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Medical Care Production and Costs Part 1 Health Economics Fall 2007 Professor Vivian Ho Outline Motivation Productivity Measures Cost Measures Mergers are transforming the industry 2000 – NE Georgia Health system proposed to buy Lanier Park Hospital in Gainesville estimated cost savings of $2 million annually. 2002 – Anthem (insurance) proposed to acquire Trigon Health Care (also an insurer) • $9 billion in assets, $13 billion in revenues, 10 million members. • would lead to $75 million in pretax savings in 2004. Mergers are transforming the industry (cont.) But will mergers help to contain costs and/or improve productivity in the industry? • Depends upon production and costs in the health care sector. Assessing the Productivity of Medical Firms Economists often describe production of output as a function of labor and capital : q = f(n,k) • In the case of health care : q = hospital services n = nurses k = medical equipment, hospital building Assessing the Productivity of Medical Firms (cont.) Short run : k is fixed, while n is variable a) At low level of n, k is abundant. Each in nurses when combined with capital greater in services. - potential synergy effect because nurses can work in teams. b) Further in nurses service, but a decreasing rate - law of diminishing marginal productivity. c) “Too many “ nurses can cause congestion, communication problems, hospital services Graphical Representation Total product = q = f(n,k*) hospital services (q) TP n1 marginal product n1 n2 Nurses (n) n2 nurses MP = Dq / Dn MP is the slope of the TP curve. Graphical Representation AP = q / n AP is the slope of a ray from the origin to the TP curve. hospital services average product C B B TP A n3 Practice Question People living in Boston are hospitalized about 1.5 times as often as those living in New Haven, However, the health outcomes of patients in these 2 cities appear to be identical. Does this mean that hospital care has no ability to improve health? health outcomes hospitalizations Substitutability in Production of Medical Care There may be more than one way to produce a given level of health care. Licenced practical nurses (LPNs) vs Registered Nurses (RNs) in hospitals. LPNs have less training. Maybe not as productive, but not as costly. Physician assistants vs physicians at ambulatory clinics. But physician assistants can’t prescribe meds in most states. Substitutability in Production of Medical Care (cont.) Potential for substitutability If price of 1 input increases, can minimize impact on total costs by substituting away. Elasticity of substitution : r = [D(I1/I2)/I1/I2] : [D(MP2/MP1)/MP2/MP1] % change in input ratio, divided by % change in ratio of inputs’ MPs. r=0 r= 8 no substitutability. perfect substitutability. Production Function for Hospital Admissions Jensen and Morrisey (1986) Sample : 3,450 non-teaching hospitals in 1983. q = hospital admissions inputs : physicians, nurses, other staff, hospital beds. q = a0 + a1physicians + a2nurses + …. + e Coefficients in regression are MPs. Results Annual Marginal Products for Admissions Input Physicians Nurses Other Staff Beds • • MP (at the means) 6.05 20.30 6.97 3.04 Each additional physician generated 6.05 more admits per year. Nurses by far the most productive Results (cont.) Elasticity of Substitution between Inputs Input pair Physicians with nurses Physicians with beds Nurses with beds • s 0.547 0.175 0.124 Each inputs is a substitute for other in production process. • If wages of nurses rise, can substitute away by having more hospital beds. Except for when s = 0 Medical Care Cost Accounting Costs Explicit costs of doing business. • e.g. staff payroll, utility bills, medical supply costs. Necessary for : • • • Comparing performance evaluation across providers/depts. Taxes Government reimbursement/rate setting Medical Care Cost (cost.) Economic Costs = Accounting Costs i.e. opportunity costs. • e.g. opportunity cost of a facility being used as an outpatient clinic = rent it could earn otherwise. Necessary for : • • optimal business planning. allows one to consider highest returns to assets anywhere, not just vs. direct competitors, or w/in health care industry. Recall Given a production function : q = f (n,k) q = hospital services n = labor = nurse = n k = capital = medical equipment, hospital building Short-Run Total Cost STC( q ) = w n + r k* w = wage rate for nurses short run k fixed r = rental price of capital w n = variable cost r k = fixed cost . cost STC STC wn rk q0 hospital service Short-Run Total Cost (cont.) STC( q ) = w n + r k* • In the short run, k is fixed. rk* is the same, regardless of the amount of hospital services (q) produced. •As q rises, increases in STC are only due to increases in the number of nurses needed (n). Short-Run Total Cost (cont.) Recall : Production function initially exhibits IRTS Total costs rise at decreasing rate up to q0 cost STC STC wn rk q0 After q0, DTRS in production increasing rate hospital service costs rise at Marginal and Average Costs DSTC SMC = Dq = D(wn + rk*)/Dq = w(Dn/Dq) = w(1/MPn) = w/MPn The short run marginal cost of nurses depends on their marginal productivity. Marginal and Average Costs (cont). STVC SAVC = q = (wn)/q = w(1/APn) = w/APn The short run average variable cost of nurses depends on their average productivity. Numerical Example See handout. Graphing Marginal and Average Costs SMC Costs SMC0 SATC SAVC SATC0 SAVC0 0 q0 q Graphing Marginal and Average Costs SATC and SAVC are u-shaped curves. Increasing returns to scale followed by decreasing returns to scale. SMC passes through the minimum of both SATC and SAVC. If marginal cost is greater than average cost, then the cost of one additional unit of output must cause the average to rise. Relating Product and Cost Curves MPn Cost SMC APn SAVC APn MPn 0 n1 n3 n q1 q3 q Average and Marginal Costs (cont.) IRTS followed by DRTS in production leads to U shaped AC curve. Hospital doesn’t necessarily produce at q* (min. cost). Depends on hospital’s objectives. Even so, will attempt to stay on the cost curve (not above it). Average and Marginal Costs (cont.) Why do all of these cost curves matter? Many hospitals operate at a loss (profits<0) in some years. If a hospital seeks to maximize profits, and it knows it’s going to lose money in a given year, why should it treat any patients? In the SR, a hospital will still stay open if treating patients will cover its fixed costs and part of its variable costs. MC Price per Patient ATC P=MR AVC 0 q* Patients The hospital will receive a price P from insurers for each patient treated. To max profits, choose q* where MR=MC. Price per Patient MC ATC C P 0 B A q* P=MC AVC Patients At output q*, the hospital’s revenues are PAq*0. The hospital’s total costs are CBq*0. The hospital earns negative profits CBAP. MC Price per Patient ATC C P B A AVC E 0 D q* Patients The hospital’s FC are (ATC-AVC)q*, or CBDE. If the hospital shuts down, it must still pay for FC. Since CBDE>CBAP, the hospital will lose less if it remains open. In the SR, FC are critical for determining whether a hospital should stay open for business. So, in general, how large are FC? Study of Cook County Hospital in Chicago (Roberts, JAMA 1999) Urban public teaching hospital, 1993 Fixed Costs: Capital Variable Costs: Worker supplies (e.g. gloves) Worker salaries & benefits Patient care supplies Building maintenance Paper Utilities Food Lab supplies Medications Why are salary & benefits a FC? Workers often have long-term contracts. Many workers won’t take jobs w/ frequent layoffs. For Cook, the budget was 84% FC, 16% VC. Often makes sense for Cook to operate at a loss, not reduce patient load. Cutting the # of patients you serve won’t save a lot if you can’t cut FC simultaneously. If you serve 5% fewer patients, you may still need to: Pay for a CT scanner & technician Pay for upkeep of the ER & OR Pay annual licensing fees to city & state