2021S2 ECON8039/3004 HEALTH ECONOMICS TUTORIAL WEEK 8 Q1: TB CH7 Q10 10 Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I (U' > 0) and convex (U" > 0). a Draw a utility function in U-I space that fits this description. b Explain the connection between U" and risk aversion. 5 ( II) " (IN) U ( E[] ) n/Is) Is E[I] > Z IH implies E [ U ( 1 ) } = P U | 1; ) + ( 1 - p ) U | IH ) expected utility > " ([[1]) utility from expected income. E[1] = U (PIS + (1 - P) IH ) Risk loving c True or false: this individual prefers no insurance to (Is, In) to an actuarially fair, full contract. 1 no insurance i receive utility E[well ) 2 actuarially fair, full contact : receive utility " E(I) ) From the graghd from b) : E [ u [ 1] ] > W ( E [ ] ) So True. 4 full contract. get certain return. fair contract. the certain return = {[1] . The expected income without the insurance.
Q2: TB CH7 Q12 12 Now consider a different insurance company that does not have the inclination to tailor contracts specifically to individuals. Instead, it will offer a "standard contract" with the premium r = $100 and payout q = $500 to anyone who will purchase it. a Peter has healthy-state income ly = $500 and sick-state income Is = $0. He has probability of illness p = 0.1. Is the standard contract fair and/or full for Peter? If he ends up getting sick, what will his final income be? insurance is zero. as if the price paid for The Fair contract: (def) the insurance firm earns zero expected profit. E[II(p, q, r)] => r = pq Full contract: (def) an insurance contract that achieve state independence, i.e., ! consumers achieve certain return under the insurance contract, i.e., ! since the return is certain, that means, the contract alleviate uncertainty for consumers, that's why we say the contract is a "full coverage" of risk/uncertainty. I'H = I'y => q = IH - Is Peter: pq = 0.1 Ă— 500 = 50 Thus the contract is unfair for peter r = 100 q = 500 In - Is = 500-0= 500 1 > q = IH - 15 Thus the contract is full It sick , Peter's final income : 1 money paid for the insurance . " premium " Income when sick under insurance Is - 1 + 9 = 0 - 100 +500 = 400 4 payment received from insurance when sick. 1 without insurance
b Tim has IH = $500 and Is = $0, but a probability of illness p = 0.2, higher than Peter's. Is the standard contract fair and/or full for Tim? How does purchasing the standard contract affect Tim's expected income? Pq = 0, 2 Ă— 500 =