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January 29, 2007
Chapter 7 Demand and Supply of Health Insurance
Health Insurance and Welfare Loss
Reading Assignments
1. Feldstein, Martin S., “The Welfare Loss of Excess Health Insurance,” Journal of
Political Economy 81 (1973): 251-280.
2. Feldman, Roger, and Bryan Dowd, “A New Estimates of the Welfare Loss of
Excess Health Insurance,” American Economic Review 81 (1991): 297-301.
We start with The Case of Moral Hazard, p. 152.
Moral Hazard
Disincentives created by insurance to reduce the probability of a loss. In other
words, an individual changes his or her behavior toward risk after purchasing the
insurance policy against risk.
There is another famous terminology attached to insurance. That is,
Adverse Selection
A situation often resulting from asymmetric information, in which individuals are
able to purchase insurance at rates that are below actuarially fair rates plus loading
costs.
That is, an individual knows his or her risk probability, which is not shared
by the insurance agent. This may result in financial loss to the insurance company.
Therefore, the company tries to raise the insurance premium to protect against the
loss, that results in an selection of risk-prone individuals, who buy the insurance.
I. Moral Hazard
Figure 7.3 A (in Text)
Price
Figure 7.3 B
Price
D
P0
P0
S
0
D
Q1 Health Care
0
1
B
C
Q1
Q2
S
Health Care
Suppose that an individual has an totally inelastic demand for health care, in
Figure 7.3A. In this case, the consumption of health care is Q1, which is determined
by the intersection of the demand (D) for and supply (P0 or S) of health care.
Now, due to the individual’s income, tastes for health care, and other
socio-economic characteristics, the demand curve becomes elastic, shown in Figure
7.3B.
In Figure 7.3A, the individual has no insurance coverage so that he or she pays
the amount of P0 x Q1, when the care is needed. However, if the insurance that the
individual bought covers all the expenses of P0 x Q1.
What would happens to the consumption of health care by the individual?
Answer: the consumption increases from Q1 to Q2.
Welfare Loss
The welfare loss due to the moral hazard, i.e., the increase in the consumption of
health care will be:
Gains to the individual: Q1 B Q2 , the area under the demand curve beyond Q1.
Costs due to the additional consumption: Q1 B CQ2 .
The Welfare Loss: The Cost minus the gain= Q1 B CQ2 − Q1 B Q2 = △B CQ2
II. Effects of Coinsurance and Deductibles
Figure 7.4 (in Text)
100% Coinsurance
Price
D2
D1
P0
A
S
C
P1
0
B
20% Coinsurance
Q0
Q1
Health Care
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Suppose that an individual has the demand for health care D1 and the care
demanded is Q0 , which is given by the intersection of D1 and P0. The total
expenditures on health care is P0 x Q0, that is the area of 0 P0 A Q0.
Now, the individual buys an insurance policy and pay only P1 due to the coinsurance
rate of 20% due per unit of health care. In this case, the consumer will increase the
consumption from Q0 to Q1.
In terms of diagram in Figure 7.4, we can draw another demand curve, as if it exists
under the coinsurance rate of 20%. Then, the new equilibrium at Q1 is determined
by the intersection of P0 and D1.
The reason why we have the D1 demand curve after the coinsurance rate is as
follows:
(1) the price of health care per unit is P0 with no insurance.
(2) Now, the new price will be effective after the purchase of health care insurance.
That is, the new price is P1. The price of P1 is simply 20% of P0 or 0.02 x P0.
(3) When the individual consumer health care Q1 for P1, the actual cost is not P1 but
still P0 for the health care per unit but the difference between P0 and P1 is paid
by the insurance.
(4) Hence, we treat the effect of coinsurance on the demand curve such that the
original demand curve D0 rotates clockwise about the x intercept.
The Welfare Loss in Figure 7.4 is:
(1) The gains for the individual due to the out-of-pocket price change from P0 to P1:
Q0 A C Q1.
(2) The additional costs for the health care from Q0 to Q1: coinsurance Q0 A B Q1.
(3) The welfare loss: Q0 A B Q1−Q0 A C Q1= △A B C.
In expenditure terms, P0 x Q1 − [P0 x Q0 + (P1+P0)x(Q1−Q0)/2]= △A B C.
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III. Welfare Loss in the case of an upward-sloping supply curve
Figure 7.6 (in Text)
Price
S: Supply
P1
P0
F
J
D1: 20% coinsurance
K
D0: 100% coinsurance
0
Q0
Q1
Q:
Quantity
of
Health Care
First, note that the upward-sloping supply curve indicates the increasing
additional costs for supplying an additional unit of health care. Hence, the area
under the supply curve is the total variable costs.
(1) To start with, Let us assume that originally there is no health insurance to cover
the costs under the demand curve D0. That is, we call it the 100 coinsurance. The
equilibrium price is P0 and the quantity is Q0; the total expenditures on health care
is
P0 x Q0.
(2) Now, there is an insurance policy to cover the cost of health care such as the 20%
coinsurance rate, which means that 20% of total expenditures on health care must
come from the out-of-pocket of the individuals.
(3) Then, we have a new demand curve for the 20% coinsurance such as D1. The new
equilibrium price will be P1 and the quantity is Q1.
(4) The additional costs on health care for the increase in the supply from Q0 to Q1
under the new price of P1 from P0 is Q0 J F Q1..
(5) The benefits from the additional consumption of health care from Q0 to Q1 are
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the area of Q0 J K Q1.
(6) The benefits or costs is the difference between the additional costs and the
additional benefits: Q0 J F Q1 − Q0 J K Q1 ＝△JFK. The costs exceed the
benefits. Therefore, the welfare loss is △JFK
IV. The Demand for Insurance and the Price of Care
The demand for insurance and the moral hazard brought on by insurance may
interact to increase health care prices.
Figure 7.7 (in Text)
Price of Health Care
I
P2:upward-sloping
product supply curve
of Health care
PC2
PC1
B
A
P1: horizontal product
supply curve of health
care
0
Q1 Q2
Quantity of Insurance
I curve refers to impact of price of health care on quantity of insurance.
P curve refers to impact of insurance on price of healthcare through induced
demand.
(1) Curve P1 shows the case that the supply curve of health care is horizontal.
(2) Then, an increase in health insurance will not increase the price of health care
above PC1. The equilibrium is at point A and the insurance quantity Q1.
(3) If the product curve of health care is upward-sloping, then the increased product
price due to the moral hazard brought on by insurance leads to an increased
demand for insurance.
(4) The moral hazard together with the upward sloping product supply curve leadas
to a new equilibrium at point B.
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