I) curve [U(5,000) and (15,000) and connect those points with a straight line Initial income = $15,000 Risk averse consumer faces 20% chance of losing $10,000 Actuarially fair insurance premium (AFP) for covering this risk equals the expected value of the loss (2X$10,000 = $2000) Where: = the sum over all possible outcomes, i 1. = the probability of outcome i 0 = the value of outcome! 2) Calculate the expected income with the gamble [0.5($15,000) +0.5155.000) - $10,000) and find the point on the line associated with this income (point C) ex.) Rolla die once and get $1 for each dot 1/6*15+1/6*2$+1/6*35+16*45+1/6*5$+1/6*6$=3.5$ 3) Find the utility value on the vertical axis associated with point C. This is the expected utility of the gamble (28) . Insurance with Deductible For this problem John is a graduate student who is currently deciding on dental insurance coverage during the open enrollment period. He is weighing the option of buying deluxe coverage, which his employer will allow him to purchase for the plan's AFP. John knows he will demand only cleanings (which his employer provides at no charge) with a probability of 80%. However, 20% of the time he will demand a significant amount of dental care (fillings, root canals, crowns) that will total $10,000. Assume the deluxe coverage would require John to pay a $2,000 deductible for these extra expenses. Suppose John income is $20,000. (a):Without insurance, what is John's expected value of out-of-pocket dental expenditures? What is John's expected income? What is the AFP of the deluxe plan? (b):If John's utility of income function is U = V, what is his expected utility without the deluxe insurance? (c):What is John's expected utility with the deluxe insurance? Will he buy the insurance? How do you know? AFP equation Expected Value Expected Value Equation Risk Aversion Expected Income Insurance Example Expected value is the average value associated with the outcome of a risky situation: Graphically, EU of a gamble with 2 possible outcomes can be determined in 3 steps: EV = 40 (1) Find the 2 outcomes on the U(I) curve [U(5,000) and (15,000) and connect those points with a straight line Initial income = $15,000 Risk averse consumer faces 20% chance of losing $10,000 Actuarially fair insurance premium (AFP) for covering this risk equals the expected value of the loss (2X$10,000 = $2000) Where: = the sum over all possible outcomes, i 1. = the probability of outcome i 0 = the value of outcome! 2) Calculate the expected income with the gamble [0.5($15,000) +0.5155.000) - $10,000) and find the point on the line associated with this income (point C) ex.) Rolla die once and get $1 for each dot 1/6*15+1/6*2$+1/6*35+16*45+1/6*5$+1/6*6$=3.5$ 3) Find the utility value on the vertical axis associated with point C. This is the expected utility of the gamble (28) . Insurance with Deductible For this problem John is a graduate student who is currently deciding on dental insurance coverage during the open enrollment period. He is weighing the option of buying deluxe coverage, which his employer will allow him to purchase for the plan's AFP. John knows he will demand only cleanings (which his employer provides at no charge) with a probability of 80%. However, 20% of the time he will demand a significant amount of dental care (fillings, root canals, crowns) that will total $10,000. Assume the deluxe coverage would require John to pay a $2,000 deductible for these extra expenses. Suppose John income is $20,000. (a):Without insurance, what is John's expected value of out-of-pocket dental expenditures? What is John's expected income? What is the AFP of the deluxe plan? (b):If John's utility of income function is U = V, what is his expected utility without the deluxe insurance? (c):What is John's expected utility with the deluxe insurance? Will he buy the insurance? How do you know