More on Production and Cost Allen C. Goodman © 2015

Labor Inputs We want to examine MP/P, the marginal product per dollar, is the relevant measure when determining which input to increase. To increase profits one should hire the extra input that has the greatest MP/P, the greatest bang for the buck. If this marginal product per dollar is not equal for each category of worker, the firm can always save money by trading a lesser producing worker per dollar for a higher producing one.

Labor Inputs Brown (1988) concluded from these data that physicians were under-utilizing nursing inputs. Consider the data for practical nurses in all physicians offices. PNs have a higher marginal product per dollar, 0.129, than do physicians, 0.114; thus the offices would become more profitable if one substituted practical nurses for physicians. In addition, Brown found that physicians in group practices were, on average, 22 percent more productive than those in solo practices. Marginal product of physician assistants, PAs, for solo practices was actually estimated to be negative; in contrast, PAs were very productive on the margin in group practices. Even so, group practices are underutilizing PAs.

More Recent Work Escarce and Pauly (1998) found that each hour of time for office-based internist substitutes for $60 in non- physician costs. What does this mean? Jacobson et al (1998) report that PAs/NPs can perform % of tasks of primary physicians without compromising work, when they work with primary physicians.

Kantarevic and Colleagues (2011) Compared traditional FFS with an enhanced FFS (that provided financial rewards for improved quality through chronic disease management and after-hours services). Results: Physicians who joined enhanced FFS had about 6 – 10% higher productivity in terms of services, visits and numbers of patients. BUT, large part of this came through increased labor rather than increases in output/unit labor

Repairing the Surgery Deficit SARIKA BANSAL New York Times August 8,

Shortage of Surgeons Across Africa, countless people die or become disabled because they cannot obtain necessary surgeries. It is conservatively estimated that 56 million people in sub-Saharan Africa — over twice the number living with H.I.V./AIDS — need a surgery today. conservatively estimated Some need cesarean sections or hernia repairs, while others require cataract surgery or treatment for physical trauma.

Implications Patients cannot get surgeries like cesarean sections. Smaller health facilities often have no choice but to refer patients to larger cities. Surgical equipment is sometimes nonexistent, especially in remote areas, and supplies are a challenge to maintain. More critical, though, is the human resource gap. In 2012, Zambia had only 44 fully licensed surgeons to serve its population of 13 million, who are spread over an area slightly larger than Texas.

The Shortage Finding fully licensed surgeons is not easy. Not only is the absolute number of surgeons low, but the distribution is also very uneven. Only 6 of Zambia’s 44 surgeons lived in rural areas, and all of them are expatriate missionaries. Fully licensed doctors are also in high demand in other lines of work. Some leave public sector clinical practice to pursue careers in administration, private clinical practice and international NGO work — all of which can be more lucrative.

Task Shifting Instead of finding ways to lure surgeons to rural areas, many African countries started experimenting with “task shifting” — that is, training non-physicians to do the basic work of surgeons. In Zambia, surgical task shifting began in 2002 with the medical licentiate program, which trains clinical officers in basic surgeries like hernia repairs, bowel obstruction surgery, hysterectomies and more. The Surgical Society of Zambia and the Ministry of Health jointly determined the procedures in which licentiates should be trained. For instance, the program emphasizes training in cesarean sections, which constitute 45 percent of major surgeries in the country.

Cost Functions & Economies of Scale, Scope With the standard formulation, we often wish to generate curves that related costs to the amount of output Q. If we believe that there are first increasing, then decreasing returns to scale, we get a standard U shaped cost curve. Quite simply, if C = C (Q), then MC = C'. If we had a competitive market, we could presume that eventually we would end up at bottom of cost curve. Take the simplest monopolistic model, where:  = TR - TC q $ AC MC Moving on …

Cost Functions & Economies of Scale, Scope Take the simplest monopolistic model, where:  = TR - TC = p(q)q - C(q) d  /dq = qp' + p - C' = 0 This is simply MR = MC qp' + p = C' p (1 + 1/  ) = C' C'/p = (1 + 1/  ), where  is the demand elasticity.  is negative, and greater in magnitude than -1, so C'/p < 1. Think  = -2,  = -3, etc. q $ AC MC D MR

Cost Functions & Economies of Scale, Scope Simple point, here, is that there is no reason for AC to be minimized at profit maximizing output. We may be at a point at which marginal costs are too high, or are too low. q $ AC MC D MR q* P* Minimum cost!

What about economies of scope. This comes from the idea of a hospital’s producing 2 or more commodities. Suppose, for example, that a hospital could produce either Q 1, Q 2 or both. Total costs of Q 1 = 100, with no Q 2 are TC (100, 0). Total costs of Q 2 = 150, with no Q 1 are TC (0, 150). Total costs of both are TC (100, 150). We have economies of scope IF: TC (100, 150) < TC (100, 0) + TC (0, 150).

Joint Production Look at teaching hospitals Medical education is a good example of joint production. That is, medical schools produce at least three products jointly: - medical education, - patient care and - research. To reimburse for patient care or to fund medical education appropriately, it is necessary to determine what are the pure costs of these activities and what are joint costs. An (old) example, taken from Newhouse (1978), illustrates these terms.

Hypothetical Example of Joint Production at a Medical School Millions of Dollars Total Cost of School 600 Cost if "school" produced only patient care 300 Cost if school produced only education 500 "Pure" cost of education * 300 "Pure" cost of patient care * 100 Joint costs * 200 The total annual cost for a medical school which produces education and patient care is $600 million. If the school produced only education, with only the minimum patient care needed to do this, its costs would be $500 million. If it produced only its present volume of patient care and no medical education, its costs would be $300 million.

Millions of Dollars Total Cost of School 600 Cost if "school" produced only patient care 300 Cost if school produced only education 500 "Pure" cost of education * 300 "Pure" cost of patient care * 100 Joint costs * 200 Hypothetical Example of Joint Production at a Medical School 600 – 300 = Incrementally, the cost of patient care raises the school's budget from $500 to $600 million. Thus the pure cost of patient care is the extra $100 million. 600 – 500 = 600 – 300 – 100 = Reasoning in a similar fashion, adding education to the cost of patient care raises the budget from $300 million to $600 million. Thus the pure cost of education is $300 million. The difference between total cost of this hypothetical medical school and all the pure costs is $200 million in this case. This $200 million is called the joint cost.

Joint Costs and Reimbursement It follows that if the school were reimbursed only for pure costs, it would run a deficit. Much of the controversy with respect to funding revolves around the problem of who will pay for the joint costs. The issue of joint production has centered on the teaching hospital, which also jointly produces patient care and medical education through its provision of internship, residency, and medical research. Joint costs are real costs, not an accounting fiction!

Joint Costs and Reimbursement In particular, with the substantial cost differences between teaching and non-teaching hospitals, third-party payers are concerned about whether they are unnecessarily subsidizing medical education. The conventional wisdom in the 1970s was that the cost of education and affiliation with a medical school was substantial. Close examination of the cost differences between teaching and non-teaching hospitals found that that non-physician costs per day were 21% higher in teaching hospitals. However, using statistical tools to sort out the causes for cost differences, non-physician costs, though still higher in teaching hospitals, the difference is typically less than 10%.

Joint Costs & Reimbursement (20 Most of the current research is 10 to 15 years old. The 10% difference seems to have held up recently, although hospitals still insist that they need more. This link was written in 2010 from the Association of American Medical Colleges. See aamc.aamc

Total Costs, Z Too many beds? Key idea w.r.t. hospital planning is whether we have too many hospital beds and/or big ticket equipment items. If we have too many of them, we could presumably cut costs by having more people use smaller numbers (of larger hospitals). It's important to consider other costs, such as transportation costs, as well. Too Many Hospitals, Too Many Beds? Number of hospitals, N Total Transportation Costs T Total Production Costs C One hospital for all Michigan? Why?

We'll consider two simple models that show some of the problems. First, suppose that demand Q is totally price inelastic. As planners we want to minimize costs. Key is to determine number of hospitals N, each of size Q/N. Assume Q is fixed. This may invoke economies of scale. However, transportation costs T are a function of N. In particular, the more N, the lower T. We get: Too Many Beds? Number of hospitals, N Total Costs, Z Total Transportation Costs T Total Production Costs C Larger N  Smaller hospital

Too Many Beds? Total Costs = # Hosp * (Cost/Hosp.) + Transportation Costs Z = N AC (Q/N) + T(N). Differentiating w.r.t. N, we get: dZ/dN = AC - N AC' Q/N 2 + T' = 0. AC - AC' x (Q/N) = - T' AC – Δ AC x hospital size = -T' If there were no transportation cost, you would have T' = 0,  AC = Δ AC x hospital size. Number of hospitals, N Average, Mgl Costs AC Δ AC x hospital size Since T' 0, so AC – Δ AC x hospital size > 0. In this example, the hospital must be smaller than “least cost”, so that there are more of them, hence reducing transportation costs. N(0)N(T) Larger N  Smaller hospital Remember, Q is constant

Second Model – Market Size Model Where hospitals are too big, and are producing on upward sloping part of cost curve. Presumably, if you break them up, you can lower costs. The key is demand. If you break up the hospital into 2, you may be breaking the demand up into 2 as well Q $ LRAC Q1Q1 AC 1 AC MIN Q2Q2

Costs Market Size Model You could have a demand curve that is below the average cost curve, for each one. This is an argument that is made by hospitals in one- hospital towns, in response to anti-trust complaints. How might price discrimination address this issue? Allows hospital to collect enough revenues to cover costs Q $ LRAC Q1Q1 AC1 AC MIN Q2Q2 D Revenues

What Have We Found? Folland is the real expert on this. Here are the major problems. 1. Many studies basically have measures of output, and measures of aggregate costs. So, they estimate: C (or C/Q) =  0 +  (Q) +   D.  (Q) is some polynomial term in Q that allows you to have curvature in your marginal and average cost curves. By differentiating the function w.r.t. Q, you get measures of marginal cost, and inferences about economies of scale. 2. Structural models go from the cost minimizing condition that we have derived. Require, for example, input costs. Some argue that omitting input costs implies that you're assuming no substitution possibilities among them.

What Have We Found? 3. Case mix, quality of care - Hospitals that take more difficult cases, or that provide higher quality of care, will have higher costs. This should be netted out. The health care profession always trots this out when you come up with a result that they don't like.

Results In a nutshell, we don't know a lot. Into the early 1980s there was a consensus that economies of scale were reached up to about 250 beds. Further work was inconclusive, but the most recent work suggests that economies of scale kick in, and the curve flattens at about 100 beds. Not clear if it rises. AG: We don’t see 1,500 or 2,000 bed hospitals so it must rise somewhere out there. AC $ Q

Results One (OLD) interesting finding is Grannemann, Brown and Pauly who argue for: - existence of diseconomies, even when case-mix is accounted for. - interesting notion that emergency departments exhibit fairly strong economies of scale, although it affords the hospital diseconomies in terms of scope.

Kathleen Carey* James F. Burgess Jr.* and Gary J. Young** AHRQ Annual Meeting – September 21, 2011 Research funded in part by the Robert Wood Johnson Foundation and by AHRQ *Boston University School of Public Health and Department of Veterans Affairs ** Northeastern University

Marginal Cost Average Cost Medical Services Cost Range of EOS

Short-run cost function Cubic functional form GEE estimator EOS = _____(1 – BED elasticity)_____ (DIS elasticity + OPV elasticity) = __________(1 – δ*BED)__________ [ (α 11 DIS + 2*α 21 DIS 2 + 3*α 31 DIS) 3 + β 11 OPV +2* β 21 OPV 2 + 3*β 31 OPV) 3 ]

General HospitalsSpecialty Hospitals Discharges Visits Beds EOS Discharges Visits BedsEOS Q1 1,60028, , Median 4,64561, , Q3 10,925121, ,

Economies of scope (ESC): present if the cost of jointly producing a set of outputs is lower than the costs of producing those outputs separately For the 2 output case: ESC = [C(DIS, 0) + C(0,OPV) – C (DIS,OPV)] / C(DIS,OPV) ESC are present if the expression is positive –Will occur if the numerator is positive –Indicates it is cheaper to produce outputs DIS and OPV jointly than in separate facilities The expression rarely applied in the case of hospitals because it is unusual that hospitals would be producing at levels of zero output

Two types: Orthopedic/Surgical and Cardiac Key differentiating factors in addition to specialization: –Size: Cardiac average 60 beds – OrthSurg average 20 –Scope of Services: Most OrthSurg SSHs do not have Emergency Departments but most Cardiac SSHs do –Payer mix: MedPAC found that ~ 2/3 of Cardiac SSH patients were reimbursed by Medicare and 1/3 by private payers; for OrthSurg SSHs just the reverse Not all Single Specialty Hospitals are the Same

A conception of economies of Scope (ESC) ESC exist if it is possible to produce outputs jointly in the same hospital cheaper than it is to produce them separately How will we measure ESC? –where System A is general hospital production, System B is SSH production, and System C is a simulation of general hospital technology cost of producing (general hospital + SSH) outputs

Specialty Hospitals General Hospitals 1 st QuartileMedian3 rd Quartile 1 st Quartile ( )/23.95 = 0.30 ( )/43.02 = 0.16 ( )/ = 0.05 Median ( )/25.07 = 0.38 ( )/44.74 = 0.18 ( )/ = rd Quartile ( )/27.62 = 0.59 ( )/48.60 = 0.28 ( )/ = 0.07 Costs measured in million $ Quartile values taken across distributions of discharges and outpatient visits [ESC = (Cost A + Cost B – Cost C) / Cost C]

Specialty Hospitals General Hospitals 1 st QuartileMedian3 rd Quartile 1 st Quartile Median rd Quartile Implicit Cost Savings (million dollars): (Cost A + Cost B – Cost C)

SSHs may lack sufficient scale to compete effectively with general hospitals on the basis of cost efficiency –Yet this supply side analysis does not account for demand side price competition pressures Simulation analyses also suggest potential improvement in cost efficiency through exploitation of economies of scope by shifting SSH production to general hospitals But only one piece of evidence in understanding a very complex issue: SSHs might be able to control costs through leaner staffing, tighter inventory control and/or effective discharge planning.

Pedro Pita Barros and Luigi Siciliani International Flavor From Handbook (Ch. 15), regarding hospitals: In terms of actual treatment, for example from a surgical operation, private hospitals may be small and have limited emergency facilities. Public hospitals may benefit from economies of scope. If the volume of patients treated is higher in public than in private hospitals, then public provision may display better outcomes. Note that even if quality is higher in the public sector, some patients may still opt for the private sector if they value highly lower waiting times and better amenities.

Older Stuff

An alternative literature has also developed about explicit substitution between physicians, and physician-extenders. Table 16.1 Marginal Products and Efficiency of Input Use AllSoloGroup PhysiciansPhysiciansPhysicians InputMPMP/PMPMP/PMPMP/P Physician Secretary Reg. Nurse Practical Nurse Technician Phys. Ass't MP = Marginal Product MP/P = Marginal Product per Dollar Spent on Input Source: Brown (1988) Elasticity of Supply among Labor Inputs

Labor Inputs Brown (1988) estimated marginal products of physician time and other inputs, calculated at mean values of the variables The marginal products of auxiliary workers are shown in the columns labeled MP for data from physician offices of various categories: all physicians, solo physicians, and group practice physicians. The columns labeled MP/P are of special interest. By dividing MP by the price of each input, to get the marginal product per dollar spent on each factor, we can draw inferences about whether physicians are underutilizing or overutilizing various categories of workers. Bang/$

Labor Inputs The MP/P, the marginal product per dollar, is the relevant measure when determining which input to increase. To increase profits one should hire the extra input that has the greatest MP/P, the greatest bang for the buck. If this marginal product per dollar is not equal for each category of worker, the firm can always save money by trading a lesser producing worker per dollar for a higher producing one.

Labor Inputs Brown concluded from these data that physicians were under- utilizing nursing inputs. Consider the data for practical nurses in all physicians offices. PNs have a higher marginal product per dollar, 0.129, than do physicians, 0.114; thus the offices would become more profitable if one substituted practical nurses for physicians. In addition, Brown found that physicians in group practices were, on average, 22 percent more productive than those in solo practices. We can see that the marginal product of physician assistants, PAs, for solo practices was actually estimated to be negative; in contrast, PAs are very productive on the margin in group practices. Even so, group practices are underutilizing PAs.