Econ 149: Health Economics
Problem Set IV (Extra credit)
Answer Key
1. Your utility function is given by
U
= ln(4
C
)
, where
C
is consumption. You make $30,000
per year and enjoy jumping out of perfectly good airplanes. There’s a 5% chance that, in
the next year, you’ll break both legs and will incur medical costs of $15,000 and will lose an
additional $5,000 from missing work because of the loss of a working pair of legs for some
time.
(a) What is your expected income without insurance? What is your expected utility with
out insurance? (See Chapter 8 for a review.)
E
(
C
) = 0
.
95(30
,
000) + 0
.
05(30
,
000

15
,
000

5
,
000) = 29
,
000
E
(
U
) = 0
.
95 ln[4(30
,
000)] + 0
.
05 ln[4(30
,
000

15
,
000

5
,
000)] = 11
.
640316
(b) Suppose you can buy insurance that will cover the medical expenses but not the fore
gone part of your salary. How much is an actuarially fair policy, and what is your
expected utility if you buy it? (Hint: you’ll need to calculate the utility of income in
each state.)
First, we need to calculate the actuarially fair premium which is deﬁned as the expected
loss for the insurance company. This insurance only covers the medical loss, so the
expected loss is
E
(
loss
) = 0
.
95(0) + 0
.
05(15
,
000) = 750
.
Now, we can use this premium to calculate expected income and utility if you buy this
type of insurance.
E
(
C
) = 0
.
95(30
,
000

750) + 0
.
05(30
,
000

5
,
000

750) = 29
,
000
E
(
U
) = 0
.
95 ln[4(30
,
000

750)] + 0
.
05 ln[4(30
,
000

5
,
000

750)] = 11
.
660556
(c) Suppose you can buy insurance that will cover your medical expenses and foregone
salary. How much would such a policy be if its actuarially fair, and what is your ex
pected utility if you buy it?
This insurance covers both the medical loss and the loss of income, so the expected loss
is
E
(
loss
) = 0
.
95(0) + 0
.
05(15
,
000 + 5
,
000) = 1
,
000
.
Now, we can use this premium to calculate expected income and utility if you buy this
type of insurance.
E
(
C
) = 0
.
95(30
,
000

1
,
000) + 0
.
05(30
,
000

1
,
000) = 29
,
000
E
(
U
) = 0
.
95 ln[4(30
,
000

1
,
000)] + 0
.
05 ln[4(30
,
000

1
,
000)] = 11
.
661345
2. How do feeforservice and capitation payment systems affect the alignment of physician
and patient desire? Under which system would we expect to see more supplierinduced
demand? What impacts do the different payment systems have on the amount of care the
patient receives?
Feeforservice is a method of payment under which the provider is paid for each procedure
or service that is provided to a patient. Capitation is a method of reimbursement in managed
care plans in which a provider is paid a ﬁxed amount per person over a given period regard
less of the amount of services rendered. Under feeforservice the physician has an incentive
to over provide service, because she is paid per procedure, but the physician’s incentives are
fairly in line with the patients (if the patient requests a procedure the physician is likely to