Medical Care Production and Costs

Medical Care Production and Costs

 

 

This topic introduces various microeconomic principles and concepts that can be used to analyze the cost structure of medical firms and thereby determine the true relation between firm size and costs of production. In addition, the topic:

•               discusses various production characteristics, including marginal and average productivity and the elasticity of substitution among inputs

•               uses the resulting production theory to derive short-run and long-run costs of production

•               examines economies and diseconomies of scale and scope.

 

 

In December 2000 it was announced that Northeast Georgia Health System, a 338-bed not-for-profit hospital in Gainesville, Georgia, proposed to buy Lanier Park Hospital, a 119-bed for-profit hospital also in Gainesville, for $40 million. The acquisition would result in only one hospital in Gainesville. Executives at the hospitals claim the acquisition would save $2 million annually (Kirchheimer, 2000). Similarly, in July 2005 it was announced that United Health Group, the nation’s second-largest health insurer, planned to join with PacifiCare Health Systems, the second-largest private administrator of Medicare health plans. The combination would create one of the nation’s largest private health plan providers with about 26 million subscribers. A spokeperson for the two insurers claimed that the merger would cut operating costs by an estimated $100 million in the first year alone (Jablon, 2005).

These are just two examples of the many mergers that take place in the health care sector. Recent combinations among firms in other health care markets, such as the physician, pharmaceutical, and nursing home industries, also testify to the assertion that larger firm size confers significant cost advantages. But are there any plausible economic reasons to support the claim that cost savings are associated with larger organizational size? If so, sound economic reasoning can justify a merger among two or more firms in the same industry. On the other hand, might operating costs actually increase as a firm gets too large? If that is the case, a merger among firms is not desirable if cost savings are the overriding concern.

 

 

The Short-Run Production Function of the Representative Medical Firm

All medical firms, including hospitals, physician clinics, nursing homes, and pharmaceutical companies, earn revenues from producing and selling some type of medical output. Production and retailing activities occur regardless of the form of ownership (that is, for-profit, public, or not-for-profit). Because these activities take place in a world of scarce resources, microeconomics can provide valuable insights into the operation and planning processes of medical firms. In this topic, we focus on various economic principles that guide the production behavior of all types of firms, including medical firms. We begin by analyzing the short-run production process of a hypothetical medical firm.

To simplify our discussion of short-run production, we make five assumptions. First, we assume the medical firm produces a single output of medical services, q. Second, we initially assume only two medical inputs exist: nurse-hours, n, and a composite capital good, k. We can think of the composite capital good as an amalgamation of all types of capital, including any medical equipment and the physical space in the medical establishment. Third, since the short run is defined as a period of time over which the level of at least one input cannot be changed, we assume the quantity of capital is fixed at some amount. This assumption makes intuitive sense, because it is usually more difficult to change the stock of capital than the number of nurse-hours in the short run. Fourth, we assume for now that the medical firm faces an incentive to produce as efficiently as possible. Finally, we assume the medical firm possesses perfect information regarding the demands for its product. We relax the last two assumptions at the end of the topic.

As we know from Topic 2, a production function identifies how various inputs can be combined and transformed into a final output. Here, the production function identifies the different ways nurse-hours and capital can be combined to produce various levels of medical services. The production function allows for the possibility that each level of output may be produced by several different combinations of the nurse and capital inputs. Each combination is assumed to be technically efficient, since it results in the maximum amount of output that is feasible given the state of technology. Later we will see that both technical and economic considerations determine a unique least-cost, or economically efficient, method of production.

In the present example, the short-run production function for medical services can be mathematically generalized as

 

(7-1)                                       q = f(n, k).

 

The short-run production function for medical services in Equation 7-1 indicates the level of medical services is a function of a variable nurse input and a fixed (denoted with a bar) capital input. We begin our analysis by examining how the level of medical services, q, relates to a greater quantity of the variable nurse input, n, given that the capital input, k, is assumed to be fixed. Various microeconomic principles and concepts relating to production theory are used to determine the precise relation between the employment of the variable input and the level of total output. As mentioned in Topic 2, one important microeconomic principle from production theory is the law of diminishing marginal productivity. This is not really a law; rather, it is a generalization about production behavior and states that total output at first increases at an increasing rate, but after some point increases at a decreasing rate, with respect to a greater quantity of a variable input, holding all other inputs constant. In Topic 2, we assumed for simplicity that the law of diminishing marginal returns sets in immediately; that is, the marginal product of medical services was always declining. In this topic, we take a less restrictive approach to allow for the theoretical possibility that the marginal product of the variable input may increase initially. The fundamental idea remains the same, how­ever. Eventually a point is reached where additional units of an input generate smaller marginal returns.

 

 

The total product curve shows that output initially increases at an increasing rate from 0 to n1 nurse-hours, then increases at a decreasing rate from ^ to n2 nurse-hours, and finally declines after n2 nurse-hours as the medical firm employs more nurse-hours. Diminishing marginal productivity provides the reason why output fails to expand at an increasing rate after nurse-hours.

 

Figure 7-1 applies the law of diminishing productivity. It shows a graphical relation between the quantity of medical services on the vertical axis and the number of nurse-hours on the horizontal axis. The curve is referred to as the total product curve, TP, because it depicts the total output produced by different levels of the variable input, holding all other inputs constant. Notice that the quantity of services first increases at an increasing rate over the range of nurse-hours from 0 to n₁. The rate of increase is identified by the slope of the curve at each point. As you can see, the slope of the total product curve increases in value as the tangent lines become steeper over this range of nurse-hours.

Beyond point n₁, however, further increases iurse-hours cause medical services to increase, but at a decreasing rate. That is the point at which diminishing productivity sets in. Notice that the slope of the total product curve gets smaller as output increases in the range from n₁ to n₂ (as indicated by the flatter tangent lines). At n₂, the slope of the total product curve is zero, as reflected in the horizontal tangent line. Finally, beyond n₂, we allow for the possibility that too many nurse-hours will lead to a reduction in the quantity of medical services. The slope of the total product curve is negative beyond n₂.

In terms of the production decision at the firm level, we have not yet accounted for the specific reasoning underlying the law of diminishing marginal productivity. Economists point to the fixed short-run inputs as the basis for diminishing productivity. For example, wheurse-hours are increased at first, there is initially a considerable amount of capital, the fixed input, with which to produce medical services. The abundance of capital enables increasingly greater amounts of medical services to be generated from the employment of additional nurses. In addition, a synergy effect may dominate initially. The synergy effect means that nurses, working cooperatively as a team, are able to produce more output collectively than separately because of labor specialization, for example.

At some point, however, the fixed capital becomes limited relative to the variable input (for example, too little medical equipment and not enough medical space), and additional nurse-hours generate successively fewer incremental units of medical services. In the extreme, as more nurses are crowded into a medical establishment of a fixed size, the quantity of services may actually begin to decline as congestion sets in and creates unwanted production problems.

In general, any physical constraint in production, such as the fixed size of the facility or a limited amount of medical equipment, can cause diminishing productivity to set in at some point. In fact, if it weren’t for diminishing productivity, the world’s food supply could be grown in a single flowerpot and the demand for medical services could be completely satisfied by a single large medical organization. What a wonderful world it would be! Unfortunately, however, diminishing productivity is the rule rather than the exception.

 

 

Marginal and Average Products

We can also use marginal and average product curves rather than the total product curve to illustrate the fundamental characteristics associated with the production process. In general, the marginal product is the change in total output associated with a one-unit change in the variable input. In terms of our example, the marginal product or quantity of medical services associated with an additional nurse-hour, MP_n, can be stated as follows:

 

(7-2)                                       MP_n = Δq/Δn.

 

The magnitude of the marginal product of a nurse-hour reveals the additional quantity of medical services produced by each additional nurse-hour. It is a measure of the marginal contribution of a nurse-hour in the production of medical services.

In Figure 7-1, the slope of the total product curve at every point represents the marginal product of a nurse-hour, since it measures the rise (vertical distance) over the run (horizontal distance), or Δq/Δn. Consequently, we can determine the marginal product of an additional nurse-hour by examining the slope of the total product curve at each level of nurse-hours. Figure 7-2 graphically illustrates the marginal product of a nurse-hour. Initially, MP_n is positive and increases over the range from 0 to n₁ due to increasing marginal productivity. In the range from n₁ to n₂, the marginal product is positive but decreasing, because diminishing marginal productivity has set in. At n₂, the marginal product of a nurse-hour is zero and becomes negative thereafter. The marginal product curve suggests that each additional nurse-hour cannot be expected to generate the same marginal contribution to total output as the previous one. The law of diminishing marginal productivity dictates that in the short run, a level of output is eventually reached where an incremental increase in the number of nurse-hours leads to successively fewer additions to total output (because some other inputs are fixed).

 

 

The marginal product of an additional nurse-hour is found by dividing the change in output by the change in the number of nurse-hours and is measured by the slope of the total product curve. Marginal productivity first increases with the number of nurse-hours because of synergy and labor specialization and then falls because of the fixed input that exists in the short run.

 

In addition to MP_n, the average product of a nurse-hour can provide insight into the production process. In general, the average product equals the total quantity of output divided by the level of the variable input. In terms of the present example, the average product of a nurse-hour, AP_n, is calculated by dividing the total quantity of medical services by the total number of nurse-hours:

 

(7-3)                                       AP_n = q/n.

 

The average product of a nurse-hour measures the average quantity of medical services produced within an hour. For example, suppose we (crudely) measure total medical services by the number of daily patient-hours at a medical facility. In addition, suppose 200 nurse-hours are employed to service 300 daily patient-hours. In this example, the average product of a nurse-hour equals 300/200 or P/ patients per hour.

We can also derive the average product of a nurse-hour from the total product curve, as shown in Figure 7-3(a). To derive AP_n, a ray from the origin is extended to each point on the total product curve. The slope of the ray measures AP_n for any given level of nurse-hours, since it equals the rise over the run, or q/n. In Figure 7-3(a) three rays, labeled 0A, 0B, and 0C, emanate from the origin to the total product curve. The slope of ray 0A is flatter than that of 0B and therefore is of a lower magnitude. In fact, as it is drawn, ray 0B has a greater slope than any other ray emanating from the origin. At this level of nurse-hours, the average product is maximized. The slope of ray 0C is flatter and of a lower magnitude than that of 0B. The implication is that average product initially increases over the range from 0 to n₃ reaches a maximum at n₃, and then decreases, as shown in Figure 7-3(b). It is the law of diminishing marginal productivity that accounts for the shape of APn.

In Figure 7-4, the marginal and average product curves are superimposed to illustrate how they are related. Some characteristics of the relation between these two curves are worth mentioning. First, the marginal product curve cuts the average product curve at its maximum point. In fact, it is a common mathematical principle that the marginal equals the average when the average is at its extreme value.

Proof: For simplicity, suppose the production function relates the quantity of output, q, to a single input of nurse-hours, n, such that q = f(n). The average product of nurse-hours, AP_n, can be written as f(n)/n. To determine where AP_n reaches a maximum point, we can take the first derivative of AP_n and set it equal to zero. Following the rule for taking the derivative of a quotient of two functions (see Chiang, 1984), it follows that

 

 

since f’ (n) equals MP_n and f(n)/n equals AP_n, MP_n = AP_n when AP_n is maximized.

Second, MP_n lies above AP_n whenever AP_n is increasing. This too reflects a common mathematical principle and should come as little surprise to the reader. For example, if your average grade in a course is a B+ until the final and you receive an A on the final exam, this incremental higher grade pulls up your final average grade. Third, MP_n lies below AP_n whenever AP_n is declining. This relation between marginal and average values also should not be surprising. As you know, your course grade slips if you receive a lower grade on the final exam relative to your previous course average.

Putting the grades aside (because learning is more important than grades – right?), we can discuss the relation between the marginal and average product curves in terms of our example concerning nurse-hours and the production of medical services. For this discussion, it helps to think of the marginal product curve as the amount of medical services generated hourly by the next nurse hired. Also, we can think of the average product curve as the average quantity of medical services generated by the existing team of nurses within an hour – that is, the “team” average.

Looking back at Figure 7-4, notice that the next nurse hired always generates more services per hour than the team average up to point n₃. Consequently, up to this point, each additional nurse helps pull up the team’s average level of output. Beyond n₃, however, the incremental nurse hired generates less services per hour than the team average; as a result, the team average falls. It is important to realize that any increase or decrease in the marginal product has nothing to do with the individual talents of each additional nurse employed. Rather, it involves the law of diminishing marginal productivity. At some point in the production process, the incremental nurse becomes less productive due to the constraint imposed by the fixed input. The marginal productivity, in turn, influences the average productivity of the team of nurses.

 

The average product of a nurse-hour is found by dividing total output by the total number of nurse-hours and can be derived by measuring the slope of a ray emanating from the origin to each point on the total product curve. Average productivity first increases with the number of nurse-hours and then declines because of increasing and then diminish­ing marginal productivity.

 

 

Average productivity rises when marginal productivity exceeds average productivity. Average productivity falls when marginal productivity lies below average productivity. Marginal productivity equals average productivity when average productivity is maximized.

 

At first glance, it seems logical to assume that a medical firm desires to produce at a point likeor n₃ in Figure 7-4. After all, they represent the points at which either the marginal or the average product is maximized. In most cases, however, a medical firm finds it more desirable to achieve some financial target, such as a maximum or break-even level of profits. As a result, we need more information concerning the revenue and cost structures the medical firm faces before we can pinpoint the desired level of production. In later topics we will see that under normal conditions, the relevant range of production in Figure 7-4 is betwee₃ and n₂.

 

 

Elasticity of Input Substitution

Up to now, we have assumed only one variable input. Realistically, however, the medical firm operates with more than one variable input in the short run. Thus, there may be some possibilities for substitution between any two variable inputs. For example, licensed practical nurses often substitute for registered nurses in the production of inpatient services, and physician assistants sometimes substitute for physicians in the production of ambulatory services. The actual degree of substitutability between any two inputs depends on technical and legal considerations. For example, physician assistants are prohibited by law from prescribing medicines in most states. In addition, licensed practical nurses normally lack the technical knowledge needed to perform all the duties of registered nurses.

In general terms, the elasticity of substitution between any two inputs equals the percentage change in the input ratio divided by the percentage change in the ratio of the inputs’ marginal productivities, holding constant the level of output, or

 

 

I_i (i= 1,2) stands for the quantity employed of each input. The ratio of marginal productivities, MP₂/MP₁, referred to as the marginal rate of technical substitution, illustrates the rate at which one input substitutes for the other in the production process, at the margin. For example, suppose the marginal product of a registered nurse-hour is four patients and the marginal product of a licensed practical nurse-hour is two patients. It follows that two licensed practical nurse-hours are needed to substitute completely for one registered nurse-hour.

Theoretically, s (Greek letter sigma) takes on values between 0 and + ‘ and identifies the percentage change in the input ratio that results from a 1 percent change in the marginal rate of technical substitution. The magnitude of s identifies the degree of substitution between the two inputs. For example, if s = 0, the variable inputs cannot be substituted in production. In contrast, when s = ‘, the two variable inputs are perfect substitutes in production. In practice, it is more common for s to take on values between these two extremes, implying that limited substitution possibilities exist.

 

A Production Function for Hospital Admissions

Jensen and Morrisey (1986) provide one of the more interesting empirical studies on the production characteristics of hospital services. In keeping with Equation 7-1, Jensen and Morrisey estimated a production function for admissions at 3,540 nonteaching hospitals in the United States as of 1983 in the following general form:

 

(7-5)  Case-mix-adjusted hospital admissions = f (Physicians, nurses, other nonphysician staff, hospital beds, X)

 

Notice that hospital admissions serve as the measure of output. Given the heterogeneous nature of hospital services, however, this output measure was adjusted for case-mix differences across hospitals by multiplying it by the Medicare patient index. This index is the weighted sum of the proportions of the hospital’s Medicare patients in different diagnostic categories where the weights reflect the average costs per case in each diagnostic group. The number of physicians, nurses (full-time equivalent [FTE] units), and other nonphysician staff (FTE) represented the labor inputs; the number of beds constituted the capital input; and × stood for a number of other production factors not central to the discussion.

To put Equation 7-5 in a form that can be estimated with a multiple regression technique, Jensen and Morrisey specified a translog production function. The form and properties of this particular mathematical function are too complex to describe briefly; it suffices to note that the translog is a flexible functional form that imposes very few restrictions on the estimated parameters. In a translog function, (the natural log of) each independent variable enters the equation in both linear and quadratic form.

In addition, a cross-product linear term is created between any two independent variables and specified in the function. Similar cross-product terms are eliminated from the specification. To ensure a well-behaved function, restrictions are normally imposed on the parameter estimates.

From the empirical estimation, Jensen and Morrisey were able to derive estimates of each input’s marginal product. As expected, the marginal products were all positive. Jensen and Morrisey noted that the marginal product of each input declined in magnitude with greater usage, as the law of diminishing marginal product suggests. The estimated marginal product of a physician implied that an additional doctor generated 6.05 additional case-mix-adjusted annual admissions. The nurse input was by far the most productive input. In particular, the marginal nurse was responsible for producing about 20.3 additional case-mix-adjusted annual admissions. The marginal products of other nonphysician staff and beds were found to be 6.97 and 3.04 case-mix-adjusted annual admissions, respectively.

The estimation procedure also generated sufficient information to enable Jensen and Morrisey to measure the input substitution possibilities available to hospitals. Each input was found to be a substitute for the others in production. In particular, the substitution elasticities between physicians and nurses, physicians and beds, and nurses and beds were reported to be 0.547, 0.175, and 0.124, respectively. The relatively large elasticity of 0.547 between physicians and nurses tells us the average hospital can more easily substitute between these two inputs. This particular input elasticity estimate can be interpreted to mean that a 10 percent increase in the marginal productivity of a doctor causes a 5.47 percent increase in the ratio of nurses to doctors, ceteris paribus. These positive substitution elasticities suggest that hospital policy makers can avoid some of the price (wage) increase in any one input by substituting with the others. For example, to maintain a given level of admissions, a wage increase for nurses might be partially absorbed by increasing the number of hospital beds.

 

Short-Run Cost Theory of the Representative Medical Firm

Before we begin our discussion of the medical firm’s cost curves, we need to address the difference between the ways economists and accountants refer to costs. In particular, accountants consider only the explicit costs of doing business when determining the accounting profits of a medical firm. Explicit costs are easily quantified because a recent market transaction is available to provide an accurate measure of cost. Wage payments to the hourly medical staff, electric utility bills, and medical supply expenses are all examples of the explicit costs medical firms incur because disbursement records can be consulted to determine the magnitudes of these expenditures.

Economists, unlike accountants, consider both the explicit and implicit costs of production. Implicit costs reflect the opportunity costs of using any resources the medical firm owns.

For example, a general practitioner (GP) may own the physical assets (such as the clinic and medical equipment) used in producing physician services. In this case, a recent market transaction is unavailable to determine the cost of using these assets. Yet an opportunity cost is incurred when using them because the physical assets could have been rented out for an alternative use. For example, the clinic could be remodeled and rented as a beauty salon, and the medical equipment could be rented out to another physician. Thus, the forgone rental payments reflect the opportunity cost of using the physical assets owned by the GP. The GP’s labor time should also be treated as an implicit cost of doing business if she independently owns the clinic. As an entrepreneur, the GP does not receive an explicit payment but instead receives any residual profits that are left over after all other costs are paid. If the physician does not receive an appropriate rate of return, she may leave the area or the profession to get a better rate of return.

Consequently, when determining the economic (rather than accounting) profits of a firm, economists consider the total costs of doing business, including both the explicit and implicit costs. Economists believe it is important to determine whether sufficient revenues are available to cover the cost of using all inputs, including those rented and owned. For example, if the rental return on the physical assets is greater than the return on use, the GP might do better by renting out the assets rather than retaining them for personal use.

 

The Short-Run Cost Curves of the Representative Medical Firm

Cost theory is based on the production theory of the medical firm previously outlined and relates the quantity of output to the cost of production. As such, it identifies how (total and marginal) costs respond to changes in output. If we continue to assume the two inputs of nurse-hours, n, and capital, k, the short-run total cost, STC, of producing a given level of medical output, q, can be written as

 

(7-6)                                       STC(q) = w ×+ r × k,

 

where w and r represent the hourly wage for a nurse and the rental or opportunity cost of capital, respectively. Input prices are assumed to be fixed, which means the single medical firm can purchase these inputs without affecting their market prices. This is a valid assumption as long as the firm is a small buyer of inputs relative to the total number of buyers in the marketplace. If the single firm were a large or an influential buyer, it might possess some “monopsony” power and could affect the market prices of the inputs.

Equation 7-6 implies that the short-run total costs of production are dependent on the quantities and prices of inputs employed. The wage rate times the number of nurse-hours equals the total wage bill and represents the total variable costs of production. Variable costs respond to changes in the level of output. For simplicity, we assume the wage rate represents total hourly compensation, including any fringe benefits. The product of the rental price and the quantity of capital represent the total fixed costs of production. Obviously, this cost component does not respond to changes in output, since the quantity of capital is fixed in the short run.

The total product curve not only identifies the quantity of medical output produced by a particular number of nurse-hours but also shows, reciprocally, the number of nurse-hours necessary to produce a given level of medical output. With this information, we can determine the short-run total cost of producing different levels of medical output by following a three-step procedure. First, we identify, through the production function, the necessary number of nurse-hours, n, for each level of medical output. Second, we multiply the quantity of nurse-hours by the hourly wage, w, to determine the short-run total variable costs, STVC, of production, or w × n. Third, we add the short-run total fixed costs, STFC, or r × k, to STVC to derive the short-run total costs, STC, of production. If we conduct this three-step procedure for each level of medical output, we can derive a short-run total cost curve like the one in Figure 7-5.

 

The short-run total cost, STC, of producing medical services equals the sum of the total variable, STVC, and fixed costs, STFC. STC first increases at a decreasing rate up to point q₁ and then increases at an increasing rate with respect to producing more output. STC increases at an increasing rate after q₁ because of diminishing marginal productivity.

 

Notice the reciprocal relation between the short-run total cost function in Figure 7-5 and the short-run total product curve in Figure 7-1. For example, when total product is increasing at an increasing rate up to point n₁ in Figure 7-1, short-run total costs are increasing at a decreasing rate up to point q₁ in Figure 7-5. This is because the increasing productivity in this range causes the total costs of production to rise slowly. Output increases at a decreasing rate immediately beyond point n₁ in Figure 7-1 (as shown by the slope of the total product curve), and, as a result, short-run total costs increase at an increasing rate beyond q₁ in Figure 7-5. Also notice that total costs increase solely because additional nurses are employed as output expands. Figure 7-5 also shows how short-run total cost can be decomposed into its variable and fixed components for the level of output q₂.

In practice, distinguishing between fixed and variable costs can be particularly challenging. Recall that variable costs change proportionately, whereas fixed costs do not change, in response to any adjustment in the quantity of output actually produced. Fixed costs occur in the short run, during the so-called operating period, when the levels of some inputs are fixed. In contrast, all inputs are variable during the long run or planning period, when, for instance, future budgets are being designed. The physical size of a production facility is often treated as a fixed input because a significant amount of time is needed to construct or relocate to a larger building. Hourly workers are typically treated as a variable input because they can be promptly hired or laid off, depending on the desired adjustment in output. As you can see, time plays a crucial role in determining the fixity of inputs and costs. It follows that long-term contracts, although potentially providing offsetting benefits, impose more fixed costs into a firm’s budget.

In an article in the Journal of the American Medical Association, Roberts et al. (1999) were interested in distinguishing between the fixed and variable costs at a hospital because they wanted to know whether a significant amount of hospital costs could be saved by discouraging unnecessary hospital services. Reductions in hospital services can result in more cost savings when variable costs comprise a greater percentage of overall costs. But as Roberts et al. note: “A computed tomographic (CT) scan is thought of as an expensive test and a source of significant cost savings if it is not performed. However, the scanner and space have already been rented or paid for, and the technician receives a salary that must be paid whether any individual receives a CT scan or not. If the radiologist who interprets the test is also receiving a salary, the additional cost to the hospital of doing the test is minimal – the price of radiographic film, paper and contrast.”

Roberts et al. examine the distribution of variable and fixed costs at Cook County Hospital in Chicago, Illinois, which was an 886-bed urban-public-teaching hospital when the study was done in 1993. The authors included capital, employee salaries, benefits, building maintenance, and utilities in the fixed-cost category. Note that employee salaries were included in the fixed-cost category, with the assumption being that Cook County was contractually obligated to pay these salaries during the budget period. Variable costs were specified to include health care worker supplies, such as gloves, patient care supplies, paper, food, radiographic film, laboratory reagents, glassware, and medications with their delivery systems such as intravenous catheters or bottles.

The authors found that the fixed costs comprised 84 percent of Cook County’s total budget at that time. However, they caution that their results may not be applicable to cases in which hospitals hire more hourly or fee-for-service workers. At Cook County Hospital, most employees were salaried. But even in the case of nonsalaried personnel, Roberts et al. note that the intense employee specialization may make it more difficult for hospitals to downsize than traditional firms. For example, pediatric nurses may not be able to promptly adapt to adult cardiac care units. Given that a majority of costs were fixed, their study implies that a reduction in hospital services would have very little impact on Cook County’s costs in the short run.

 

Short-Run Per-Unit Costs of Production

Another way to look at the reciprocal relation between production and costs is to focus on the short-run marginal and average variable costs of production. The short-run marginal costs, SMC, of production are equal to the change in total costs associated with a one-unit change in output, or

 

(7-7)                                       SMC = ΔSTC/Δq.

 

In terms of Equations 7-6 and 7-7, the short-run marginal costs of production look like the following:

 

(7-8)                              SMC = Δ(w ×+ r × k)/Δq.

 

Because the wage rate and short-run fixed costs are constant with respect to output, Equation 7-8 can be rewritten in the following manner:

 

(7-9)                    SMC = w × (Δn/Δq) = w × (1/MP_n) = w/MP_n.

 

Notice on the right-hand side of Equation 7-9 that short-run marginal costs equal the wage rate divided by the marginal product of nurse-hours.

The short-run average variable costs, SAVC, of production equal the short-run total variable costs, STVC, divided by the quantity of medical output. Because STVC is the total wage bill (that is, w × n),

 

(7-10)          SAVC = STVC/q = (w × n)/q = w × (l/AP_n) = w/AP_n

 

such that SAVC equals the wage rate divided by the average product of a nurse-hour. Notice that the short-run marginal and average variable costs are inversely related to the marginal and average products of labor, respectively. Thus, marginal and average variable costs increase as the marginal and average products fall, and vice versa. Figure 7-6 shows the graphical relation between the per-unit product and cost curves.

The two graphs in Figure 7-6 clearly point out the reciprocal relation between production and costs. For example, after point n₁ in Figure 7-6(a), diminishing productivity sets in and the marginal product begins to decline. As a result, the short-run marginal costs (=w/MP_n) increase beyond output level q₁ given a fixed wage. Similarly, the average product of a nurse-hour declines beyond n3, so the average variable costs of production increase beyond q₃. Obviously, the shapes of the marginal cost and average variable cost curves reflect the law of diminishing marginal productivity. Because of this reciprocal relation, production and costs represent dual ways of observing various characteristics associated with the production process.

It is apparent from Equations 7-9 and 7-10 that the maximum points on the marginal and average product curves correspond directly to the minimum points on the marginal and average variable cost curves. Note in Figure 7-6(b) that the short-run marginal cost curve passes through the minimum point of the short-run average variable cost curve. In addition, the SMC curve lies below the SAVC curve when the latter is decreasing and above the SAVC curve when it is increasing.

In simple terms, the graph in Figure 7-6(b) identifies how costs behave as the medical firm alters output in the short run. Initially, as the medical firm expands output and employs more nurse-hours, both the marginal and average variable costs of production decline. Eventually, diminishing productivity sets in due to the fixed inputs, and both marginal and average variable costs increase. It follows that the marginal and average variable costs of production depend in part on the amount of output a medical firm produces in the short run.

Besides the marginal and average variable costs of production, decision makers are interested in the short-run average total costs of operating the medical firm. Following Equation 7-6, we can find the short-run average total costs of production by summing the average variable costs and average fixed costs.

 

 

Short-run marginal cost, SMC, equals the change in total costs brought on by a one-unit change in output. Short-run average variable cost, SAVC, equals short-run total variable cost divided by total output. SMC and SAVC are inversely related to marginal and average productivity. For example, marginal costs decline as marginal productivity increases.

Short-run average fixed costs (SAFC) are simply total fixed costs (STFC) divided by the level of output, or

 

(7-11)                                     SAFC = STFC/q.

 

Because by definition the numerator in Equation 7-11 is fixed in the short run, the SAFC declines as the denominator, medical services, increases in value. Consequently, the average fixed costs of production decline with greater amounts of output because total fixed costs (or overhead costs) are spread out over more and more units.

Figure 7-7 shows the graphical relation among SMC, SAVC, and, short-run average total cost, SATC. Note that the marginal cost curve cuts the average total cost curve at its minimum point. (The minimum SATC lies to the right of the minimum SAVC. Why?) Also, note that the vertical distance between the average total and variable cost curves at each level of output represents the average fixed costs of production. This should not be surprising, since total costs include both variable and fixed costs. The vertical distance between the two curves gets smaller as output increases because the SAFC approaches zero with increases in output. One implication of the model is that average total costs increase at some level of output because eventually the cost-enhancing impact of diminishing productivity outweighs the cost-reducing tendency of the average fixed costs.

 

 

The unwitting reader may think that the medical firm should choose to produce at the minimum point on the SATC curve because average costs are minimized. As mentioned earlier, however, the level of output the medical firm chooses depends on the firm’s objective (for example, to achieve maximum or break-even level of profits). Hence, a proper analysis requires some knowledge of the revenue structure in addition to the cost structure. In later topics, we entertain some alternative objectives that may motivate the production behavior of medical firms. For now, however, assume for pedagogical purposes that the firm has chosen to produce the level of medical output, q₀, in Figure 7-7. Let’s identify the various costs associated with producing q₀ units of medical output.

The identification of the per-unit cost of producing a given level of output is a fairly easy matter. We can determine the per-unit cost by extending a vertical line from the appropriate level of output until it crosses the cost curves. For example, the average total cost of producing q0 units of output is SATC0, while the average variable cost is SAVC0. The average fixed cost of producing q0 units of output is represented by the vertical distance between SATC₀ and SATC₀, or distance ab. In addition, SMC₀ identifies the marginal cost of producing one more unit assuming the medical firm is already producing q₀ units of medical services.

Now suppose that instead of the per-unit costs, we want to identify the various total costs (that is, STC, STVC, and STFC) associated with producing q₀ units of output. We can do this by multiplying the level of output by the per-unit costs of production. For example, the rectangle SAVC₀-b-q₀-0 in Figure 7-7 measures the total variable costs of producing q₀ units of output, since it corresponds to the area found by multiplying the base of 0-q₀ by the height of 0-SAVC₀. Following similar logic, the total fixed costs are represented by rectangle SATC₀-a-b-SAVC₀, and total costs can be measured by area SATC₀-a-q₀-0. The ability to interpret and read these cost curves is useful for the discussion that follows.

 

Factors Affecting the Position of the Short-Run Cost Curves

A variety of short-run circumstances affect the positions of the per-unit and total cost curves. The position of the average and total fixed cost curves is influenced by the price of the fixed input. Fixed costs do not affect the typical marginal decision in the short run. Therefore, we do not discuss the factors affecting the position of the fixed cost curves. Among them are the prices of the variable inputs, the quality of care, the patient case-mix, and the amounts of the fixed inputs. Whenever any one of these variables changes, the positions of the cost curves change through either an upward or a downward shift depending on whether costs increase or decrease. For example, if input prices increase in the short run, the cost curves shift upward to reflect the higher costs of production (especially since SAVC = w/AP_n and SMC = w/MP_n). If input prices fall in the short run, the cost curves shift downward to indicate the lower production costs.

Furthermore, if the medical firm increases the quality of care or adopts a more severe patient case-mix, the cost curves respond by shifting upward. That is because a higher quality of care or a more severe patient case-mix means that a unit of labor is less able to produce as much output in a given amount of time. In terms of our formal analysis, a higher quality of care or a more severe patient case-mix reduces the average and marginal productivity of the labor input and thereby raises the costs of production. For example, a nurse can care for many more patients within an hour when these patients are less severely ill and quality of care is of secondary importance. Conversely, a reduction in the quality of care or a less severe patient case-mix is associated with lower cost curves.

Finally, a change in the amount of the fixed inputs can alter the costs of production. For example, it can be shown that excessive amounts of the fixed inputs lead to higher short-run costs (Cowing and Holtmann, 1983). We discuss the specific reasoning underlying the relation between fixed inputs and short-run costs when we examine the long-run costs of production later in this topic.

In sum, a properly specified short-run total variable cost function for medical services should include the following variables:

 

(7-12) STVC = f (output level, input prices, quality of care, patient case-mix, quantity of the fixed inputs).

 

We suspect that these factors can explain cost differentials among medical firms in the same industry. Specifically, output influences short-run variable costs by determining where the medical firm operates along the cost curve, whereas the other factors affect the location of the curve. Most likely, high-cost medical firms are associated with more output, higher wages, increased quality, more severe patient case-mixes, and/or an excessive quantity of fixed inputs.

 

Estimating a Short-Run Cost Function for Hospital Services

Cowing and Holtmann (1983) empirically estimated a short-run total variable cost function for a sample of 138 short-term general care hospitals in New York using 1975 data. Along the lines of Equation 7-12, they specified the short-run total variable cost, STVC, function in the following general form:

 

(7-13)                            STVC = f (q1, q2, q3, q₄, q5, w1, w2, w3, w₄, w5, w₆, K, A).

 

Each q_i (i = 1,5) represents the quantity of one of five different patient services – emergency room care, medical-surgical care, pediatric care, maternity care, and other inpatient care – measured in total patient days; each w_j (j = 1,6) stands for one of six different variable input prices for nursing labor, auxiliary labor, professional labor, administrative labor, general labor, and material and supplies; K is a single measure of the capital stock (measured by the market value of a hospital); and A is the fixed number of admitting physicians in the hospital. Cowing and Holtmann also specify two dummy variables reflecting for-profit versus not-for-profit ownership status and teaching versus nonteaching institution as a way to control for differences in quality and case-mix severity across hospitals. The inadequate control for quality and severity of case-mix is one of the few faults we can find with this paper.

Compared to Equation 7-12, Cowing and Holtmann’s specification of the cost function is more complex and introduces a greater degree of realism into the empirical analysis. First, the hospital is realistically treated as a multiproduct firm, simultaneously producing and selling five different types of patient services. Second, instead of our single variable input price (that is, hourly nurse wage), six different variable input prices are specified. Finally, Cowing and Holtmann include the number of admitting physicians in the model because they play such a key role in the hospital services production process.

The authors assumed a multiproduct translog cost function for Equation 7-13. We do not discuss the properties associated with this specific functional form; it suffices to note that this flexible form enables us to assess a large number of real-world characteristics associated with the production process.

First, this functional form allows for an interaction among the various outputs so that economies of scope can be examined. Economies of scope result from the joint sharing among related outputs of resources, such as nurses, auxiliary workers, and administrative labor. Scope economies exist if the joint cost of producing two outputs is less than the sum of the costs of producing the two outputs separately. For example, many colleges and universities produce both an undergraduate and a graduate education jointly due to perceived cost savings from economies of scope. The same professors, library personnel, and buildings can be used in producing both educational outputs simultaneously.

Cowing and Holtmann found some very intriguing results. First, their study reveals evidence of short-run economies of scale, meaning that an increase in output results in a less than proportionate increase in short-run total variable costs. Evidence of short-run economies indicates that the representative hospital operates to the left of the minimum point on the short-run average variable cost curve and implies that larger hospitals produce at a lower cost than smaller ones in the short run. They point out that this result is consistent with the view that aggregate hospital costs could be reduced by closing some small hospitals and merging the services among the remaining ones.

Second, in contrast to scale economies, Cowing and Holtmann discovered only limited evidence for economies of scope with respect to pediatric care and other services. They also found limited evidence to support diseconomies of scope with respect to emergency services and other services. In fact, they argued that the results for both scope and scale economies indicate that larger but more specialized hospitals may be more effective given the significance of the scale effects and the general lack of any substantial economies of scope.

Third, Cowing and Holtmann also noted that the short-run marginal cost of each output, ASTVC/Aq_i, declined and then became constant over the levels of output observed in their study. For example, the marginal cost of an emergency room visit was found to be approximately $32 for 54,000 visits per year and about $20 for 100,000 visits per year. For medical-surgical care, marginal cost was found to fall from $255 per patient day for 6,000 annual patient days to around $100 for 300,000 annual total patient days. For maternity care, the evidence suggests that the marginal costs of $540 per patient day for hospitals with 1,500 total annual patient days declined to $75 for hospitals with 20,000 total annual patient days. Eventually each of the marginal costs leveled off.

Finally, Cowing and Holtmann estimated the short-run elasticities of input substitution between all pairs of variable inputs. They reported that the results indicate a substantial degree of substitutability betweeursing and professional workers, nursing and general workers, nursing and administrative workers, and professional and administrative labor.

 

The Cost-Minimizing Input Choice

A medical firm makes choices concerning which variable inputs to employ. Recognizing that there is usually more than one way to produce a specific output, medical firms typically desire to produce with the least-cost or cost-minimizing input mix. For example, suppose administrators desire to produce some given amount of medical services, q₀, at minimum total cost, TC, using two variable inputs: registered nurses, RN, and licensed practical nurses, LPN. (For ease of exposition, we ignore the capital input in this example.) These two inputs are paid hourly wages of w_R and w_L, respectively. The medical firm wants to minimize

 

(7-14)                            TC(q₀) = w_R × RN + w_L × LPN

 

subject to

 

(7-15)                                     q₀ = f(RN,LPN)

 

by choosing the proper mix of registered nurses and licensed practical nurses.

Taken together, Equations 7-14 and 7-15 mean that administrators want to minimize the total cost of producing q₀ units of medical services by choosing the “right,” or efficient, mix of RNs and LPNs so that TC(q₀) is as low as possible and sufficient amounts of the two inputs are available to produce q0. The efficient combination depends on the marginal products and relative prices of the two inputs. By using a mathematical technique called constrained optimization, we can show that the efficient mix of RNs and LPNs is chosen when the following condition holds:

 

(7-16)                                     MP_RN/w_R = MP_LPN/w_L.

 

Equation 7-16 means that the marginal product to price ratio is equal for both registered nurses and licensed practical nurses in equilibrium. The equality implies that the last dollar spent on registered nurses generates the same increment to output as the last dollar spent on licensed practical nurses. As a result, a rearranging of expenditures on the two inputs cannot generate any increase in medical services, since both inputs generate the same output per dollar at the margin. The astute reader most likely recognizes that Equation 7-16 is similar to the utility-maximizing conditiooted in Topic 5.

To more fully appreciate this point, suppose this condition does not hold such that

 

(7-17)                                     MP_RN/w_R > MP_LPN/w_L.

 

In that case, the last dollar spent on a licensed practical nurse generates more output than the last dollar spent on a registered nurse. A licensed practical nurse is more profitable for the hospital at the margin, because the medical organization receives a “bigger bang for the buck.” But as the organization hires more LPNs and fewer RNs, the marginal productivities adjust until the equilibrium condition in Equation 7-16 results. Specifically, the marginal productivity of the LPNs decreases, while the marginal productivity of the RNs increases due to diminishing marginal productivity.

For example, suppose a newly hired RN can service six patients per hour and a newly hired LPN can service only four patients per hour. At first blush, with no consideration of the price of each input, the RN might appear to be the “better buy” because productivity is 50 percent higher. But suppose further that the market wage for an RN is $20 per hour, while an LPN requires only $10 per hour to work at the medical facility. Given relative input prices, the 50 percent higher productivity of the RN costs the medical facility 100 percent more. Obviously, the LPN is the better buy. That is, the last dollar spent on an LPN results in the servicing of 0.4 additional patients per hour, while a dollar spent on an RN allows the servicing of only 0.3 more patients per hour.

As another example, most physicians are not hospital employees and paid an explicit salary; instead they are granted admitting privileges by the hospitals. The granting of admitting privileges comes at a cost to the hospital, however. For example, the hospital incurs costs when it reviews and processes the physician’s application, monitors the physician’s performance to ensure quality control, and allows the physician to use its resources. Based on their empirical procedure discussed earlier, Jensen and Morrisey (1986) were able to estimate the shadow price, or implicit cost, of a physician with admitting privileges at a representative hospital. They imputed the shadow price of a physician by using the condition for optimal input use. Following the format of Equation 7-16, the optimal combination of doctors, doc, and nurses, n, is chosen when

 

(7-18)                                     MP_doc/w_doc = MP_n/w_n.

 

By substituting in the estimated marginal products for doctors (6.05) and nurses (20.3) from their study, and the sample average for the annual nurses’ salary ($23,526), Jensen and Morrisey solved for the shadow price of a doctor, w_doc. The resulting figure implies that the typical hospital in the sample incurred implicit costs of approximately $7,012 per year from granting admitting privileges to the marginal physician.

 

 

Long-Run Costs of Production

Up to now, we have focused on the short-run costs of operation and assumed that one input is fixed. The fixed input leads to diminishing returns in production and to U-shaped average variable and total cost curves. In the long run, however, when the medical firm is planning for future resource requirements, all inputs, including capital, can be changed. Therefore, it is also important to analyze the relation between output and costs when all inputs are changed simultaneously in the long run.

 

Long-Run Cost Curves

The long-run average total cost curve can be derived from a series of short-run cost curves, as shown in Figure 7-8. The three short-run average total cost curves in the figure reflect different amounts of capital. For example, each curve might reflect the short-run average total costs of producing units of medical services in physically larger facilities of sizes k₁, k₂, and k₃. If decision makers know the relation among different-size facilities and the short-run average total costs, they can easily choose the SATC or size that minimizes the average cost of producing each level of medical services in the long run.

For example, over the range 0 to qa, facility size k1 results in lower costs of production than either size k₂ or k₃. Specifically, notice that at output level q₁, SATC₂ exceeds SATC₁ by a significant amount. Therefore, the administrators choose size k₁ if they desire to produce q_x units of medical services at least cost in the long run. Similarly, from q_a to q_b, facility size k₂, associated with SATC₂, results in lower costs than either size k or k₃. Beyond q_b units of medical services (say, q₂), a size of k₃ enables lower costs of production in the long run.

 

All inputs are variable in the long run. SATC_V SATC2, and SATC3 represent the cost curves for small, medium, and large facilities, respectively. If decision makers choose the efficiently sized firm for producing output in the long run, a long-run average total cost, LATC, can be derived from a series of short-run average total cost curves brought on by an increase in the stock of capital. The U shape of the LATC reflects economies and diseconomies of scale.

 

The three short-run cost curves in Figure 7-8 paint a simplistic picture, since conceptually each unit of medical services can be linked to a uniquely sized cost-minimizing facility (assuming capital is divisible). If we assume a large number of possible sizes, we can draw a curve that connects all the cost-minimizing points on the various short-run average total cost curves. Each point indicates the least costly way to produce the corresponding level of medical services in the long run when all inputs can be altered. Every short-run cost curve is tangent to the connecting or envelope curve, which is referred to as the long-run average total cost (LATC) curve. The curve drawn below the short-run average cost curves in Figure 7-8 represents a long-run average total cost curve.

Notice that the U-shaped long-run average cost curve initially declines, reaches a minimum, and eventually increases. Interestingly, both the short-run and long-run average cost curves have the same shape, but for different reasons. The shape of the short-run average total cost curve is based on the law of diminishing productivity setting in at some point. In the long run, however, all inputs are variable, so by definition a fixed input cannot account for the U-shaped long-run average cost curve. Instead, the reason for the U-shaped LATC curve is based on the concepts of long-run economies and diseconomies of scale.

Long-run economies of scale refer to the notion that average costs fall as a medical firm gets physically larger due to specialization of labor and capital. Larger medical firms are able to utilize larger and more specialized equipment and to more fully specialize the various labor tasks involved in the production process. For example, people generally get very proficient at a specific task when they perform it repeatedly. Therefore, specialization allows larger firms to produce increased amounts of output at lower per-unit costs. The downward-sloping portion of the LATC curve in Figure 7-8 reflects economies of scale.

Another way to conceptualize long-run economies of scale is through the direct relation between inputs and output, or returns to scale, rather than output and costs. Consistent with long-run economies of scale is increasing returns to scale. Increasing returns to scale result when an increase in all inputs results in a more than proportionate increase in output. For example, a doubling of all inputs that results in three times as much output is a sign of increasing returns to scale. Similarly, if a doubling of output can be achieved without a doubling of all inputs, the production process exhibits long-run increasing returns, or economies of scale.

Most economists believe that economies of scale are exhausted at some point and diseconomies of scale set in. Diseconomies of scale result when the medical firm becomes too large. Bureaucratic red tape becomes common, and top-to-bottom communication flows break down. The breakdown in communication flows means management at the top of the hierarchy has lost sight of what is taking place at the floor level. As a result, poor decisions are sometimes made when the firm is too large. Consequently, as the firm gets too large, long-run average costs increase. Diseconomies of scale are reflected in the upward-sloping segment of the LATC curve in Figure 7-8.

Diseconomies of scale can also be interpreted as meaning that an increase in all inputs results in a less than proportionate increase in output, or decreasing returns to scale. For example, if the number of patient-hours doubles at a dental office and the decision maker is forced to triple the size of each input (staff, office space, equipment, and so on), the production process at the dental office is characterized by decreasing returns, or diseconomies of scale.

Another possibility, not shown in Figure 7-8, is that the production process exhibits constant returns to scale. Constant returns to scale occur when, for example, a doubling of inputs results in a doubling of output. In terms of long-run costs, constant returns imply a horizontal LATC curve, in turn implying that long-run average total cost is independent of output.

 

Shifts in the Long-Run Average Cost Curve

The position of the long-run average cost curve is determined by a set of long-run circumstances that includes the prices of all inputs (remember, capital is a variable input in the long run), quality (including technological change), and patient case-mix. When these circumstances change on a long-run basis, the long-run average cost curve shifts up or down depending on whether the change involves higher or lower long-run costs of production. For example, an increase in the long-run price of medical inputs leads to an upward shift in the long-run average cost curve. A cost-saving technology tends to shift the long-run average cost curve downward. Conversely, a cost-enhancing technology increases the average costs of production in the long run and shifts the LATC curve upward. Higher quality of care and more severe patient case-mixes also shift the LATC curve upward.

 

Long-Run Cost Minimization and the Indivisibility of Fixed Inputs

Long-run cost minimization assumes that all inputs can be costlessly adjusted upward or downward. For an input such as an hourly laborer, employment adjustments are fairly simple because hours worked or the number of workers can be changed relatively easily. Capital inputs cannot always be as easily changed, however, because they are less divisible. As a result, a medical firm facing a sharp decline in demand may be unable to reduce the physical size of its facility. For example, Salkever (1972) found that hospitals realize less than 10 percent of the desired cost savings per year. Therefore, medical firms may adjust slowly to external changes, not produce in long-run equilibrium, and operate with excess capital relative to a long-run equilibrium point.

Figure 7-9 clarifies this point. Suppose that initially a dental clinic produces q0 amount of output (say, dental patient-hours) with a facility size of 1,200 square feet, as represented by the curve SATC₂. This represents a long-run equilibrium point because the efficient plant size is chosen such that SATC₂ is tangent to the LATC curve at q₀; that is, q₀ is produced at the lowest possible long-run cost and 1,200 square feet is the efficiently sized facility. Now suppose output sharply falls to q1 due to a decline in demand. Long-run cost minimization suggests that the dental firm will reduce the size of its facility to that represented by SATC₁ and operate at point a on the LATC curve. It might do this by selling the old facility and moving into a smaller one. Because it may take time to adjust to the decline in demand, the dental clinic may not operate on the long-run curve at q₁ (point a) but instead continue to operate with the larger facility as represented by point b on SATC₂. The dental clinic incurs higher costs of production as indicated by the vertical distance between points b and a in the figure.

Cowing and Holtmann (1983) derived a test to determine whether firms are operating in long-run equilibrium. Using a simplified version of Equation 7-12, we can write a long-run total cost (LTC) function as

 

(7-19)                            LTC = STVC (q, w, k) + r × k,

 

where all variables are as defined earlier. According to Equation 7-19, long-run total costs equal the sum of (minimum) short-run total variable costs and capital costs. The level of short-run total variable costs is a function of, or depends on, the quantity of output, the wage rate, and the quantity of capital (and other things excluded from the equation for simplification).

According to Cowing and Holtmann, a necessary condition for long-run cost minimization is that ASTVC/Ak = -r¹. The equality implies that the variable cost savings realized from substituting one more unit of capital must equal the rental price of capital in long-run equilibrium. That is, the marginal benefits and costs of capital substitution should be equal when the firm is minimizing the long-run costs of production. A nonnegative estimate for ASTVC/Ak is a sufficient condition for medical firms to be overemploying capital. A nonnegative estimate implies that the cost of capital substitution outweighs its benefit in terms of short-run variable cost savings.

In their study, Cowing and Holtmann specified two fixed inputs: capital and the number of admitting physicians. As with capital, hospitals may operate with an excessive number of admitting physicians relative to a long-run equilibrium position. That is because the loss of one admitting physician can mean the loss of many more patients in the future. Cowing and Holtmann estimated the change in short-run total variable costs resulting from a one-unit change in capital and number of admitting physicians. Both estimates were found to be positive rather thaegative. Thus, the authors found that the “average” hospital in their New York sample operated with too much capital and too many physicians. Their empirical results suggest that hospitals could reduce their costs by limiting the amount of capital and controlling the number of physicians.

 

 

A firm may not operate in long-run equilibrium because of the sizeable costs of adjusting to a sharp change in demand. For example, assuming that the dental clinic is initially producing in long-run equilibrium at q₀ and output sharply falls to q₁, it may take time for the dental clinic to downsize its capital facility. As a result, the dental clinic may operate with costs, point b, that are higher than that predicted by long-run equilibrium, point a.

 

 

Neoclassical Cost Theory and the Production of Medical Services

The cost theory introduced in this topic, typically referred to as neoclassical cost theory under conditions of perfect certainty, assumes firms produce as efficiently as possible and possess perfect information regarding the demands for their services. Based on the underlying theory, the short-run or long-run costs of producing a given level of output can be determined by observing the relevant point on the appropriate cost curve. However, when applied to medical firms, this kind of cost analysis may be misleading for two reasons.

First, some medical firms, such as hospitals or nursing homes, are not-for-profit entities or are reimbursed on a cost-plus basis or both. Therefore, they may not face the appropriate incentives to produce as cheaply as possible and, consequently, may operate above rather than on a given cost curve. Second, medical firms may face an uncertain demand for their services. Medical illnesses occur irregularly and unpredictably, and therefore medical firms such as hospitals may never truly know the demand for their services until the actual events take place. Accordingly, medical firms may produce with some amount of reserve capacity just in case an unexpected large increase in demand occurs.

Although these two considerations may pose problems when conducting a cost analysis of medical firms, do not be misled into thinking that the material in this topic is without value. That is clearly not the case. These two considerations are modifications that can and should be incorporated into the cost analysis when possible. Indeed, a strong grounding ieoclassical cost analysis under conditions of perfect certainty is necessary before any sophisticated analyses or model extensions can be properly conducted and understood.

 

 

Oligopolistic Behavior in Medical Care Markets

The two different models just discussed indicate that oligopolistic firms are more likely to compete among themselves, rather than tacitly or overtly coordinate their policies, when firms are more numerous and entry barriers are lower, among other factors. Consequently we may witness only two firms in an industry yet aggressive price competition because entry barriers are low, for instance. In contrast, another industry may be characterized by five firms that coordinate their policies because entry barriers are high and the firms share similar histories and common bonds. Sorting out the behavior of real-world oligopolistic firms typically requires a careful study that simultaneously controls for a host of conditions that impact how firms may react to each other’s decisions.

With that caveat in mind, we illustrate a couple of real-world situations that portray two different medical care industries as reflecting the behavior of a competitive oligopoly. That is, the existence of rivals resulted in lower prices. The first example relates to the $2 billion blood banking industry during the late twentieth century. Interestingly, this case involves two dominant not-for-profit firms.

In the mid-1990s, American Red Cross held a 46 percent share of the nation’s blood banking business. Its closest national rival, America’s Blood Centers (ABC), an affiliation of local independent blood banks, controlled another 47 percent. Individual hospital blood banks across the nation collectively held the remaining 7 percent of the market. Despite their relatively equivalent national market shares, either American Red Cross or a local member of ABC enjoyed a monopoly position in many regional markets at that time because federal policy since the 1970s had sanctioned local blood monopolies.

However, in 1998, American Red Cross made a bold move to increase its national market share to 65 percent by entering various regional markets such as Kansas City, Dallas, and Phoenix, originally monopolized by one of the local members of ABC. Based on this aggressive behavior, a competitive oligopoly model appears to do a better job of predicting the behavior of these two dominant firms than does a collusive oligopoly model. Evidence indicates that a lower price of blood resulted in local markets where a member of ABC coexisted with American Red Cross than in markets where an independent operated alone. For example, the price of a unit of blood cells was about $60 in Florida, one of the nation’s most cutthroat markets, and $105 in upstate New York, where competition was minimal (Hensley, 1998).

Our other example pertains to Johnson and Johnson (J&J), the well-known drug and medical device manufacturer. The relevant product in this case is a stent.

A stent resembles a small metal mesh tube, no thicker than a pencil lead, which is squeezed onto a tiny balloon and threaded into the heart’s arteries. At the blockage site, the balloon is inflated to expand and deposit the stent, creating a scaffolding device resembling a ballpoint pen spring that remains in place to keep the vessel open after the balloon is withdrawn. Blood can then flow through the previously blocked artery.

At the beginning of 1997, J&J was a dominant firm controlling 95 percent of the $600 million stent market through its patent protection. By the middle of 1998, the stent market had grown to yearly sales of $1 billion but J&J only held a meager 8 percent market share at that time (Winslow, 1998)! How could a company lose nearly 90 percent of its market share with a patented product over an eighteen-month span? It appears that J&J made a major blunder by failing to consider potential competition.

To be more specific, J&J angered key customers with rigid pricing for its $1,600 stent, refusing discounts even for hospitals that purchased more than $1 million worth of stents per year. With no comparable stent options, the buyers of stents had little alternative but to pay the high price. The high prices eventually caused cardiologists to pressure the Food and Drug Administration to approve new stents as quickly as possible. Physicians helped quicken the approval process by willingly testing the stents offered by new firms. Guidant Corporation took advantage of this new approval process and, 45 days after its patent was approved, controlled 70 percent of sales in the stent industry. Interestingly, J&J developed new types of stents and began merger proceedings with Guidant Corporation over the next several years.

While both of our examples provide evidence to support the competitive oligopoly model, it is important to note that a collusive oligopoly model may be more relevant in other situations, depending on the precise market conditions. Because overt price-fixing per se is illegal in the United States (see Topic 9), it doesn’t reveal itself as competitive behavior does. Tacit collusion is also hard to detect in practice given that the prices charged by firms in the same industries, even competitive ones, tend to move together. Nevertheless, industrial organization theory suggests that firms may collude when certain structural conditions hold in a market. When firms collude to make additional profits, economic theory tells us that they restrict output (and quality), raise price and thereby harm consumers. Topic 9 provides some examples of noncompetitive oligopoly in the context of antitrust enforcement.

 

Defining the Relevant Market, Measuring Concentration, and Identifying Market Power

This topic has focused on the theoretical relationship between market structure, conduct, and performance. We learned that the structural characteristics of a market influence how firms conduct themselves with respect to pricing and other business practices, which in turn affects the performance of the industry. Little regard, however, has been given to delineating the precise boundaries of a market. Hypothetically, we know that a market reflects a place where the buyers and sellers of a product, through their collective negotiations, determine the price and quantity of a good or service that is bought and sold. While a hypothetical definition may be fine for theoretically studying the welfare implications of various market structures such as monopoly, a more practical definition of the market is necessary when conducting real-world analysis for private and public policy purposes. If a market is defined too broadly (narrowly) in practice, firms will appear to possess less (more) market power than they actually hold.

Consequently, if we intend to apply the SCP model to better understand and predict market behavior and performance, determining the precise boundaries of a market becomes an important exercise. To begin with, we have to determine the precise product being bought and sold. We also have to figure out how many sellers of that particular product are located in the market area. We discuss next some of the theoretical issues and practical limitations involved when defining markets. We also consider how market concentration and market power are often measured in practice.

 

The Relevant Product and Geographical Markets

While hypothetically easy to imagine, a market is very hard to define in practice. Economists note that a market has two dimensions. The first dimension, the relevant product market (RPM) considers all of the various goods and services that a set of buyers might switch to if the price of any one good or service is raised by a nontrivial amount for more than a brief amount of time. Obviously, these goods and services must share some similarity or substitutability in terms of satisfying demand. For instance, general and family practitioners are likely to substitute for one another whereas urologists and pediatricians are not, because the latter two types of physicians fulfill different demands. As another example, suppose clinic-based physicians raise their fees by 5 percent or more and hold them at that level for at least a year. If a reasonable number of insurers, as the buyers of physician services, respond to this nontrivial and nontransient price increase by adding the outpatient facilities of hospitals to their network of ambulatory care providers, then services of clinic-based and hospital-based doctors can be considered as offering goods and services in the same RPM. If insurers do not switch, then hospital outpatient facilities most likely cannot be considered to be in the same RPM as clinic-based services.

The relevant geographical market (RGM) represents the second dimension of the market. The RGM establishes the spatial boundaries in which a set of buyers purchase their products. A RGM may be local (physician, nursing home care, acute hospital care, and dialysis services), regional (tertiary care hospitals, health insurance), national (prestigious medical academic centers) or international (pharmaceuticals, medical devices) in scope. For example, a hospital in Utica, New York, is unlikely to compete with a hospital in Hartford, Connecticut (about 205 miles away) for the same patients or insurers, but it may compete with a hospital in Rome, New York (about 16 miles away). Similar to determining the RPM, the conceptual exercise is to imagine all of the sellers of the same good or service that a set of buyers might switch to as a result of a nontrivial, nontransient price increase (or quality decrease). The RGM is then defined to include all of the seller locations to which buyers might switch. For example, suppose dental practices in Ivy Towers raise their prices by 5 percent or more and the price increase is expected to last indefinitely. If consumers and insurers are observed switching to dental practices in communities other than Ivy Towers, then all of the dental practices in all of those communities to which the buyers switch should be included in the RGM.

Although its practical relevance is limited, this conceptual exercise of a nontrivial, nontransient price increase is helpful because it tells us that we cannot necessarily rely on current purchasing practices when defining the relevant market for different types of medical care. For example, suppose several health insurers have contracts for all of their ambulatory care needs with three independent group physician practices in an area. Now suppose that these three independent group practices announce that they plan to merge their organizations in the upcoming year. If only current purchasing arrangements are relied on, we might be led into believing that the consolidated physician practice would result in monopoly pricing. However, that may not be the case if the insurers can switch to other providers of ambulatory care in that same immediate area or switch to providers outside the immediate area. The availability of substitutes can be expected to inhibit the newly consolidated practice from raising price. In fact, the consolidation of the three physician clinics might actually benefit the community if scale economies exist and lower rather than higher prices result.

In any case, it should be evident that determining the scope of the RGM and the RPM remains more of an art than a science. Typically, analysts refer to current purchasing practices and expert opinion when determining the current willingness of buyers to substitute among products and among sellers at different locations. They also must consider that other substitute products and sellers at different locations may be available but are not yet economical at existing prices. Their mere existence, however, prevents current sellers from raising price. We must also remember that new suppliers help maintain reasonable prices when entry barriers are low and they can easily and quickly enter markets.

 

Measuring Market Concentration

Suppose we are reasonably comfortable with our definition of the relevant market for a good or service after considering both its product and geographical dimensions. Further suppose that we want to measure the degree of market concentration as reflected in the number and size distribution of the firms within an industry. For instance, we learned that perfectly competitive markets are characterized by a large number of firms with tiny market shares whereas a few dominant firms characterize an oligopolistic industry. We want to capture the structural aspect of an industry with a relatively simple statistic, with the general idea that a market can be viewed as being more highly concentrated when fewer firms produce a larger share of industry output.

Economists typically offer the concentration ratio and the Herfindahl-Hirschman index as measures of market concentration. The concentration ratio identifies the percentage of industry output produced by the largest firms in an industry. The four-firm concentration ratio, CR₄, which is the most common, equals the sum of the market shares of the four largest firms. Industry output is often measured in terms of sales, volume of output, or employment. The CR₄ ranges between 0 and 100 percent, with a higher value reflecting that the largest four firms account for a larger share of industry output or, alternatively stated, that the industry is more highly concentrated. For example, a CR 4 of 60 percent indicates that the four largest firms account for 60 percent of all industry output.

Over the years, economists have assigned labels to industries depending on their four-firm concentration ratios. An industry with a CR₄ of 60 percent or more is considered to be tightly oligopolistic whereas an industry with a CR₄ between 40 and 60 percent is labeled as a loose oligopoly. Industries with a CR₄ of 40 percent or less are treated as being reasonably competitive. However, some words of caution: these industry classifications consider only the number and size distribution of firms. As we learned earlier, other market conditions, such as the height of any entry barriers, should also be considered when evaluating the relative structural competitiveness of an industry.

When data are available only for total industry output and the output produced by the few largest firms but not for the rest of the firms in an industry, a concentration ratio must be used to gauge the degree of industrial concentration. But concentration ratios possess a shortcoming because they do not identify the distribution of industry output among the largest firms. For example, if the CR₄ in some market equals 60 percent, it is unclear whether the largest four firms each produce 15 percent of industry output or the largest firm produces 57 percent and the others each produce 1 percent. The distribution of output among the largest firms can make a difference in terms of the market conduct of firms. Economists tend to agree that firms are more likely to engage in active price competition when they are more similarly sized compared to a market environment where one firm dominates the industry and the others are much smaller. In the latter case, the smaller firms are likely to act as followers and simply mirror the pricing behavior of the dominant firm. We talked earlier about this type of tacit collusion in the context of the price leadership model.

Because a concentration ratio fails to reveal the distribution of industry output among the largest firms, most economists prefer to use the Herfindahl-Hirschman index (HHI), when the necessary data are available, to measure the degree of industry concentration. The disadvantage of the HHI is that market share data are needed for all of the firms in the industry with shares of more than 1 percent. The four-firm concentration ratio requires only market share data for the largest four companies. The HHI is derived by summing the squared market shares of all the firms in the relevant market, or

 

where S. stands for the percentage market share or percentage of industry output produced by the ith firm and 0 < HHI # 10,000.

When a market is dominated by one firm, the HHI equals its maximum value of 10,000 or 100². The HHI takes on a value closer to zero when a greater number of firms, N, exist in the market and/or when the existing firms are more equally sized. As the value of the HHI approaches zero, an industry is considered to be less concentrated or more structurally competitive.

For example, in 2003 the five largest manufacturers of soft contact lenses were Vistakon (J&J), Ciba Vision, Bausch & Lomb, Cooper Vision, and Occular Sciences, with market share based on total patient visits when dispensed of 36.2%, 23.1%, 14.0%, 13.1%, and 12.4%, respectively. Supposing that soft contact lenses represent the RPM, the CR₄ can be calculated by summing the four largest market shares. The resulting figure of 86.4 percent suggests that the four major producers of soft contact lenses in the United States account for slightly more than 86 percent of all soft contact lenses dispensed. In terms of market concentration, the soft contact lens industry clearly resembles a tight oligopoly given that the CR₄ greatly exceeds 60 percent. But notice that the CR₄, by itself, does not reveal the distribution of output among the four largest firms. For example, the CR₄ would also equal 86.4 percent if Vistakon’s market share were 80 percent and the three other firms accounted for the remaining amount of industry output.

The distribution of market shares among the largest firms in the soft contact lens industry can be considered by applying Equation 8-1 and computing the HHI as 2,370.2. To gain some insight into the meaning of this figure, suppose that the two smallest contact lens suppliers, Occular Sciences and Cooper Vision, decide to consolidate their companies. The postmerger HHI would be (36.2² + 23.1² + 14² + 25.5²) or 2,690.3. Notice that a smaller number of firms leads to a higher value for the HHI and reflects the greater concentration of output among a smaller number of firms in the industry. Now suppose the market shares of the four remaining soft contact lens suppliers become equal over time. If so, the HHI declines to 2,500 (25² times 4). In general, it can be shown that the HHI takes on a lower value when a larger number of equally sized firms exists in an industry.

Although the SCP model predicts that firms are more likely to unilaterally or collectively exploit their market power by restricting output and raising price (and reducing quality) when firms are fewer iumber, that same theory is unable to predict the precise value of the HHI at which behavior of this kind takes place. The HHI reflects only the structural competitiveness of the market; it reveals nothing explicit about the behavioral intensity of competition among firms. Consequently, economic theory alone is unable to identify a specific competition-monopoly cutoff level for the HHI.

However, the Department of Justice (DOJ) has established some guidelines concerning the level of the HHI that the agency believes triggers a concern about the potential exploitation of market power. That is, the DOJ generally challenges a merger when the postmerger HHI exceeds 1,800 and the merger increases the premerger HHI by 50 points or more. The DOJ may also challenge a merger that results in a postmerger HHI above 1,000 and raises the the premerger HHI by more than 100 points. A merger that results in a postmerger HHI of less than 1,000 is seldom challenged by the DOJ.

The DOJ therefore believes that reasonably competitive conditions hold when the HHI is less than 1,000. In addition, the industry is treated by the DOJ as being mildly concentrated when the HHI falls between 1,000 and 1,800. Finally, the DOJ regards the industry as being highly concentrated when the HHI exceeds 1,800. Interestingly, these cutoffs for the HHI correspond fairly closely to the benchmarks for the CR₄ mentioned previously with regard to an industry being labeled as reasonably competitive and loosely or tightly oligopolistic. If all of the firms in an industry are equally sized, the HHI equals 1,000 when the CR₄ equals 40 percent and roughly 1,800 when the CR₄ equals 60 percent. There is also a measure referred to as the numbers equivalent HHI, which is found by dividing 10,000, the maximum value of the HHI, by the actual HHI for an industry. This measure provides a picture of an industry regarding the number of equally sized firms potentially represented by a given HHI. For example, an HHI of 1,800 reflects a market environment where roughly 5.6 (10,000/1,800) similarly sized firms exist in an industry. Rounding this number up to 6 and supposing each firm holds an equal market share of 16 percent results in a CR₄ of 64 percent. Notice that the 60 percent cutoff for the CR₄ compares closely to the 1,800 cutoff for the HHI. A similar argument can be made for the 40 percent CR₄ cutoff.

 

 

 

Procompetitive and Anticompetitive Aspects of Product Differentiation

In the perfectly competitive model, buyers are treated as being perfectly informed about the prices and quality of all goods and services in the marketplace. The assumption that all buyers possess perfect information about prices implies that all identical products sell at the same lowest possible price. Otherwise, high-priced businesses lose sales to low-priced businesses when buyers are perfectly informed.

But, realistically, there are both costs and benefits to acquiring information. Therefore, in many situations, people choose to be less than perfectly informed, or rationally ignorant, because the marginal costs of additional information outweigh the additional benefits. Positive information and search costs mean that buyers may find it uneconomical to seek out all available suppliers. As a result, any one individual supplier faces a less than perfectly elastic demand and is able to restrict output and raise price to some degree. As a result, the price of a product in the real world is likely to be dispersed and higher, on average, than the competitive ideal (since theoretically prices cannot be lower than the competitive level). The average price and degree of price dispersion depend on the marginal benefits and costs of acquiring price information. Higher benefits and lower costs of acquiring information imply lower and less dispersed prices.

Imperfect buyer information may also affect the level of quality observed in a market, but the relation between information and product quality is more involved. It stands to reason that high-quality goods cost more to produce than low-quality goods. If buyers are perfectly informed, high-quality goods sell at a higher price than low-quality goods in a competitive market. In the real world with imperfect information, however, buyers are not fully knowledgeable about product quality. Consequently, if buyers base their willingness to pay on the average quality in the market and pay the average price, low-quality products drive out high-quality products, and the process continues until only low-quality products remain. The implication is that the level of product quality is higher when buyer information is more readily available.

Given imperfect information about various products in the real world, some economists argue that various features of production differentiation, such as advertising, trademarks, and brand names, convey important information regarding the value of a good or service. For example, they argue that advertising provides relatively cheap information to buyers about the price and quality of a good and thereby promotes lower prices and higher quality. In fact, studies by Benham (1972), Cady (1976), and Kwoka (1984) found that the prices of eyeglasses and prescription drugs were higher, on average, in areas where price advertising was prohibited. Even when price and quality information is not directly conveyed, a large advertisement in the Yellow Pages or the local newspaper, for example, may signal consumers that the firm is willing to incur a sizeable expense because it is confident that it is offering a quality product at a reasonable price. Through repeat buying, the firm hopes to get a sufficient return on its advertising investment. In this case, the mere presence of an expensive advertising message generates information about the value of a product.

Other economists such as Klein and Leffler (1981) argue that brand names and trademarks serve a similar purpose for promoting competition. Because the quality of many products cannot be properly evaluated until after purchase (or repeat purchase), brand names and trademarks help identify businesses that have enough confidence in the quality of their products to invest in establishing a reputation. Given the sunk-cost nature of the investment, the argument is that a business will not sacrifice its established reputation by offering shoddy products on the market and take the chance of losing repeat buyers. A firm that expends considerable sums of money to polish its image and establish a brand name can lose a valuable investment by selling inferior products and tarnishing that image.

However, not all economists agree that advertising, trademarks, and brand names are always procompetitive. Some economists are concerned that promotional activities are used to establish brand loyalty, mislead consumers, and thereby cause “habit buying” rather than “informed buying.” In this view, promotional activities are anticompetitive and advertising is treated as persuasive rather than informative. Persuasive advertising attempts to convince consumers that the attributes of product A are better than those of product B. Sometimes the advertising message points out real differences, but often the advertising is used to create imaginary or perceived differences across goods or services. For example, both Bayer and generic brands contain the same aspirin ingredient, yet many people are willing to pay a higher price for the Bayer product. Some argue that people pay a premium for branded products because past advertising successfully convinced people that Bayer aspirin, for example, is a superior product. Instead of creating a new market demand, persuasive advertising attempts to attract consumers from competitor firms. Considering advertising, trademarks, and brand names as quality signals, Robinson (1988) points out “a signal can be heard as long as it stands out over and against the background level of noise. As each seller amplifies his or her signal, the background noise level rises, necessitating further amplification on the part of individual sellers. This is clearly undesirable from a social perspective because the signaling mechanism imposes costs” (p. 469).

According to the anticompetitive view, product differentiation manipulates the demand for a product. For example, a successful advertising campaign can influence consumer tastes and preferences and thereby affect the position of the demand curve for the product. Advertising may affect the position of the demand curve in two ways. First, the demand curve may shift upward as a result of successful advertising because consumers are now willing to pay a higher price for the firm’s product. Second, advertising may cause the demand curve to become less elastic with respect to price and, as a result, give the firm some ability to reduce output and raise the price of the good or service.

As an example, many public health officials claim that the purpose behind cigarette advertising is to manipulate the demand for cigarettes. Of major concern is advertising aimed at influencing teenager demand for cigarettes. A report by the Centers for Disease Control found that among smokers aged 12 to 18, preferences were greater for Marlboro, Newport, and Camel, three brands that are heavily advertised (Ruffenach, 1992). RJR Nabisco’s Old Joe advertising campaign for Camel cigarettes was of particular concern to health officials. As George Will (1992) writes:

 

A study of children aged 3 to 6 showed that Old Joe was not quite as familiar as the McDonald’s and Coca-Cola emblems but was more familiar than the Cheerios emblem. An astonishing 91 percent of 6-year-olds recognized Old Joe, about as many as recognized Mickey Mouse.

 

Existing firms may also use advertising or other types of product differentiation to create barriers to entry. If existing firms can control consumers through advertising, for example, new firms have a difficult time entering a market because they are unable to sell a sufficient amount of output to break even financially. It follows that product differentiation directed toward creating artificial wants, habit buying, or barriers to entry results in a misallocation of society’s scarce resources. Resources are misused if they are employed to create illusory rather than real value.

When evaluating the social desirability of product differentiation, it is useful to remember that all products are homogeneous within the abstract model of the competitive industry and that most people agree that variety is the spice of life. People like diversity and enjoy choosing among a wide assortment of services selling at different money and time prices. People also receive utility when buying goods of different colors, shapes, and sizes. In this vein, the higher-than-competitive price that is paid for product differentiation may simply reflect the premium consumers place on variety. Nevertheless, economic theory suggests that firms may use product differentiation as a way to increase demand in some situations. If supply creates demand in this manner, some of society’s scarce resources may be wasted.

Oligopoly involves a market structure with a few large or dominant firms and relatively high barriers to entry. While there may be a large number of firms in the industry, those other than the few dominant firms have relatively small market shares and act as price takers. The important aspect of oligopoly is that the dominant firms must be sufficiently sized and limited so the behavior of any one firm influences the pricing and output decisions of the other major firms in the market. It is this mutual interdependence among firms that distinguishes oligopoly from the other market structures. Because the nature of the interdependence varies, economists have been unable to develop a single model of oligopoly behavior. As a result, many formal and informal models of oligopoly have been developed that depict firm behavior under a variety of different scenarios. It is beyond the scope of this text to delve into all of these models so we have limited the discussion to two broad models of firm behavior: the collusive and competitive models of oligopoly.

 

Collusive Oligopoly

According to the collusive oligopoly model, all the firms in the industry cooperate rather than compete on price and output and jointly maximize profits by collectively acting as a monopolist. To illustrate, assume that there are only three identical firms in a given market with similar demand curves and that these firms have decided to collude and jointly maximize profits. Under these circumstances, the firms collectively act like a monopolist and jointly set the price and output indicated by point M on the market demand curve in Figure 8-5. It follows that a deadweight loss and a misallocation of society’s scarce resources results from the collusive oligopoly.

The collusion among the oligopolistic firms may be of an overt or a tacit nature. Overt collusion refers to a situation in which representatives of the firms formally meet, perhaps in a clandestine location such as a smoke-filled room, and coordinate prices and divide up markets. Tacit collusion occurs when firms informally coordinate their prices. The price leadership model represents an example of tacit collusion in which the firms in an industry agree that one firm will serve as a price leader. The rest of the firms in the industry simply match or parallel the price of the leader. The resulting conscious parallelism can theoretically produce the same monopoly outcome as overt collusion and deadweight losses result (point M in Figure 8-5).

While it appears that firms in an oligopoly have a strong incentive to collude and form a cartel, a number of factors make collusion difficult. First and foremost are legal and practical considerations. The Sherman Antitrust Act prohibits overt collusion. Firms found in violation of overt price fixing can be subjected to severe financial penalties and the CEOs of these companies can be imprisoned.

However, antitrust officials, largely because of the difficulty of establishing proof, do not pursue cases involving tacit collusion. Firms in an industry may parallel their actions simply because they react to the same swings of demand and costs in the marketplace. But a tacit collusive arrangement has its practical difficulties. The informality of a tacit price-fixing arrangement can lead to problems because other firms in the industry may have a difficult time interpreting why the industry leader adjusts price. For example, suppose that the price leader decreases its price. Other firms in the industry can interpret this either as a simple reaction to an overall decrease in market demand or as an aggressive attempt on the part of the price leader to improve market share. In the first case, the other firms would simply lower prices and go about their business. In the second case, however, they may aggressively counteract this move by decreasing their prices even further in an attempt to initiate a price war.

Second, cost differences make it more difficult for firms to cooperate and agree on a common price. High-cost firms will desire a higher price than low-cost firms. But the success of a cartel depends on all of the firms adhering to a common price. Third, collusion is less successful when entry barriers are low. New firms offering lower prices will seize market share away from the cartel members when entry barriers are low. Fourth, for several reasons, collusion is more likely when few firms exist in an industry. One reason is that the ability to collude becomes more difficult as more firms enter into collusive agreement. Low negotiation costs make it much easier for two firms to collude than a dozen. Another reason is that more firms increase the probability that any one firm will act as a maverick and act independently by charging a lower price than others. Finally, more firms increase the probability that one firm may cheat or chisel on the agreement. For example, one firm may grant a secret price concession to a large buyer to improve sales. Naturally, when the other firms in the industry learn of this behavior they will abandon the collusive agreement and strike out on their own. The potential for cheating behavior is greater when more firms exist in the industry because of high monitoring and detection costs. For these four reasons, collusive agreements are more difficult to negotiate and maintain than most people imagine.

 

Competitive Oligopoly

Competitive oligopoly lies at the opposite extreme of collusive oligopoly. Competitive oligopoly considers that rivals in an oligopolistic industry may not coordinate their behavior but instead aggressively seek to individually maximize their own profits. If the firms in an oligopolistic market sell relatively homogeneous products, and thus one firm’s product is a strong substitute for the others, each firm may realize that buyers will choose to purchase the product offering the lowest price. If so, each firm faces an incentive to lower its price to marginal cost because at that level it will at least share part of the market with the others and not be undersold. If oligopolistic firms act in a competitive manner like this, market output is produced at the point where price equals marginal cost and resources are efficiently allocated (point C in Figure 8-5) even though a few dominant firms exit in the industry.

 

Collusive or Competitive Oligopoly?

Whether firms act as a collusive or competitive oligopoly, or somewhere in between, depends on how each firm forms its beliefs or conjectural variations about how its rivals will react to its own price and output decisions. Conjectural variations consider how, say, firm A believes its rivals will react to its output decision. For example, firm A might believe that rivals will offset its behavior by producing more if it reduces output. Firm A has no incentive to restrict output given that market output and price remain the same because of offsetting behavior. On the other hand, Firm A might believe that its rivals will react by matching its behavior and producing less. The matching behavior results in less market output and a higher price for the product. Thus, if firms form similar conjectural variations and each expects matching behavior, a point closer to point M in Figure 8-5 and the associated deadweight losses result. In contrast, if firms form similar conjectural variations and each expects offsetting behavior, a point closer to point C in Figure 8-5 and the related efficiency gains occur.

Economic theory indicates that firm characteristics and market conditions influence the conjectural variations held by oligopolistic rivals. Many involve the same characteristics and conditions mentioned earlier that affect the success of a collusive oligopoly. First, firms are more likely to expect matching behavior when fewer firms exist and entry barriers are high because each firm realizes the greater profit potential from engaging in matching behavior. For example, each firm receives 50 percent of the monopoly profits when only two firms exist in the industry, so greater expectations can be attached to matching behavior.

Rivals are more likely to expect matching behavior when they share social and historical ties. Social and historical ties consider such things as industry trade associations, maturity and growth of an industry, and the proximity of firms in an industry. Specifically, rivals are more likely to anticipate matching behavior in industries in which trade associations play an important role. Trade associations foster cooperative behavior by establishing common bonds and the sharing of information among firms. Anticipation of matching behavior is greater among rivals in older industries that are growing slowly. Less entry takes place and fewer new owners exist in older, slow-growing industries. New owners are more likely to act as independent mavericks and reduce the likelihood of matching behavior.

The proximity of firms in an industry considers how close firms are on a number of dimensions including location, products, technologies, and sources of capital. Rivals in closer proximity more likely share similar expectations. The organizational structure of the firms in an industry may also affect conjectural variations. More centralized firms respond slowly to market changes and thus may be biased toward cooperation and expecting matching behavior. Also, prices tend to be determined at the top of the hierarchy while output decisions are made at the lower levels in more centralized organizations. If firms within an industry possess similar centralized organizational structures, the hierarchical arrangement may lead to price rigidity but output flexibility. Lastly, bounded rationality may favor expectations of matching behavior among rivals. Bounded rationality refers to the limited ability of human behavior to solve complex problems. Bounded rationality may lead to rules of thumb for pricing in an industry and act as facilitating device for firms to match or coordinate their behavior.

 

 

 

Summary

In this topic, we focused on characteristics and concepts pertaining to the costs of producing medical services. First, we examined the underlying production behavior of a single medical firm. The short-run production function that resulted from this examination relates productivity to input usage. Among the more important principles we examined was the law of diminishing marginal productivity, the notion that the marginal and average productivities of a variable input first increase but eventually fall with greater input usage because a fixed input places a constraint on production.

Second, we discussed the inverse relation between productivity and costs. Simply stated, increasing marginal and average productivities translate into decreasing marginal and average variable costs. Conversely, declining productivities imply higher per-unit costs of production. As a result, the average variable cost curve is U-shaped, implying that the average variable cost of production first decreases with greater production but at some point begins to increase as output expands. Taking the property of fixed costs into consideration, we also derived a U-shaped short-run average cost curve, which relates average operating costs to the amount of medical services produced.

Finally, we examined some concepts relating to long-run costs of production, including economies and diseconomies of scale. We also discussed the determinants of the optimal input mix.

 

 

Review Questions and Problems

1.                Suppose you are to specify a short-run production function for dental services. What inputs might you include in the production function? Which would be the variable inputs and which the fixed inputs?

2.                In your own words, explain the law of diminishing marginal productivity. Be sure to mention the reason this law tends to hold in the short run.

3.                Explain the difference between technical efficiency and economic efficiency.

4.                Discuss the relation between the marginal and average productivity curves and the marginal and average variable cost curves.

5.                What does the elasticity of substitution illustrate? How is it expressed mathematically? What two factors affect its magnitude?

6.                Explain the difference between the explicit and implicit costs of production. Cite an example of each.

7.                Suppose that with 400 patients per year, the SAFC, SATC, and SMC of operating a physician clinic are $10, $35, and $30 per patient, respectively. Furthermore, suppose the physician decides to increase the annual patient load by one more patient. Using short-run cost theory, explain the impact of this additional patient on the SAVC and SATC. Do they increase or decrease? Why?

8.                What factors shift the short-run average variable and total cost curves? Explain why these curves would shift up or down in response to changes in these factors.

9.                Suppose you are to specify a short-run total variable cost function for a nursing home. Explain the variables you would include in the function. What is the expected relation between a change in each of these variables and short-run total variable costs?

10.           What does economies of scope mean? Provide an example.

11.           Explain the reasoning behind the U shape of the long-run average total cost curve. Why might this cost curve shift upward?

12.           You are responsible for hiring one of two hygienists for a dental office. The first dental hygienist has 25 years of experience. Given her record, she is likely to satisfactorily service 16 patients per day. Her hourly wage would be approximately $16 per hour. The other hygienist is new to the industry. He is expected to satisfactorily service 10 patients per day at an hourly wage of $8. Which dental hygienist would be the better hire? Why?

13.           Santerre and Bennett (1992) estimated the short-run total variable cost function for a sample of 55 for-profit hospitals in Texas (t-statistics are in parentheses below the estimated coefficients).

ln STVC = 1.31 + 0.47ln q + 0.80ln w + 0.73ln QUALITY

(0.69) (3.31) (4.42) (2.58)

                     + 0.11ln CASEMIX + 0.29ln k + 0.07ln DOC

                                   (1.48) (3.16) (0.88)

                     + Other factors

Adj. R¹ = 0.95

N = 55

 

where STVC = short-run total variable cost, q = a measure of output (total inpatient days), w = average wage rate or price of labor, QUALITY = a measure of quality (number of accreditations), CASEMIX = an indicator of patient case-mix (number of services), k = a measure of capital (beds), and DOC = number of admitting physicians. All variables are expressed as natural logarithms (ln), so the estimated coefficients can be interpreted as elasticities.

A.                 How much of the variation in STVC is explained by the explanatory variables? How do you know that?

B.                  Which of the estimated coefficients are not statistically significant? Explain.

C.                  Does the estimated coefficient on output represent short-run economies or diseconomies of scale? Explain.

D.                 What are the expected signs of the coefficient estimates on w, QUALITY, and CASEMIX? Explain.

E.                  Provide an economic interpretation of the magnitude of the estimated coefficient on w.

F.                   What do the estimated coefficient on k and DOC suggest about the amount of capital and physicians at the representative hospital?

14.           Draw a U-shaped LATC curve. Then draw the related long-run marginal cost (LMC) curve, keeping in mind the geometric relation between marginal cost and average cost (see the discussion on short-run cost curves). What is the relation between LATC and LMC when increasing returns to scale are present? Between LATC and LMC when the production process exhibits decreasing returns to scale? What type of returns to scale holds when LMC equals LATC?

15.           Describe the two limitations associated with the cost theory provided in this topic when it is applied to explain the behavior of medical firms.

16.           Suppose that you are interested in comparing the costs of producing inpatient services at Saving Grace Hospital with those at ACME Hospital. Further suppose that the two hospitals annually admit about 24,000 and 32,000 patients, respectively, at average short-run total costs per admission of roughly $11,000 and $12,000.

A.                 Why may these two dollar figures not represent the economic cost of providing inpatient services at these two hospitals? Explain fully.

B.                  Suppose that these cost figures accurately reflect the economic costs of providing inpatient services at these two hospitals and that the two hospitals face the same average total cost curve. Draw a graphical representation of the average total cost curve (only) and graphically show and verbally explain why ACME Hospital produces at a higher cost than Saving Grace Hospital.

C.                  Using cost theory as presented in class and the text, identify and fully explain four other factors that might explain why ACME Hospital has higher average costs of production than Saving Grace Hospital.

D.                 Fully explain how the comparative analysis becomes muddled if one considers that one (or both) of the two hospitals is not organized on a for-profit basis.

 

 

References

 

Chiang, Alpha C. Fundamental Methods of Mathematical Economics. New York: McGraw-Hill, 1984.

Cowing, Thomas G., and Alphonse G. Holtmann. “Multiproduct Short-Run Hospital Cost Functions: Empirical Evidence and Policy Implications from Cross-Section Data.” Southern Economics Journal 49 (January 1983), pp. 637-53.

Cowing, Thomas G., Alphonse G. Holtmann, and S. Powers. “Hospital Cost Analysis: A Survey and Evaluation of Recent Studies.” In Advances in Health Economics and Health Services Research, Vol. 4, eds. Richard M. Scheffler and Louis F. Rossiter. Greenwich, Conn.: JAI Press, 1983, pp. 257-303.

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