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 Peter’s 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 Peter’s case, I 0H = IH r = 500 100 = 400; I 0S = IS r + q =
0 100 + 500 = 400: Thus the contract is full.
Peter’s income in the sick state, I 0S , is 400.
(b) In Tim’s 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.