Econ 3004 / 6039 Health Economics Week 7 Tutorial Solutions Question 1: Textbook Chapter 7, Q10. Answer: (a) (b) U 00 > 0 implies that E[U(I)] = pU(IS) + (1 p)U(IH) > U(E[I]) = U(pIS + (1 p)IH): So this person is "risk-loving". (c) The statement is true. The individual likes risks and thus do not want insurance. Question 2: Textbook Chapter 7, Q12. Answer (a) Recall that a fair contract means r = pq: In Peters case, r = 100; pq = 0:1
500 = 50. Since r > pq, the contract is unfair. Recall that a full contract means I 0H = I 0 S . In Peters case, I 0H = IH r = 500 100 = 400; I 0S = IS r + q = 0 100 + 500 = 400: Thus the contract is full. Peters income in the sick state, I 0S , is 400. (b) In Tims case, pq = 0:2
500 = 100 = r, and thus the contract is fair. Under a fair contract, the expected income is (1 p)(IH r) + p(IS r + q) = (1 p)IH (1 p)r + pIS pr + pq = (1 p)IH + pIS + (pq r) (note r = pq under a fair contract) = (1 p)IH + pIS : Semester 2 2022, Instructor: Dr. Yijuan Chen, Research School of Economics, Australian National University. 1 Thus the expected income under a fair contract is the same as the expected income without insurance. (c) Since pq = 0:2
500 = 100 = r, the contract is fair. Since I 0H = IH r = 1000 100 = 900; I 0S = IS r + q = 0 100 + 500 = 400 < I 0H ; the contract is partial. (d) For the contract to be unfair, we need r > pq ) 100 > p
500 ) p < 0:2: For the contract to be partial, we need I 0H > I 0 S ) IH r > IS r + q ) IH IS > q ) IH IS > 500: (e) From (d), we can see that the upper bound of p is 0:2, and the lower bound of IH is 500 + IS = 700. (f) The statement is false. Without knowing the speci c utility function form we cannot tell who gains more from buying isurance. 2 51作业君版权所有
