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Considering the effects of financial incentives and professional ethics on ‘appropriate’ medical care
Journal of Health Economics 3 (1984) 223-237. North-
obert S. Washington University, St. Louis, A40 63110, USA
U.S. Department of Justice,
Washington, DC 20530, USA
Received May 1983, final version received March 1984 This manuscript presents a model of an ‘ethical’ physician’s allocation of time and income between work and leisure activities for various remuneration types and income levels. The physician is ‘ethical’ because, ceteris paribus, he prefers to provide that amount of medical care which he b&eves to be in the patient’s best interests. Remuneration systems include faed, timebased and output-based incomes. Only output-based income provides the physician with incentives which may (if the physician density and medical care price are sufliciently high) generate more-than-‘appropriate’ care per patient. Fixed and time-based incomes necessarily lead the physician to provide less-than-‘appropriate’ care.
The physician’s Hippocratic Oath’ is an ethical incentive to provide ‘appropriate’2 amounts of care. Yet physicians are accused of increasing their incomes by capitalizing on their patients’ uncertainties [Arrow (1963)] and shifting the demand for medical services [Evans et al. ( 1973), Evans ( 1974), *The authors wish to thank Peter McMenamin, Trout Rader, James Ramsey, Stuart Boxerman, and the editor and referees of this Journal for their helpful comments. This research was funded, in part, by contract 500-78-0055 between Washington University and HCFA, DHHS. Neither organization necessarily endorses the views and opinions expressed by the authors. I‘1 will apply dietetic measures for the benefit of the sick according to my ability and judgment; I will keep them from harm and injustice’ [Edelstein (1943)]. ‘By a purely medical standard, care is only ‘appropriate’ if its expected contribution to the patient’s health status is positive. By the economist’s societal standard, medical care is inefficient if its value to patients, however that may be defined, is less than the opportunity cost of the resources consumed. Because cost factors are ignored by the purely medical standard, medica!ly ‘appropriate’ care always involves more care than that indicated by the economist’s measure of efficiency. Nevertheless, the model’s results are not affected by the definition of ‘appropriate’. Whether physicians make decisions on pure medical appropriateness or on ‘suo2r-ethical grounds by taking social opportunity costs into account is unimportant to this analysis. ~\J?Tis any attempt made to provide an empirical or an operational definition of ‘appropriate’ cart:. Rather, our purpose is to demonstrate how financial factors may cause physicians to provide more or less care than they themselves would judge ‘appropriate’, whatever their definition may be.
224
R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
(1980), Wilensky and Rossiter (1981)]. This note professional ethics and financial incentives jointly addresses the issue the amount of medical care provided each patient. iamson’s (1975) terms, medical care is one situation where ‘inforndeed: we can mation impactedness’ makes opportunistic beh names, is society’s argue that the basic designation ‘professional’, attempt to repress such opportun :tic behavior. As this note points out, the amount of such behavior and thus the need for such instituti will depend critically on the way economic incentives are strut This note models the work and leisure behavior of a physician who acts as an ethical procurement ‘agent’ for his patients and who is constrained by time and income. The physician is ethical because, ceteris paribus, he prefers to provide exactly the ‘appropriate’ amount of medical care. The physician allocates his time between work and leisure activities, which are both produced using time and purchased material inputs. This integration of professional ethics with a work-leisure model allows us to examine the effects of (1) the type of remuneration, (2) the level of remuneration, and (3) the number of patients (the inverse of physician density). The model may be interpreted as a stylized description of one physician’s supply decisions in a medical care system in which the fee schedules of thirdparty insurers, or other physicians, set prices exogenously. In this context, we examine how different compensation methods a&t this physician’s production decisions. Conclusions about the effects of supplier-induced demand are drawn from an understanding of how exogenously determined prices will affect the physician’s supply under each of the compensation alternatives. The specific policy issues addressed include the following questions. Which methods of physician remuneration are capable of restricting the potential e care? Wow much care per patient does a physician attempt to o higher prices necessarily imply more care? If the physician is able to shift demand, will he necessarily provide ‘too much’ care? What dynamic adjustments might be expected when the average population per doctor (the inverse of physician density) is not equal to the desired number of patients? And finally, if the model predicts sizable ineficiencies under simple remuneration systems, what institutional or market responses would we expect, and what public policy actions would reduce such inefficiencies? The following sections of the note introduce a model of physician workleisure decisions, analyze the effects of three alternative remunerations and of the number of patients on the supply of medical care, and consider a number of qualifications and policy implications. Fuchs (1978), US
a model of physicians who maximize their leisure objectives subject to production constraints deter-
R.S.
Income, ethics and medical care
225
mined by their limited time and income reso hysicians are assum maximize utility from two outputs, medical care per patient and leisure. produce these using their own time and ysicians finance both practice and leisure expenditures with earn under one of three remuneration alternatives: fixed, time-based, or output-based methods.3 2.1. Utility function
This model presumes that each physician derives additional utility both from positive consumption of the product of his leisure activities Z and from roviding addiiional medical care per patient V/N up to the ‘appropriate’ amount VX4
u = U[Z,
(V/N) - VA],
(1%‘5
where
u = the physician’s utility level, Z = the physician’s total production (and consumption) of leisure activities, V/N= the actual production of medical care per patient, V2l = the ‘appropriate’ care per patient determined by the physician’s own ethical standards, U, >O, ?Yvln > 0 when V/N c VA, and U,,,, CO when V/N > VA. A simple example of eq. (1) is the following quadratic utility function: U=Z--(V/N-
VA)2.
(W
The notion of utility from the composite leisure activity 2 rather than from leisure time and net income follows Becker (1965). The assumption that a doctor derives satisfaction from his professional activity, measured here by production of medical care per patient, is less common.5 While Evans (1974) and Wilensky and Rossiter (1981) presume that all care provides neptive utility, this overlooks the physician’s professional and ethical objectives. Scitovsky (1951, p. 87) recognized the issue 33 years ago: 3This pedantic terminology is adopted to call attention to the difference between these conceptually pure alternatives and the observable - but realistically mixed - income methods such as fee-for-service and salary. oodward 4Earlier versions of the model included only total care V in the utility function for our and Warren-Boulton (1981)]. The ‘care-per-patient’ specification, which is necess supplier-induced demand arguments, was suggested by Feldman ( 1979). ‘Of course, consumer utility is an important factor in optimal price dete Harris (1978).
R.S. Woodward and F. Warren-&n&on, Income, ethics and medical care
226
‘Artists, scientists, professional people, and businessmen ofte their work not merely as a means of earning income but as an important and interesting part of their lives.’ nthoven (1978) has defined physicians’ joint objectives: other health professionals are motivated by nonfinancial goals, including a desire to cure the sick d to achieve professional excellence and esteem of peers and public. t their use of resources is inevitably shaped by fmancial incentives.’ ‘Physicians
and
Our model includes medical care per patient in the utility function as a direct representation of physicians’ ‘desire to cure the sick’. Our designation of the ‘appropriate’ amount of medical care per patient VA is included to recognize that too much care may be possible, but should not be assumed. We presume that VA represents the physician’s own best judgment of the ‘appropriate’ level of care for each patient, which may be based upon medical factors alone or may include considerations of patients’ out-of-pocket expenses or resource opportunity costs. The physician’s perception of ‘appropriate’ may be affected by his professional standards, personal morals, fear of professional or legal punishment, and medical education. While the exact specEcation of ‘appropriate’ medical care and its sensitivity to changes in any of these determinants is beyond the scope of this research, our policy recommendations will obviously depend upon the extent to which physicians recognize resource costs in the definition of VA. 2.2. Leisure activity Following Becker (1965), we assume that physicians produce leisure activities using consumer purchases X, and their own time t,. 2 = z(t,,
x,),
(2)
where 2 =production of leisure activities, tz = leisure time, xz = consumer goods purchased from income, Zt, > 0, and ZX,> 0. edical care production e&al
output V is produced using expenditures o e t,6 and patients N,
‘we drop the subscripto to t
practice inputs x,
and x to minimize clutter in the subsequent equations.
R.S. Woodward a& F. Warren-Bouiton, Income, ethics and m
v = V( t, x, Iv), where V = the total quantity of medical care produced, t = the individual’s (physician’s) time at work, x = the quantity of (practice) inputs purchased with income, N = the number of patients under the physician’s care, v,,1G;,Kl>o. The number of patients per physician N is inclu input for two reasons. First, the number of patients per ph productivity of the other factors. For example, a larger per physician (which might result from a reduction physicians in the country) forces the physician to triage sicker patients. In such a case, each physician’s time and ex produce more medical care per patient at the margin. Second, the number of patients per physician N is in supplier-induced demand. The last section of the note cons of physician densities on supplier-induced demand in the c tions about the aggregate population, the number of physic adjustments. 2.4. Constraints The physician’s production of medical care and leis e activities constrained by his income and his time. T=t+t,
and
Y=x+x,,
is
WY(5)
where T = total time, Y =gross physician real earnings (gross dollar earnings divided by the price of goods).’ Income is earned according to one of three remuneration alternatives: fixed, time-based, and output-based. The simplest income is fixed: the physician receives a predetermined amount per time period regardless of his labor (or non-labor) activities during that (or any sequential) period.
Y'y,, where & is exogenously determined. ‘For expositional simplicity, the units of consumption goods x, and of practice inputs x, have been normalized so that their prices are equal to one, pX=pX, = 4.
228
R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
Time-based income, t second remuneration alternative, is directly proportional to the physic ‘s hours of work. Although wages are the best understood time-base remuneration, physicians seldom receive the Nevertheless, the fees the fee-for-service system may be determined in par by the time taken by
(7)
Y=wt,
where w is an exogenously determined wage rate. utput-based income, the third remuneration alternative, is a fixed payment per unit of output regardless of the physician’s time or use of practice inputs or equipment. It most closely corresponds to physicians’ case rates, payments per unit of health output or for treatment of specific conditions, such as a normal delivery or setting a simple fracture. Fee-for-service remuneration may also have a substantial output-based component.
(8)
Y=P
where P is an exogenou,c:price per unit of health care output. Thus in its general form, allowing for pure and combined systems, the income constraint becomes
2.5. Summary The general constrained utility function for this work-leisure model is U=U{Z[T-t,Y,+wt+PV(t,x,N)-X-J,
ww
v(t,x,N)/N-VA}.
An algebraic specification employed to demonstrate some indeterminate results is U=(T-t)“(Y,+
wt+PV--x)l-‘“+
(
2
f(Nta,l-P_j7~. >
-jy-
Answers to the questions about the effects of the financial incentives on a physician’s provision of medical care are provided by two theorems. For the al simplicity, the following sections develop each of these three remunerations separately. We start with the fixed re relatively straightforward and which provide a
R.S. ‘Woodwardand F. Warren-Boulton, Income, ethics and medical care
readily understandable point income models.
229
for the time- and output-based
3.1. Fixed income
The fixed income model is simply an application of the well-known two input, two output international trade (or regional growth) models and their Edgeworth box representations. Propositim 1. Physicians paid a fixed thau-‘appropriate’ care per patient.
income will necessarily provide less
A suficient condition for less-than-‘appropriate’ care being provided by a physician with our ‘ethical’ utility function is a negatively sloped production possibility frontier (PPF), dZ 14~J~4V) c 0. We derive the conditions for a downward sloping PPF with a general envelope theorem based on maximizing V/N subject to a given level of 2. To avoid repetition for time- and output-based incomes, we write the function in its general form. max &= ?(t,x,N)/N+il[Z(T-t,
q-t-wt+PV-x)-Z].
For the fixed income case (w = P = 0, yf > 0), the first order conditions are
&= K/N-Zt=O, Ex = v,/N--&U,
and
=o.
(12)
(13)
Since il can be interpreted as -d( V/N)*/dz, where (V/N)* is the optimum level of V/N, the condition for the PPF to be downward sloping is that A>O. Since ;1= K(NZ,) = VJ(NZ,) for a fixed income system, this is satisfied if all marginal products are positive. Suffkient second order conditions for a maximization are that all marginal products are diminishing and all cross products are positive. A more intuitive argument also establishes that physicians with fixed incomes will never provide too much care. Suppose the physician with a fixed income is providing more than the ‘appropriate’ amount of care. T by reallocating his expenditures and time from medical care to increases his utility both from the additional leisure activities an closer-to-‘appropriate’ amount of medical care Proposition 2. The change in the quantity of care attributable incomes depends on the relative factor intensities of work
R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
230
the slope of the supply of medical care provided by an ethical fixed income physician is not uniquely determined, we develo Proposition 2 using the Cob ouglas production model, eq fixed incomes have two effect the provision of medical ca ybczynski effect and a change in the slope of the utility function. The ybczynski theorem states that if the endowment of some resource increases in a model with fixed relative output prices, the activity that uses that resource more intensively will increase its output while the other activity will decrease its output [Silberberg (1978, p. 408)]. Fixed output prices of the ybczynski theorem correspond to a simplified utility function U = AZ+ B(V/N). If A and B aId con@ants, increased physician income will increase the production of medical care only if medical care uses purchased inputs more intensively than does leisure production. The first order conditions of the model, eq. (lob), with the simplified utility function and where w = P =O, are Because
U,=A(-a)(T-t)“-l(Y-x)lwa+BB_
f(N)plxI-p,o,
Ux=A(a-l)(T-t~(Y-x)-a+B(l-@~tflxe@=O.
The contract curve is derived by solving both equations for X, x=a(l -@tY((l -a)/?(T-- :)+a(1 +)t). Substituting x from eq. (16) into eq. (15) and solving explicitly for 4
and then for X,
x
a(l ~)y (p ) --f(N)\'4p-a)T -a. N ,I - -
The supply curve, the change in V/N attributable to an increase in fixed income, is where aN = 0.
(19) s relat
t
R.S. Woodward and F. Warren-h&en,
p > a, (dx/d u) < 0, (dt/d
Income, ethics and me.“icalcare
and
(d V/d Y)c 0.
and
(dV/dY)>O.
231
If V is relatively x intensive, then a>/?,
(dx/dY)>O,
(dt/dY)>O
(21)
The second effect of an increased fixed income is the change in the shadow prices of medical care and leisure caused by the uadratic utility representation of the ‘ethical’ physician. If Z and C/,‘lVare al goods, the second effect will reduce or eliminate the Rybczynski result. While such a change may be represented by examinirg the impact of dx/d(B/A) and dt/d(B/A), the basic dependency of d( V/N)/dY on a - j3 is unaffected. 3.2. Time-based income
The models for time-based and output-based income differ in one important respect from the fixed remuneration framework: income (and therefore the sum of practice expenditures and consumption goods) is not predetermined. By definition, time-based income implies that the total expenditures are constrained to be proportional to time at work. The following paragraphs develop the two propositions about the behavior of physicians on a time-based income. Proposition 3. Physicians paid a time-based income will necessarily provide too little care per patient.
Again, a sufficient condition for less-than-‘appropriate’ care is a negatively sloped PPF which can only be tangent to the utility curve at some less-than‘appropriate’ level of medical care. As in the fixed income case, we can derive the conditions for a downward sloping PPF using a general envelope theorem. For the time-based income case P=O in eq. (1 l)], the first order conditions are
[rf=
&=F/N+a[-Z,+wZ,]=O,
and
ic,=vJlv+iz[-Z,]=O.
Again since jLcan be interpreted as - d( V*/ (fig. 1)8 to be downward sloping is il>O. oreover if ZC9l$ ;1> satisfied if ZX, ‘Figs. 1 and 2 a re derived from a simulation ~=(5~-t)0.~(y-JC)0.5+[t0.6~X6.2J~-0.9_20]IZ, where y = 6525r, V = 9.2 t: an
(22)
232
R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
Fig. 1
A more intuitive explanation ~follcwsfrom a description of the impact of shifting resources from 2 to K Holding t, and t, constant, if one unit of x is shifted from 2 to V production, V will increase if VX>O and 2 will decrease if 2, >O. If one unit of time is shifted from 2 to V production, V will increase if K >O. However, the increase in time spent at work leads to an increase in income which can be spent on consumption goods. Thus 2 will fall only if Zt > ~2,. Thus a sufficient set of conditions for dZ/d( V/IV) ~0 is Vx, Zx and K >O, and Zt > ~2,. Proposition 4. The slope of the supply curve, the change in medical care per patient attributable to higher wage rates, is also determined by relative factor intensities.
ecause time-based income introduces an extra term in the first order condition U, =0, explicit solutions for x and t are impossible, even in the case of the linear utility function employed for Proposition 2. Nevertheless, some results may be derived from the implicit function theorem. The first order conditions for the linear utility, Cobb-Douglas, time-based income model are U,=
U,=
--A(1 -a)
+B(1-j?)?
and
R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
x=(1 -&wt[t-(1 v;here the condition U, = 0 gives
-a)TJ/((I
-a)/3(T-t)+a(l
+)t),
t > (I- a)T follows from 2, > ~2,.
233
(261 Substituting
x into
As in the fixed income case, the slope of the supply curve, dV/dw, will depend upon dt/dw and dx/dw. As an example of the indeterminacy of dt/dw, we calculate aglat and ag/aw.
If the conditions of the implicit function theorem are satisfied, that is if g(t, can be written as g[t(w), w] and if aglat #0, then dt,‘dw = - (WwMW0
l
w)
(30)
No simple conditions relating the size of a and /? appear to determirle the slope of the supply function. If medical care production is relatively expenditure intensive, a>/3 and dg/aw 4, but the sign of ag/i?t is indeterminate. If medical care production is relatively time intensive, a c/? and ag/at CO, but the sign of ag/aw is indeterminate. 3.3. Output-based income Output-based income has a considerably different effect on the amount of care provided each patient. Leisure production is directly affected by the allocation of all three production inputs - time, expenditu of patients. As a consequence, the utility maximizing num greater than zero and more-th After a brief description of following paragraphs develop these results. Pro position 5. the ‘appropriate’ level of medical care.
234
R.S. Woodward and F. Warren-Boulton, Income,
ethics ati medical care
Output-based income incorporates finanGia1 incentives which do not necessarily force the physician to provide iese-than-‘appropriate’ care per patient (fig. 2). An envelope theorem demonstrates tha.t dZ/d VlN) cannot be generally signed. The first order conditions of eq. (I l), where Y = w =0 and P>O, are &= K/N+&-Z,+PZ,K)=O,
100-f
z
and
(31)
PRODUCTION POSSIBILITY FRONTIER OUTPUT-BASED INCOME
90 88 78 60 58 40 36 20 10 +..........I.......... 4..........I.......... I.......... I.......... t ..........1. 0 ! ..........+..........I.......... 0 5 18 15 28 25 38 35 48 45 50 U/N
Fig. 2
fficient condition for the PPF to be downward sloping is that r, positive marginal products are insufficient to establish the two extra conditions indicated by eqs. (3 1) and (32), Zt > Pz, K and PY, < 1. Rather, the slope of the PPF will be negative if either of these two conditions holds and positive if either of the inequalities is reversed. Moreover, eqs. (31) a -Zt and PV, - 1 have the same sign. onditions can be seen by examining the impact of shifting resources from Z olding t and t, constant, if one unit of x is transferred to V production, V will increase if Vx>O. But this increase in V leads to an increase in income of PV,. If this is greater than unity, a transfer will allow an increase in both % and V. Thus if PV,> 1, then >O. Similarly, if a unit of time is transferred to V production, V will increase if K >O. The resulting increase in income, PV,, if spent on Z 1 increase Z by P&Z, units. If this increase is greater than the of reducing t,, i.e., if Pb$Z, > Zt, then dZ/dV > 0. Thus, we may being nlY is st be
R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
235
possible to increase both V and Z by transferring either time or production inputs from work to leisure. Proposition 6. The slope of the physician’s SUPPlY response prices is not uniquely determined.
to
higher output
The same set of parameters determines the slope of output-based income supply as determines the time-based remuneration’s slope. of the Cobb-Douglas model reduces to x= t[a(l +?)Pt/((l -a)j?(T-
t) +cl(l
+)t)-j?
Substituting x into the model’s first order condition U, yields g=A(l
-a)(T-t)“[(l
-A(T-t)“-l[(l
-a)jw+(a-/3)t-J1’@/t[a(l
-a)T+(a-j?)t]
-/3)Pt]“B
-B[(l -a)T+(a-/?)t]/aPt.
(34)
The (a -/I) coefficients of t cause ihe sign of aglat, aglaP, and t and dV/dP to depend upon the relative factor intensities. This indeterminacy has important implications for the supplier-induced demand controversy. While output-based income may be a necessary condition for more-than-‘appropriate’ care, it is not a suficient condition. Indeed output-based remuneration, even when coupled with a moderate ability to shift the prices of medical care, does not necessarily generate more-than‘appropriate’ care. If a physician is able to shift. the demand curve and increase the price of care, it is not possible to determine a priori whether or not the resultant increase in medical care provided per patient is a move toward, or away from the ‘appropriate’ levels. 4. Conclusions
This note presents a model of an ‘ethical’ professional’s allocation of time and income between leisure and work activities for various remuneration types, income levels, and numbers of patients. ‘Ethics’ are represented by a utility function which generates disutility from providing ‘either more- or lessthan-‘appropriate’ amounts of care per patient by the physician’s own standards. Of the three remuneration types, only physicians with the financial incentives which is sufficiently low and the price ‘appropriate’ amounts of medical care incomes necessarily lea selves believe to be ‘
236
R.S. Woodward and F. Warren-Boulton, income, ethics a
patient, regardless of the z,umber of patients, wage rates, or fixed income levels. Indeed, physicians with fixed or time-based i come maximized their utility by minimizing the number of patients. emand suggests that The conventional understanding of suppher-induce physicians are able to inflate prices and ‘sell’ more tities by shifting their patient’s demand for me empirical support is drawn from ceteris par&us co cian density, prices, and utilization. Although this Note makes no statement about price determination and includes no direct measure of physician density, our propositions do address all the supplier-induced demand factors, at least indirectly. In the context of our stylized representation of the medical care market, we completely define the physician’s supply function and are thereby able to draw conclusions about the over- or undersupply of medical care at any price that the insurance companies or physicians set. First, we find that physicians with either fixed or time-based incomes will necessarily provide less-than-‘appropriate’ care regardless of their incomes or number of patients. This means that whether or not fixed and tie-based physicians are able to set their own incomes, and however densely the physicians are packed, the care that they provide will be less-than‘appropriate’. Therefore, one of the major implications of supplier-induced demand, that physicians will induce excessive utilization of their own services, is impossible for fixed and time-based incomes. A second basic implication of supplier-induced demand, that physicians with output-based incomes will provide more-than-‘appropriate’ care, is supported by the model, but only under certain circumstances. At low prices and large numbers of patients (low physician densities), physicians with output-based incomes may provide less-than-‘appropriate’ care. More-than‘appropriate’ care is only possible for physicians with output-based income, high medical care prices, and small numbers of patients. Even if the physicians are able to shift their patient’s demand, output-based income is not a sufficient condition for more-than-‘appropriate’ patient care. The additional utilization generated by a physician-induced increase in price may simply reduce the previous gap between the ‘appropriate’ and the less-than‘appropriate’ care previously supplied.
Arrow, Kenneth, 1963, Uncertainty and the welfare economics of medical care, American Economic Review 53, no. 5,941-973. , Gary, 1965, A theory of the allocation of time, Economic Journal 75, no. 299,493-517. 3, The hippocratic oath: Text, translation and interpretation, Bulletin of tine, Supp. 1 (Johns Hopkins University Press, Baltimore, MD) 3. Enthoven, Alain, 1978, Shattuck lecture - Cutting cost without cutting the quality of care, New England Journal of edicine 298, no. 22, 1229-1238.
R.S. Woodward and F. Warren-B&ton, Income, ethics and medical care
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Evans, Robert, 1974, Supplier-induced demand: Some empirical evidence and implications, in: Mark Perlman, ed., The economics of health and medical care (Wiley, New York). Evans, Robert, E.M.A. Parish and Floyd Sully, 1973, edical productivity, scale effects, and demand generation, Canadian Journal of Economics Feldman, Roger, 1979, The economic theory of health maintenance organizations, Mimeo., Ian. Fuchs, Victor, 1978, The supply of surgeons and the demand for operations, The Journal of Human Resources 8, Suppl., 35-56. Harris, 1978, Scitovsky, Tibor, 1951, Welfare and competition: The economics of a fully employed economy (Irwin, Chicago, IL). Silberberg, Eugene, 1978, The structure of economics: A mathematical analysis (McGraw-Hill, New York). of Health Manpower, 1980, The US Department of Health Education and Welfare, manpower policy, DHEW publitarget income hypothesis and related issues in cation no. (HRA) 80-27. Wilensky, Gail and Louis Rossiter, 1981, The magnitude and determinants of physicians initiated visits in the United States, in: Macques Vandergaag and Mark Perlman, eds., Health, economics, and health economics (North-Holland, Amsterdam). Williamson, Oliver, 1975, Markets and hierarchies: Analysis and antitrust implications (Free Press, New York). Woodward, Robert and Frederick Warren-Boulton, 1981, Physician productivity, remuneration method, and supplier-induced demand, in: Nancy Greenspan, ed., Health Care Financing Conference proceedings: Issues in physician reimbursement (DHHS, Health Care Financing Administration) Aug., 11S-1 34.
obert S. Washington University, St. Louis, A40 63110, USA
U.S. Department of Justice,
Washington, DC 20530, USA
Received May 1983, final version received March 1984 This manuscript presents a model of an ‘ethical’ physician’s allocation of time and income between work and leisure activities for various remuneration types and income levels. The physician is ‘ethical’ because, ceteris paribus, he prefers to provide that amount of medical care which he b&eves to be in the patient’s best interests. Remuneration systems include faed, timebased and output-based incomes. Only output-based income provides the physician with incentives which may (if the physician density and medical care price are sufliciently high) generate more-than-‘appropriate’ care per patient. Fixed and time-based incomes necessarily lead the physician to provide less-than-‘appropriate’ care.
The physician’s Hippocratic Oath’ is an ethical incentive to provide ‘appropriate’2 amounts of care. Yet physicians are accused of increasing their incomes by capitalizing on their patients’ uncertainties [Arrow (1963)] and shifting the demand for medical services [Evans et al. ( 1973), Evans ( 1974), *The authors wish to thank Peter McMenamin, Trout Rader, James Ramsey, Stuart Boxerman, and the editor and referees of this Journal for their helpful comments. This research was funded, in part, by contract 500-78-0055 between Washington University and HCFA, DHHS. Neither organization necessarily endorses the views and opinions expressed by the authors. I‘1 will apply dietetic measures for the benefit of the sick according to my ability and judgment; I will keep them from harm and injustice’ [Edelstein (1943)]. ‘By a purely medical standard, care is only ‘appropriate’ if its expected contribution to the patient’s health status is positive. By the economist’s societal standard, medical care is inefficient if its value to patients, however that may be defined, is less than the opportunity cost of the resources consumed. Because cost factors are ignored by the purely medical standard, medica!ly ‘appropriate’ care always involves more care than that indicated by the economist’s measure of efficiency. Nevertheless, the model’s results are not affected by the definition of ‘appropriate’. Whether physicians make decisions on pure medical appropriateness or on ‘suo2r-ethical grounds by taking social opportunity costs into account is unimportant to this analysis. ~\J?Tis any attempt made to provide an empirical or an operational definition of ‘appropriate’ cart:. Rather, our purpose is to demonstrate how financial factors may cause physicians to provide more or less care than they themselves would judge ‘appropriate’, whatever their definition may be.
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R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
(1980), Wilensky and Rossiter (1981)]. This note professional ethics and financial incentives jointly addresses the issue the amount of medical care provided each patient. iamson’s (1975) terms, medical care is one situation where ‘inforndeed: we can mation impactedness’ makes opportunistic beh names, is society’s argue that the basic designation ‘professional’, attempt to repress such opportun :tic behavior. As this note points out, the amount of such behavior and thus the need for such instituti will depend critically on the way economic incentives are strut This note models the work and leisure behavior of a physician who acts as an ethical procurement ‘agent’ for his patients and who is constrained by time and income. The physician is ethical because, ceteris paribus, he prefers to provide exactly the ‘appropriate’ amount of medical care. The physician allocates his time between work and leisure activities, which are both produced using time and purchased material inputs. This integration of professional ethics with a work-leisure model allows us to examine the effects of (1) the type of remuneration, (2) the level of remuneration, and (3) the number of patients (the inverse of physician density). The model may be interpreted as a stylized description of one physician’s supply decisions in a medical care system in which the fee schedules of thirdparty insurers, or other physicians, set prices exogenously. In this context, we examine how different compensation methods a&t this physician’s production decisions. Conclusions about the effects of supplier-induced demand are drawn from an understanding of how exogenously determined prices will affect the physician’s supply under each of the compensation alternatives. The specific policy issues addressed include the following questions. Which methods of physician remuneration are capable of restricting the potential e care? Wow much care per patient does a physician attempt to o higher prices necessarily imply more care? If the physician is able to shift demand, will he necessarily provide ‘too much’ care? What dynamic adjustments might be expected when the average population per doctor (the inverse of physician density) is not equal to the desired number of patients? And finally, if the model predicts sizable ineficiencies under simple remuneration systems, what institutional or market responses would we expect, and what public policy actions would reduce such inefficiencies? The following sections of the note introduce a model of physician workleisure decisions, analyze the effects of three alternative remunerations and of the number of patients on the supply of medical care, and consider a number of qualifications and policy implications. Fuchs (1978), US
a model of physicians who maximize their leisure objectives subject to production constraints deter-
R.S.
Income, ethics and medical care
225
mined by their limited time and income reso hysicians are assum maximize utility from two outputs, medical care per patient and leisure. produce these using their own time and ysicians finance both practice and leisure expenditures with earn under one of three remuneration alternatives: fixed, time-based, or output-based methods.3 2.1. Utility function
This model presumes that each physician derives additional utility both from positive consumption of the product of his leisure activities Z and from roviding addiiional medical care per patient V/N up to the ‘appropriate’ amount VX4
u = U[Z,
(V/N) - VA],
(1%‘5
where
u = the physician’s utility level, Z = the physician’s total production (and consumption) of leisure activities, V/N= the actual production of medical care per patient, V2l = the ‘appropriate’ care per patient determined by the physician’s own ethical standards, U, >O, ?Yvln > 0 when V/N c VA, and U,,,, CO when V/N > VA. A simple example of eq. (1) is the following quadratic utility function: U=Z--(V/N-
VA)2.
(W
The notion of utility from the composite leisure activity 2 rather than from leisure time and net income follows Becker (1965). The assumption that a doctor derives satisfaction from his professional activity, measured here by production of medical care per patient, is less common.5 While Evans (1974) and Wilensky and Rossiter (1981) presume that all care provides neptive utility, this overlooks the physician’s professional and ethical objectives. Scitovsky (1951, p. 87) recognized the issue 33 years ago: 3This pedantic terminology is adopted to call attention to the difference between these conceptually pure alternatives and the observable - but realistically mixed - income methods such as fee-for-service and salary. oodward 4Earlier versions of the model included only total care V in the utility function for our and Warren-Boulton (1981)]. The ‘care-per-patient’ specification, which is necess supplier-induced demand arguments, was suggested by Feldman ( 1979). ‘Of course, consumer utility is an important factor in optimal price dete Harris (1978).
R.S. Woodward and F. Warren-&n&on, Income, ethics and medical care
226
‘Artists, scientists, professional people, and businessmen ofte their work not merely as a means of earning income but as an important and interesting part of their lives.’ nthoven (1978) has defined physicians’ joint objectives: other health professionals are motivated by nonfinancial goals, including a desire to cure the sick d to achieve professional excellence and esteem of peers and public. t their use of resources is inevitably shaped by fmancial incentives.’ ‘Physicians
and
Our model includes medical care per patient in the utility function as a direct representation of physicians’ ‘desire to cure the sick’. Our designation of the ‘appropriate’ amount of medical care per patient VA is included to recognize that too much care may be possible, but should not be assumed. We presume that VA represents the physician’s own best judgment of the ‘appropriate’ level of care for each patient, which may be based upon medical factors alone or may include considerations of patients’ out-of-pocket expenses or resource opportunity costs. The physician’s perception of ‘appropriate’ may be affected by his professional standards, personal morals, fear of professional or legal punishment, and medical education. While the exact specEcation of ‘appropriate’ medical care and its sensitivity to changes in any of these determinants is beyond the scope of this research, our policy recommendations will obviously depend upon the extent to which physicians recognize resource costs in the definition of VA. 2.2. Leisure activity Following Becker (1965), we assume that physicians produce leisure activities using consumer purchases X, and their own time t,. 2 = z(t,,
x,),
(2)
where 2 =production of leisure activities, tz = leisure time, xz = consumer goods purchased from income, Zt, > 0, and ZX,> 0. edical care production e&al
output V is produced using expenditures o e t,6 and patients N,
‘we drop the subscripto to t
practice inputs x,
and x to minimize clutter in the subsequent equations.
R.S. Woodward a& F. Warren-Bouiton, Income, ethics and m
v = V( t, x, Iv), where V = the total quantity of medical care produced, t = the individual’s (physician’s) time at work, x = the quantity of (practice) inputs purchased with income, N = the number of patients under the physician’s care, v,,1G;,Kl>o. The number of patients per physician N is inclu input for two reasons. First, the number of patients per ph productivity of the other factors. For example, a larger per physician (which might result from a reduction physicians in the country) forces the physician to triage sicker patients. In such a case, each physician’s time and ex produce more medical care per patient at the margin. Second, the number of patients per physician N is in supplier-induced demand. The last section of the note cons of physician densities on supplier-induced demand in the c tions about the aggregate population, the number of physic adjustments. 2.4. Constraints The physician’s production of medical care and leis e activities constrained by his income and his time. T=t+t,
and
Y=x+x,,
is
WY(5)
where T = total time, Y =gross physician real earnings (gross dollar earnings divided by the price of goods).’ Income is earned according to one of three remuneration alternatives: fixed, time-based, and output-based. The simplest income is fixed: the physician receives a predetermined amount per time period regardless of his labor (or non-labor) activities during that (or any sequential) period.
Y'y,, where & is exogenously determined. ‘For expositional simplicity, the units of consumption goods x, and of practice inputs x, have been normalized so that their prices are equal to one, pX=pX, = 4.
228
R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
Time-based income, t second remuneration alternative, is directly proportional to the physic ‘s hours of work. Although wages are the best understood time-base remuneration, physicians seldom receive the Nevertheless, the fees the fee-for-service system may be determined in par by the time taken by
(7)
Y=wt,
where w is an exogenously determined wage rate. utput-based income, the third remuneration alternative, is a fixed payment per unit of output regardless of the physician’s time or use of practice inputs or equipment. It most closely corresponds to physicians’ case rates, payments per unit of health output or for treatment of specific conditions, such as a normal delivery or setting a simple fracture. Fee-for-service remuneration may also have a substantial output-based component.
(8)
Y=P
where P is an exogenou,c:price per unit of health care output. Thus in its general form, allowing for pure and combined systems, the income constraint becomes
2.5. Summary The general constrained utility function for this work-leisure model is U=U{Z[T-t,Y,+wt+PV(t,x,N)-X-J,
ww
v(t,x,N)/N-VA}.
An algebraic specification employed to demonstrate some indeterminate results is U=(T-t)“(Y,+
wt+PV--x)l-‘“+
(
2
f(Nta,l-P_j7~. >
-jy-
Answers to the questions about the effects of the financial incentives on a physician’s provision of medical care are provided by two theorems. For the al simplicity, the following sections develop each of these three remunerations separately. We start with the fixed re relatively straightforward and which provide a
R.S. ‘Woodwardand F. Warren-Boulton, Income, ethics and medical care
readily understandable point income models.
229
for the time- and output-based
3.1. Fixed income
The fixed income model is simply an application of the well-known two input, two output international trade (or regional growth) models and their Edgeworth box representations. Propositim 1. Physicians paid a fixed thau-‘appropriate’ care per patient.
income will necessarily provide less
A suficient condition for less-than-‘appropriate’ care being provided by a physician with our ‘ethical’ utility function is a negatively sloped production possibility frontier (PPF), dZ 14~J~4V) c 0. We derive the conditions for a downward sloping PPF with a general envelope theorem based on maximizing V/N subject to a given level of 2. To avoid repetition for time- and output-based incomes, we write the function in its general form. max &= ?(t,x,N)/N+il[Z(T-t,
q-t-wt+PV-x)-Z].
For the fixed income case (w = P = 0, yf > 0), the first order conditions are
&= K/N-Zt=O, Ex = v,/N--&U,
and
=o.
(12)
(13)
Since il can be interpreted as -d( V/N)*/dz, where (V/N)* is the optimum level of V/N, the condition for the PPF to be downward sloping is that A>O. Since ;1= K(NZ,) = VJ(NZ,) for a fixed income system, this is satisfied if all marginal products are positive. Suffkient second order conditions for a maximization are that all marginal products are diminishing and all cross products are positive. A more intuitive argument also establishes that physicians with fixed incomes will never provide too much care. Suppose the physician with a fixed income is providing more than the ‘appropriate’ amount of care. T by reallocating his expenditures and time from medical care to increases his utility both from the additional leisure activities an closer-to-‘appropriate’ amount of medical care Proposition 2. The change in the quantity of care attributable incomes depends on the relative factor intensities of work
R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
230
the slope of the supply of medical care provided by an ethical fixed income physician is not uniquely determined, we develo Proposition 2 using the Cob ouglas production model, eq fixed incomes have two effect the provision of medical ca ybczynski effect and a change in the slope of the utility function. The ybczynski theorem states that if the endowment of some resource increases in a model with fixed relative output prices, the activity that uses that resource more intensively will increase its output while the other activity will decrease its output [Silberberg (1978, p. 408)]. Fixed output prices of the ybczynski theorem correspond to a simplified utility function U = AZ+ B(V/N). If A and B aId con@ants, increased physician income will increase the production of medical care only if medical care uses purchased inputs more intensively than does leisure production. The first order conditions of the model, eq. (lob), with the simplified utility function and where w = P =O, are Because
U,=A(-a)(T-t)“-l(Y-x)lwa+BB_
f(N)plxI-p,o,
Ux=A(a-l)(T-t~(Y-x)-a+B(l-@~tflxe@=O.
The contract curve is derived by solving both equations for X, x=a(l -@tY((l -a)/?(T-- :)+a(1 +)t). Substituting x from eq. (16) into eq. (15) and solving explicitly for 4
and then for X,
x
a(l ~)y (p ) --f(N)\'4p-a)T -a. N ,I - -
The supply curve, the change in V/N attributable to an increase in fixed income, is where aN = 0.
(19) s relat
t
R.S. Woodward and F. Warren-h&en,
p > a, (dx/d u) < 0, (dt/d
Income, ethics and me.“icalcare
and
(d V/d Y)c 0.
and
(dV/dY)>O.
231
If V is relatively x intensive, then a>/?,
(dx/dY)>O,
(dt/dY)>O
(21)
The second effect of an increased fixed income is the change in the shadow prices of medical care and leisure caused by the uadratic utility representation of the ‘ethical’ physician. If Z and C/,‘lVare al goods, the second effect will reduce or eliminate the Rybczynski result. While such a change may be represented by examinirg the impact of dx/d(B/A) and dt/d(B/A), the basic dependency of d( V/N)/dY on a - j3 is unaffected. 3.2. Time-based income
The models for time-based and output-based income differ in one important respect from the fixed remuneration framework: income (and therefore the sum of practice expenditures and consumption goods) is not predetermined. By definition, time-based income implies that the total expenditures are constrained to be proportional to time at work. The following paragraphs develop the two propositions about the behavior of physicians on a time-based income. Proposition 3. Physicians paid a time-based income will necessarily provide too little care per patient.
Again, a sufficient condition for less-than-‘appropriate’ care is a negatively sloped PPF which can only be tangent to the utility curve at some less-than‘appropriate’ level of medical care. As in the fixed income case, we can derive the conditions for a downward sloping PPF using a general envelope theorem. For the time-based income case P=O in eq. (1 l)], the first order conditions are
[rf=
&=F/N+a[-Z,+wZ,]=O,
and
ic,=vJlv+iz[-Z,]=O.
Again since jLcan be interpreted as - d( V*/ (fig. 1)8 to be downward sloping is il>O. oreover if ZC9l$ ;1> satisfied if ZX, ‘Figs. 1 and 2 a re derived from a simulation ~=(5~-t)0.~(y-JC)0.5+[t0.6~X6.2J~-0.9_20]IZ, where y = 6525r, V = 9.2 t: an
(22)
232
R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
Fig. 1
A more intuitive explanation ~follcwsfrom a description of the impact of shifting resources from 2 to K Holding t, and t, constant, if one unit of x is shifted from 2 to V production, V will increase if VX>O and 2 will decrease if 2, >O. If one unit of time is shifted from 2 to V production, V will increase if K >O. However, the increase in time spent at work leads to an increase in income which can be spent on consumption goods. Thus 2 will fall only if Zt > ~2,. Thus a sufficient set of conditions for dZ/d( V/IV) ~0 is Vx, Zx and K >O, and Zt > ~2,. Proposition 4. The slope of the supply curve, the change in medical care per patient attributable to higher wage rates, is also determined by relative factor intensities.
ecause time-based income introduces an extra term in the first order condition U, =0, explicit solutions for x and t are impossible, even in the case of the linear utility function employed for Proposition 2. Nevertheless, some results may be derived from the implicit function theorem. The first order conditions for the linear utility, Cobb-Douglas, time-based income model are U,=
U,=
--A(1 -a)
+B(1-j?)?
and
R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
x=(1 -&wt[t-(1 v;here the condition U, = 0 gives
-a)TJ/((I
-a)/3(T-t)+a(l
+)t),
t > (I- a)T follows from 2, > ~2,.
233
(261 Substituting
x into
As in the fixed income case, the slope of the supply curve, dV/dw, will depend upon dt/dw and dx/dw. As an example of the indeterminacy of dt/dw, we calculate aglat and ag/aw.
If the conditions of the implicit function theorem are satisfied, that is if g(t, can be written as g[t(w), w] and if aglat #0, then dt,‘dw = - (WwMW0
l
w)
(30)
No simple conditions relating the size of a and /? appear to determirle the slope of the supply function. If medical care production is relatively expenditure intensive, a>/3 and dg/aw 4, but the sign of ag/i?t is indeterminate. If medical care production is relatively time intensive, a c/? and ag/at CO, but the sign of ag/aw is indeterminate. 3.3. Output-based income Output-based income has a considerably different effect on the amount of care provided each patient. Leisure production is directly affected by the allocation of all three production inputs - time, expenditu of patients. As a consequence, the utility maximizing num greater than zero and more-th After a brief description of following paragraphs develop these results. Pro position 5. the ‘appropriate’ level of medical care.
234
R.S. Woodward and F. Warren-Boulton, Income,
ethics ati medical care
Output-based income incorporates finanGia1 incentives which do not necessarily force the physician to provide iese-than-‘appropriate’ care per patient (fig. 2). An envelope theorem demonstrates tha.t dZ/d VlN) cannot be generally signed. The first order conditions of eq. (I l), where Y = w =0 and P>O, are &= K/N+&-Z,+PZ,K)=O,
100-f
z
and
(31)
PRODUCTION POSSIBILITY FRONTIER OUTPUT-BASED INCOME
90 88 78 60 58 40 36 20 10 +..........I.......... 4..........I.......... I.......... I.......... t ..........1. 0 ! ..........+..........I.......... 0 5 18 15 28 25 38 35 48 45 50 U/N
Fig. 2
fficient condition for the PPF to be downward sloping is that r, positive marginal products are insufficient to establish the two extra conditions indicated by eqs. (3 1) and (32), Zt > Pz, K and PY, < 1. Rather, the slope of the PPF will be negative if either of these two conditions holds and positive if either of the inequalities is reversed. Moreover, eqs. (31) a -Zt and PV, - 1 have the same sign. onditions can be seen by examining the impact of shifting resources from Z olding t and t, constant, if one unit of x is transferred to V production, V will increase if Vx>O. But this increase in V leads to an increase in income of PV,. If this is greater than unity, a transfer will allow an increase in both % and V. Thus if PV,> 1, then >O. Similarly, if a unit of time is transferred to V production, V will increase if K >O. The resulting increase in income, PV,, if spent on Z 1 increase Z by P&Z, units. If this increase is greater than the of reducing t,, i.e., if Pb$Z, > Zt, then dZ/dV > 0. Thus, we may being nlY is st be
R.S. Woodward and F. Warren-Boulton, Income, ethics and medical care
235
possible to increase both V and Z by transferring either time or production inputs from work to leisure. Proposition 6. The slope of the physician’s SUPPlY response prices is not uniquely determined.
to
higher output
The same set of parameters determines the slope of output-based income supply as determines the time-based remuneration’s slope. of the Cobb-Douglas model reduces to x= t[a(l +?)Pt/((l -a)j?(T-
t) +cl(l
+)t)-j?
Substituting x into the model’s first order condition U, yields g=A(l
-a)(T-t)“[(l
-A(T-t)“-l[(l
-a)jw+(a-/3)t-J1’@/t[a(l
-a)T+(a-j?)t]
-/3)Pt]“B
-B[(l -a)T+(a-/?)t]/aPt.
(34)
The (a -/I) coefficients of t cause ihe sign of aglat, aglaP, and t and dV/dP to depend upon the relative factor intensities. This indeterminacy has important implications for the supplier-induced demand controversy. While output-based income may be a necessary condition for more-than-‘appropriate’ care, it is not a suficient condition. Indeed output-based remuneration, even when coupled with a moderate ability to shift the prices of medical care, does not necessarily generate more-than‘appropriate’ care. If a physician is able to shift. the demand curve and increase the price of care, it is not possible to determine a priori whether or not the resultant increase in medical care provided per patient is a move toward, or away from the ‘appropriate’ levels. 4. Conclusions
This note presents a model of an ‘ethical’ professional’s allocation of time and income between leisure and work activities for various remuneration types, income levels, and numbers of patients. ‘Ethics’ are represented by a utility function which generates disutility from providing ‘either more- or lessthan-‘appropriate’ amounts of care per patient by the physician’s own standards. Of the three remuneration types, only physicians with the financial incentives which is sufficiently low and the price ‘appropriate’ amounts of medical care incomes necessarily lea selves believe to be ‘
236
R.S. Woodward and F. Warren-Boulton, income, ethics a
patient, regardless of the z,umber of patients, wage rates, or fixed income levels. Indeed, physicians with fixed or time-based i come maximized their utility by minimizing the number of patients. emand suggests that The conventional understanding of suppher-induce physicians are able to inflate prices and ‘sell’ more tities by shifting their patient’s demand for me empirical support is drawn from ceteris par&us co cian density, prices, and utilization. Although this Note makes no statement about price determination and includes no direct measure of physician density, our propositions do address all the supplier-induced demand factors, at least indirectly. In the context of our stylized representation of the medical care market, we completely define the physician’s supply function and are thereby able to draw conclusions about the over- or undersupply of medical care at any price that the insurance companies or physicians set. First, we find that physicians with either fixed or time-based incomes will necessarily provide less-than-‘appropriate’ care regardless of their incomes or number of patients. This means that whether or not fixed and tie-based physicians are able to set their own incomes, and however densely the physicians are packed, the care that they provide will be less-than‘appropriate’. Therefore, one of the major implications of supplier-induced demand, that physicians will induce excessive utilization of their own services, is impossible for fixed and time-based incomes. A second basic implication of supplier-induced demand, that physicians with output-based incomes will provide more-than-‘appropriate’ care, is supported by the model, but only under certain circumstances. At low prices and large numbers of patients (low physician densities), physicians with output-based incomes may provide less-than-‘appropriate’ care. More-than‘appropriate’ care is only possible for physicians with output-based income, high medical care prices, and small numbers of patients. Even if the physicians are able to shift their patient’s demand, output-based income is not a sufficient condition for more-than-‘appropriate’ patient care. The additional utilization generated by a physician-induced increase in price may simply reduce the previous gap between the ‘appropriate’ and the less-than‘appropriate’ care previously supplied.
Arrow, Kenneth, 1963, Uncertainty and the welfare economics of medical care, American Economic Review 53, no. 5,941-973. , Gary, 1965, A theory of the allocation of time, Economic Journal 75, no. 299,493-517. 3, The hippocratic oath: Text, translation and interpretation, Bulletin of tine, Supp. 1 (Johns Hopkins University Press, Baltimore, MD) 3. Enthoven, Alain, 1978, Shattuck lecture - Cutting cost without cutting the quality of care, New England Journal of edicine 298, no. 22, 1229-1238.
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Evans, Robert, 1974, Supplier-induced demand: Some empirical evidence and implications, in: Mark Perlman, ed., The economics of health and medical care (Wiley, New York). Evans, Robert, E.M.A. Parish and Floyd Sully, 1973, edical productivity, scale effects, and demand generation, Canadian Journal of Economics Feldman, Roger, 1979, The economic theory of health maintenance organizations, Mimeo., Ian. Fuchs, Victor, 1978, The supply of surgeons and the demand for operations, The Journal of Human Resources 8, Suppl., 35-56. Harris, 1978, Scitovsky, Tibor, 1951, Welfare and competition: The economics of a fully employed economy (Irwin, Chicago, IL). Silberberg, Eugene, 1978, The structure of economics: A mathematical analysis (McGraw-Hill, New York). of Health Manpower, 1980, The US Department of Health Education and Welfare, manpower policy, DHEW publitarget income hypothesis and related issues in cation no. (HRA) 80-27. Wilensky, Gail and Louis Rossiter, 1981, The magnitude and determinants of physicians initiated visits in the United States, in: Macques Vandergaag and Mark Perlman, eds., Health, economics, and health economics (North-Holland, Amsterdam). Williamson, Oliver, 1975, Markets and hierarchies: Analysis and antitrust implications (Free Press, New York). Woodward, Robert and Frederick Warren-Boulton, 1981, Physician productivity, remuneration method, and supplier-induced demand, in: Nancy Greenspan, ed., Health Care Financing Conference proceedings: Issues in physician reimbursement (DHHS, Health Care Financing Administration) Aug., 11S-1 34.