More on Production and Cost

More on Production and Cost
755_l12 7/4/2018 More on Production and Cost Allen C. Goodman © 2017

755_l12 7/4/2018 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.

755_l12 7/4/2018 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.

755_l12 7/4/2018 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)
7/4/2018 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
755_l12 7/4/2018 Repairing the Surgery Deficit SARIKA BANSAL New York Times August 8, 2012

755_l12 7/4/2018 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. 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.
7/4/2018 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.

755_l12 7/4/2018 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.

755_l12 7/4/2018 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
Moving on … 7/4/2018 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 MC AC $ q

7/4/2018 Cost Functions & Economies of Scale, Scope D MR 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. MC AC $ q

7/4/2018 Cost Functions & Economies of Scale, Scope D MR 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. MC P* AC $ Minimum cost! q* q

What about economies of scope.
755_l12 7/4/2018 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 Q1, Q2 or both. Total costs of Q1 = 100, with no Q2 are TC (100, 0). Total costs of Q2 = 150, with no Q1 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
7/4/2018 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
7/4/2018 Hypothetical Example of Joint Production at a Medical School 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 Cost if "school" produced only patient care Cost if school produced only education 500 "Pure" cost of education* "Pure" cost of patient care* Joint costs*

Hypothetical Example of Joint Production at a Medical School
7/4/2018 Hypothetical Example of Joint Production at a Medical School 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. Millions of Dollars Total Cost of School Cost if "school" produced only patient care 300 Cost if school produced only education "Pure" cost of education* "Pure" cost of patient care* Joint costs* 600 – 300 = 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. 600 – 500 = 600 – 300 – 100 = 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
755_l12 7/4/2018 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
755_l12 7/4/2018 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
755_l12 7/4/2018 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.

Too Many Hospitals, Too Many Beds?
7/4/2018 Too Many Hospitals, Too Many Beds? Total Transportation Costs T Total Production Costs C 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. Total Costs, Z Why? Number of hospitals, N One hospital for all Michigan?

755_l12 7/4/2018 Too Many Beds? Total Transportation Costs T Total Production Costs C 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: Total Costs, Z Number of hospitals, N Larger N  Smaller hospital

Too Many Beds? Remember, Q is constant
755_l12 7/4/2018 Remember, Q is constant 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/N2 + 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 . AC Δ AC x hospital size Average, Mgl Costs Since T' < 0, then –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) Number of hospitals, N Larger N  Smaller hospital

Second Model – Market Size Model
7/4/2018 Second Model – Market Size Model LRAC 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. 1 5 $ 2 4 3 AC1 ACMIN Q2 Q1 Q

Market Size Model Costs Revenues
7/4/2018 Market Size Model LRAC 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. 1 5 $ 2 4 3 AC1 ACMIN Costs D Revenues Q2 Q1 Q

755_l12 7/4/2018 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.

755_l12 7/4/2018 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.

755_l12 7/4/2018 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 100 200 300 400 Q

755_l12 7/4/2018 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.

AHRQ Annual Meeting – September 21, 2011
7/4/2018 SINGLE SPECIALTY HOSPITALS AND ECONOMIC EFFICIENCY: EVIDENCE FROM THE SUPPLY SIDE 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

Production Cost Efficiency Construct I: EOS
755_l12 7/4/2018 Production Cost Efficiency Construct I: EOS

Graphic Conceptualization of EOS
7/4/2018 Graphic Conceptualization of EOS 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)__________ [ (α11DIS + 2*α21DIS2 + 3*α31DIS)3 + β11OPV +2* β21OPV2 + 3*β31OPV)3] EOS is a long run concept, and we are estimating a short-run cost function here Methods have been developed to estimate EOS from a SR cost function The most theoretically faithful approach is to applying the envelope condition to solve for the optimal level of the fixed factor using the parameter estimates from the estimated cost function and price data on the fixed factor (essentially deriving the long-run cost function) Vita (1990) has demonstrated that using the actual level of the fixed factor, rather than the optimal value in production, applied to the short-run cost function estimates is a reasonably reliable alternative …………………..that is what the numerator in this expression is doing 33

Results: EOS General Hospitals Specialty Hospitals 1,600 28,555 52
7/4/2018 Results: EOS General Hospitals Specialty Hospitals Discharges Visits Beds EOS Discharges Visits Beds Q1 1,600 28,555 52 2.70 262 3,882 9 2.13 Median 4,645 61,478 119 1.11 498 5,224 14 1.44 Q3 10,925 121,633 233 0.658 987 9,499 24 1.05

Production Cost Efficiency Construct II: ESC
755_l12 7/4/2018 Production Cost Efficiency Construct II: ESC 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

Not all Single Specialty Hospitals are the Same
7/4/2018 Not all Single Specialty Hospitals are the Same 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

ESC: What if orthopedic and surgical SSHs closed their doors?
7/4/2018 ESC: What if orthopedic and surgical SSHs closed their doors? 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

Results: ESC [ESC = (Cost A + Cost B – Cost C) / Cost C] = 0.30 = 0.16
7/4/2018 Results: ESC [ESC = (Cost A + Cost B – Cost C) / Cost C] Specialty Hospitals General Hospitals 1st Quartile Median 3rd Quartile ( )/23.95 = 0.30 ( )/43.02 = 0.16 ( )/108.69 = 0.05 ( )/25.07 = 0.38 ( )/44.74 = 0.18 ( )/111.65 ( )/27.62 = 0.59 ( )/48.60 = 0.28 ( )/118.19 = 0.07 Costs measured in million $ Quartile values taken across distributions of discharges and outpatient visits

Results: ESC, continued
7/4/2018 Results: ESC, continued Implicit Cost Savings (million dollars): (Cost A + Cost B – Cost C) Specialty Hospitals General Hospitals 1st Quartile Median 3rd Quartile 7.38 6.72 5.37 9.40 8.14 5.55 16.18 13.61 8.34

755_l12 7/4/2018 Conclusions 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
7/4/2018 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.

755_l12 7/4/2018 Older Stuff

Elasticity of Supply among Labor Inputs
7/4/2018 Elasticity of Supply among Labor Inputs An alternative literature has also developed about explicit substitution between physicians, and physician-extenders. Table Marginal Products and Efficiency of Input Use All Solo Group Physicians Physicians Physicians Input MP MP/P MP MP/P MP MP/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)

755_l12 7/4/2018 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/$

755_l12 7/4/2018 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.

755_l12 7/4/2018 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.

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