physician services, policy-makers may conclude that SID, if it exists, does not constitute a practical problem in Norway, independent of what motives physicians
may have. The paper is organized as follows. In Section 2, a simple theoretical model is
developed to explain the meaning and consequences of SID when primary physician services are funded and regulated by the state, as is the case in Norway.
The section also contains a discussion about how policy-makers can use survey data to calculate the socially optimal density of physicians without having detailed
knowledge about the market for primary physician services. In Section 3, the survey data and our econometric specification are presented. The empirical results
are presented in Section 4, and Section 5 provides concluding remarks.
2. Theoretical framework
In this section, a simple model of the market for primary physician services is presented. In Norway, there are two types of primary care physicians. Contract
Ž . Ž
. physicians about 75 of all primary care physicians
Statistics Norway, 1998 are self-employed, but receive a grant from the municipality to cover some of their
Ž .
expenses auxiliary personnel, etc. . The size of this grant is regulated by the normal tariff and contributes about 30 of contract physicians’ gross income
Ž .
Statistics Norway, 1996 . The normal tariff is an agreement that is negotiated annually between the Norwegian Medical Association and the Ministry of Govern-
ment Administration. Contract physicians obtain additional income from patient fees and from payments from the National Insurance Administration. Patient fees
Ž contribute about 30 of contract physicians’ gross income Statistics Norway,
. 1996 . Patients pay a set fee for every consultation with the physician, whereas
items of treatment are free. Payments received from the National Insurance Administration contribute about 40 of contract physicians’ gross income from
Ž .
practice Statistics Norway, 1996 . The level of patient fees and the level of payments from the National Insurance Administration are regulated by the normal
Ž .
tariff. Salaried physicians about 25 of all primary care physicians , are em- ployed by the municipalities. Since employed physicians do not have financial
incentives to induce demand for their services, our analyses focus on contract physicians.
We consider a representative municipality where L is the patient population per contract physician; physician density D s 1rL. For simplicity, we assume that the
population consists of identical individuals and that all contract physicians are identical. The physicians provide one type of services, denoted consultations. C is
the number of consultations per contract physician and c s DC the number of consultations per patient. The contract physicians receive patient and state fees,
p
P
and p
S
, per consultation and a fixed grant R .
Patients are assumed to derive utility from consultations c and disposable income I s I
y p
P
c, where I is exogenous income. The patient utility function
Ž
P
. is U I y p c,c , where U 0, U - 0, U 0, U - 0 and U s 0. Contract
I II
c c c
Ic
Ž
P S
. Ž
P
physicians are assumed to care about revenues R s R q p q p C s R q p
S
. Ž
. q p
crD, workload W s t C s t crD t is the time intensity of consultations , and the utility of the patients. We write the contract physician utility function as:
1 y l V R ,W q l U I
y p
P
c,c , 1 l 0
Ž . Ž
. Ž
.
Ý
L
where l is the relative weight that contract physicians place on patient utility, and Ž
. V R,W
captures contract physicians’ motives not related to patient utility: V 0, V
- 0, V - 0, V
- 0, V
s 0. Without loss of generality, we
R R R
W W W
RW
normalize p
P
and t to one and set R s I
s 0. The contract physician utility function can then be written as:
1 y l V p crD,crD q l U yc,c
1
Ž . Ž
. Ž
. Ž .
Ý
L
where p s p
P
q p
S
s 1 q p
S
. If patients have complete information about the utility of consultations, the demand for consultations per patient c
D
is given by the first-order condition:
U c
D
y U yc
D
s 0. 2
Ž .
Ž .
Ž .
c I
Ž .
D
It follows from Eq. 2 that c does not depend on D or l. The contract
physicians’ supply of consultations per patient c
S
is obtained by maximizing Eq. Ž .
1 with respect to c:
S S
S S
1 y l p V p c rD q V
c rD q l U c
y U yc s 0
3
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
R W
c I
Ž . where we have set L s 1rD. Differentiation of Eq. 3 yields:
S S
2 2
E c rED s 1 y l c
p V q V
r 1 y l D p V
q V
Ž .
Ž .
Ž .
Ž .
R R W W
R R W W
2
ql D U q U
0.
Ž .
c c I I
Each contract physician prefers to supply fewer consultations when the number of physicians increases, but the decrease is not sufficient to offset the increase in
S
Ž . physicians; c is therefore an increasing function of D. A comparison of Eqs. 2
Ž .
S
Ž .
S D
Ž
S D
. and 3 shows that c is increasing decreasing in l if c - c
c c ; since
contract physicians place more weight on patient utility the higher is l, c
S
moves closer to c
D
when l increases. We are now ready to analyse the market for consultations. Fig. 1 shows
demand per patient for consultations and supply per patient for consultations as functions of physician density. The broken line represents the market outcome c
M
. We define rationing of consultations as a situation where c
M
- c
D
and SID as a situation where c
M
c
D
.
Fig. 1. The market for consultations.
Ž .
Suppose first Case 1 that patients have complete information about their utility function. Then, the short side of the market determines quantity: c
M
s c
D
if D D
X
; c
M
s c
S
if D - D
X
. Hence, we have rationing in physician-scarce munici- palities and neither rationing nor SID in physician-dense municipalities. The
threshold D
X
does not depend on the preference parameter l; the weight that contract physicians place on patient utility affects the amount of rationing in
physician-scarce municipalities but not whether rationing takes place.
1
Ž .
Suppose next Case 2 that patients do not know the utility of consultations, and that the market outcome is determined by the contract physicians: c
M
s c
S
. Compared to Case 1, the outcome does not change in physician-scarce municipali-
1
Ž . Ž .
S S
D
Inspection of Eqs. 2 and 3 shows that the impact of l on c at c s c is zero.
ties; we still have rationing and the amount of rationing depends on the physician preference parameter. In physician-dense municipalities, we now have SID. In
these municipalities, the extent to which contract physicians care about their patients has no effect on whether SID takes place, but affects the amount of
inducement; the more contract physicians care about patient utility, the lower is
Ž
M D
. the amount of inducement c y c
. Consider now the policy-maker’s decision problem. In order for policy-makers
to be able to compute the physician density which maximizes social welfare for a given fee structure, they need to have information about demand and supply
functions. In practice, policy-makers have limited information about the parame- ters of the model; as mentioned in the introduction, there is not even agreement
about whether SID exists at all. However, if we accept the assumption that surveys provide information about patient utility, then the policy-maker can use surveys to
examine whether physician density is too high or too low.
Suppose that the social welfare function is equal to the utility of a representa- tive patient minus the cost of state expenditure per patient, and that consultations
are determined by the physicians. Then the policy-maker prefers the physician density which maximizes:
U yc
S
D ,c
S
D y gp
S
c
S
D
Ž . Ž .
Ž .
Ž .
where g is the marginal cost of public funds; g captures the deadweight loss of taxes as well as administrative costs. The first-order condition can be written as:
S S
S
U Ec rED s U q gp E
c rED . 4
Ž .
Ž .
Ž .
c I
Ž . Ž
. The right-hand side of Eq. 4 is the total private q public marginal cost of
physician density and can be computed from aggregate data on consultations and Ž
. other primary care services provided g is known . The left-hand side is the
marginal patient utility of physician density and can be computed from surveys provided that reported satisfaction is a valid proxy for patient utility. Thus, even
with limited information about the market for primary physician services, includ- ing whether SID takes place, the policy-maker can use surveys to examine whether
the marginal utility of physician density is higher or lower than the marginal cost of physician density and thus whether physician density is above or below the
social optimum.
3. Data and empirical specification
