HMGT 435 WK 4 DISC 4

CHAPTER

169

11MAXIMIZING PROFITS

Learning Objectives

After reading this chapter, students will be able to

• define measures of profitability, • describe two strategies for increasing profits, • explain how to respond if marginal revenue exceeds marginal cost, • identify the profit-maximizing level of output, and • discuss differences between for-profit and not-for-profit providers.

Key Concepts

• All healthcare managers need to understand how to maximize profits. • Most healthcare organizations are inefficient, so cost reductions can

increase profits. • To maximize profits, firms should expand as long as marginal revenue

exceeds marginal cost. • Marginal cost is the change in total cost associated with a change in

output. • Marginal revenue is the change in total revenue associated with a

change in output. • Managers need to distinguish incremental cost from average cost. • An agency problem arises because the goals of stakeholders may not

coincide.

11.1 Introduction

Substantial numbers of healthcare managers serve firms that seek to maxi- mize profits. For example, for-profit hospitals, most insurance firms, most physician groups, and a broad range of other organizations explicitly seek

profits Total revenue minus total cost.

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C o p y r i g h t 2 0 1 9 . H e a l t h A d m i n i s t r a t i o n P r e s s .

A l l r i g h t s r e s e r v e d . M a y n o t b e r e p r o d u c e d i n a n y f o r m w i t h o u t p e r m i s s i o n f r o m t h e p u b l i s h e r , e x c e p t f a i r u s e s p e r m i t t e d u n d e r U . S . o r a p p l i c a b l e c o p y r i g h t l a w .

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Economics for Healthcare Managers170

maximum profits. In addition, recognizing that “with no margin, there is no mission,” many not-for-profit healthcare organizations act like profit- maximizing firms. And even organizations that are not exclusively focused on the bottom line must balance financial and other goals. Bankrupt orga- nizations accomplish nothing. As a result, even healthcare managers with objectives other than maximizing profits need to understand how to maxi- mize profits. A manager who does not understand the opportunity cost (in terms of forgone profits) of a strategic decision cannot lead effectively. All healthcare managers need to understand how to maximize profits. Finally, as markets become more competitive, the differences between for-profit and not-for-profit firms are likely to narrow.

Profits are the difference between total revenue and total cost. To maximize profits, you must identify the strategy that makes this difference the largest. In other words, identify the product price (or quantity) and char- acteristics that maximize profits.

11.2 Cutting Costs to Increase Profits

An obvious way to increase profits is to cut costs. Most healthcare organiza- tions are inefficient, meaning that they could produce the same output at less cost or produce higher-quality output (that sells for a higher price) for the same cost. The inference that healthcare organizations are inefficient is based on two types of evidence. First, studies by quality management and reengineering teams have identified that costs can be cut by increasing the quality of care. For example, a transportation project at CareMore Health System (that used Lyft) reduced wait times, reduced cost, and increased patient satisfaction (Eapen and Jain 2017). The second type of evidence results from statistical studies. For example, a sophisticated study of hospital efficiency concluded that inefficiency represented more than 15 percent of costs (Zhivan and Diana 2012). Some improvement appears to have been made in recent years, but inefficiency remains substantial (Khushalani and Ozcan 2017).

As exhibit 11.1 illustrates, the payoff from cost reductions can be sub- stantial. The organization in the exhibit earns $40,000 on revenue of $2.4 million. This operating margin (profits divided by revenue) of 1.7 percent suggests that the organization is not greatly profitable. Reducing costs by only 2 percent changes this picture entirely. As long as the cost cuts represent more efficient operations (not cuts in quality or customer service), all the cost reductions will increase profits, in this case by 118 percent.

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Chapter 11: Maximizing Prof i ts 171

11.2.1 Cost Reduction Through Improved Clinical Management Cost reductions often require improvements in clinical management because differences in costs are primarily driven by differences in resource use, not differences in the cost per unit of resource. (An organization cannot maxi- mize profits if it overpays for the resources it uses.) In turn, differences in resource use are driven by differences in how clinical plans are designed and executed. Improvements in clinical management require physician coopera- tion and, more typically, physician involvement. Even though many health- care professionals make clinical decisions, physicians in most settings have a primary role in decision making.

Having recognized the importance of physicians in increasing effi- ciency, managers need to ask whether the interests of the organization and its physicians are aligned. In other words, will changes that benefit the orga- nization also benefit its physicians? If not, physicians cannot be expected to be enthusiastic participants in these activities, especially if the advantages for patients are not clear.

Managers are responsible for ensuring that the interests of individual physicians are aligned with the organization or for changing the environment. For example, physicians usually benefit from changes in clinical processes that improve the quality of care or make care more attractive to patients. If man- agers present the change proposal in this fashion, physicians may understand how they will benefit. In other cases, however, physicians cannot be expected to participate in quality improvement activities without compensation. For independent physicians, explicit payments for participation may be required. The same may be true for employee physicians, or participation may be a part of their contractual obligations. In both cases, managers must be aware of the high opportunity cost of time spent away from clinical practice.

Where feasible, physicians’ compensation can incorporate bonuses based on how well they meet or exceed clinical expectations. This system helps align the incentives of the organization and its physicians and provides a continuing reminder to improve clinical management.

Status Quo 2% Cost Reduction

Quantity 24,000 24,000

Revenue $2,400,000 $2,400,000

Cost $2,360,000 $2,312,800

Profit $40,000 $87,200

EXHIBIT 11.1 The Effects of Cost Reductions on Profits

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Economics for Healthcare Managers172

Profiting from Clinical Improvement

Surgical complications reduce patients’ quality of life and survival. As exhibit 11.2 shows, surgical

complications also increase hospital length of stay, readmission rates, and costs. Such complications can significantly reduce profitability, especially in bundled payment, capitated, or other value-based pay- ment environments.

Hospitals are sometimes paid more when patients experience complications (although Medicare has ended reimbursement for some clinical shortcomings). Because incremental revenues are highly vis- ible and incremental costs due to complications are not, hospital administrators may think that clinical shortcomings are not eroding margins. Michard and colleagues (2015) conclude that implementing goal-directed fluid therapy (which significantly reduces complications) would return $2.50 to $4.00 for each dollar invested. In this case, improving quality is highly profitable.

Poor quality reduces hospital profits, even if it substantially increases payments by insurers. And poor quality is a terrible strategy in both the short run and the long run. For example, Gutacker and col- leagues (2016) conclude that the elasticity of hospital demand with respect to a typical health gain (measured by the Oxford Hip Score) is 1.4, and the demand elasticities for readmission and mortality rates are −0.02 and −0.004. Poor quality leads to market share losses, and this effect is likely to become larger as insurers increasingly use cost and quality data to try to steer patients to efficient, effective, safe providers (Avalere Health 2017).

Length of Stay Readmission Rate Cost

With Without With Without With Without

Gastrectomy 4 2 12.7 5.2 $27,794 $12,641

Vascular bypass 6 3 21.3 14.1 $31,979 $16,849

Esophagectomy 13 9 18.5 15.4 $67,924 $37,382

Source: Michard et al. (2015).

EXHIBIT 11.2 Surgeries With

and Without Complications

Case 11.1

(continued)

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Chapter 11: Maximizing Prof i ts 173

11.2.2 Reengineering Reengineering and quality improvement initiatives can increase profits, but this does not mean that they will or that they will do so easily. Nothing guar- antees that costs will fall, and nothing guarantees that revenues will not fall faster than costs. Especially in hospitals, improvement initiatives often coin- cide with downsizing efforts, making the staff wary (and sometimes causing the organization to lose the employees it most wants to keep).

Skilled leadership does not guarantee success but is essential to improvement initiatives. Many projects fail, but alignment of the board, management, and clinicians appears to increase the odds of success (Pannick, Sevdalis, and Athanasiou 2016). Reengineering and quality management initiatives demand the time and attention of everyone in the organization, meaning that other things are left undone or are done less well. If not done skillfully, reengineering and quality management initiatives can make things worse.

11.3 Maximizing Profits

Organizations can also increase profits by expanding or contracting output. The basic rules of profit maximization are to expand as long as marginal revenue (or incremental revenue) exceeds marginal cost (or incremental

marginal or incremental revenue The revenue from selling an additional unit of output.

marginal or incremental cost The cost of producing an additional unit of output.

Discussion Questions • Is there other evidence that providers profit

from improving quality?

• What is Medicare currently doing to measure quality? Safety? Efficiency?

• What are private health plans currently doing to measure quality? Safety? Efficiency?

• What are Medicaid plans currently doing to measure quality? Safety? Efficiency?

• How large are the potential effects on hospital profits of Medicare’s value-based payments?

• How large are the potential effects on physician profits of Medicare’s value-based payments?

• How will value-based payments from private insurers affect profits?

• How could better quality not cost more?

• What is inefficiency in healthcare? How common is it?

Case 11.1 (continued)

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Economics for Healthcare Managers174

cost), to shrink as long as marginal cost exceeds marginal revenue, and to shut down if the return on investment is not adequate. If increasing output increases revenue more than costs, profits rise. If reducing output reduces costs more than it reduces revenue, profits rise.

Marginal cost (or incremental cost) is the change in total cost associ- ated with a change in output. Marginal revenue (or incremental revenue) is the change in total revenue associated with a change in output. The chal- lenges lie in forecasting revenues and estimating costs.

As shown in exhibit 11.3, increasing output from 100 to 120 increases profits because the marginal revenue is greater than the marginal cost. Rev- enue increases from $2,000 to $2,400 as sales increase from 100 to 120 units, so marginal revenue equals $20 ($400 ÷ 20). Costs increase from $1,500 to $1,600, so marginal cost equals $5 ($100 ÷ 20). The same is true for the expansion from 120 to 140. Marginal revenue falls because the firm has to cut prices to increase sales, and marginal cost rises because the firm is approaching capacity. Even though marginal revenue is nearly equal to marginal cost, profits still rise. Expanding from 140 to 160 reduces profits. Further price cuts push marginal revenue below marginal cost.

Managers need to understand what their costs are and must not con- fuse incremental costs with average costs. Average costs may be higher or lower than incremental costs. As long as the organization operates well below capacity, average costs usually will exceed incremental costs because of fixed costs. As the firm approaches capacity, however, incremental costs can rise quickly. If the firm needs to add personnel, acquire new equipment, or lease new offices to serve additional customers, incremental costs may well exceed average costs.

The following example illustrates why managers need to understand marginal costs and compare them to marginal revenues. A clinic is operating near capacity when a small PPO (preferred provider organization) approaches it. The PPO wants to bring 100 additional patient visits to the clinic and pay $50 per visit. The manager accepts the deal, even though $50 is less than the clinic’s average cost or average revenue. Shortly thereafter, another PPO approaches the clinic. It too wants to bring 100 additional patient visits to

Quantity Revenue Cost Profit Marginal Revenue

Marginal Cost

100 $2,000 $1,500 $500

120 $2,400 $1,600 $800 $20 $5

140 $2,660 $1,840 $820 $13 $12

160 $2,880 $2,120 $760 $11 $14

EXHIBIT 11.3 Marginal

Cost, Marginal Revenue, and

Profits

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Chapter 11: Maximizing Prof i ts 175

the clinic and pay $50 per visit. The manager turns down the offer. When criticized for this apparent inconsistency, the manager defends the decision, explaining that the clinic had excess capacity when the first PPO contacted it. The marginal cost for those additional visits was only $10 (see exhibit 11.4). Signing the first contract increased profits by $4,000 because the marginal revenue was $50 for those visits. When the second PPO contacted the clinic, it no longer had excess capacity and would have had to add staff to handle the additional visits. As a result, marginal costs for the second set of visits would have been $510, and profits would have plummeted.

11.4 Return on Investment

When examining an entire organization rather than a well-defined project, most analysts focus on return on equity rather than return on investment. Equity is an organization’s total assets minus outside claims on those assets. Equity also can be defined as the initial investments of stakeholders (donors or investors) plus the organization’s retained earnings.

What is an adequate return on investment? The answer to this ques- tion depends primarily on three factors: what low-risk investments (e.g., short-term US Treasury securities) are yielding, the riskiness of the enter- prise, and the objectives of the organization.

All business investments entail some risk. Those risks may be high, as they are for a pharmaceutical company considering allocating research and development funds to a new drug, or they may be low, as they are for a pri- mary care physician purchasing an established practice in a small town. In any case, a profit-seeking investor will be reluctant to commit funds to a project

return on equity Profits divided by shareholder equity.

Status Quo Adding the First PPO

Adding the Second PPO

Quantity 24,000 24,100 24,200

Revenue $2,400,000 $2,405,000 $2,410,000

Average revenue $100.00 $99.79 $99.59

Marginal revenue $50.00 $50.00

Cost $2,040,000 $2,041,000 $2,092,000

Average cost $85.00 $84.69 $86.45

Marginal cost $10.00 $510.00

Profit $360,000 $364,000 $318,000

EXHIBIT 11.4 Marginal Cost and Profits

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Economics for Healthcare Managers176

that promises a rate of return similar to the yield of low-risk securities. Conse- quently, when rates of return on low-risk investments are high, investors will demand high yields on higher-risk investments. The size of this risk premium will usually depend on a project’s perceived risk. An investor may be content with the prospect of a 9 percent return on investment from a relatively low- risk enterprise but will not find this yield adequate for a high-risk venture.

Because managers must be responsive to the organization’s stake- holders, they must also avoid high-risk investments that do not offer at least a chance of high rates of return. What constitutes a high rate of return depends on the goals of the organization and the nonfinancial attributes of an investment. In some cases, an organization that is genuinely committed to nonprofit objectives will be willing to accept a low return (or even a negative return) on a project that furthers those goals.

11.5 Producing to Stock or to Order

Organizations can produce to stock or produce to order. One that pro- duces to stock forecasts its demand and cost and produces output to store in inventory. Medical supply manufacturers are an example of this sort of organization. More commonly in the healthcare sector, firms produce to order. They also forecast demand and cost, but they do not produce any- thing up front. Instead, they set prices designed to maximize profits and wait to see how many customers they attract. Hospitals are an example of this type of organization. This distinction is important because discussions of profit maximization are usually framed in terms of choosing quantities or choosing prices.

Thus far, the content of this chapter has been largely framed in terms of firms that produce to stock; however, its implications apply to healthcare organizations that produce to order. Only by setting prices based on their expectations about demand and cost do they discover whether they have set prices too high or too low. An organization has set prices too high if its mar- ginal revenue is greater than its marginal cost, because that means additional profitable sales at a lower price were missed. An organization has set prices too low if its marginal revenue is less than its marginal cost. Organizations that produce to order must also make the same decisions about rates of return on equity discussed earlier. Is a 5 percent return on investment large enough to justify operating an organ transplant unit? How important is the unit to the organization’s educational goals? What are the alternatives?

When organizations contract with insurers or employers, estimates of marginal revenue should be easy to develop. To estimate marginal revenue for a new contract, calculate projected revenue under the new contract,

producing to stock Producing output and then adjusting prices to sell what has been produced.

producing to order Setting prices and then filling customers’ orders.

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Chapter 11: Maximizing Prof i ts 177

subtract revenue under the old contract, and divide by the change in volume. For sales to the general public, economics gives managers a tool: Marginal revenue equals p × (1 + 1/ε), where p is the product price and ε is the price elasticity of demand. (See chapter 8 for more information about elasticity.) Most healthcare organizations face price elasticities in the range of −3.00 to −6.00, so marginal revenue can be much less than the price. For example, if a product sells for $1,000 and the price elasticity of demand is −3.00, its marginal revenue will equal $1,000 × (1 − 1/3.00), or $667. In contrast, if the price elasticity of demand is −6.00, its marginal revenue will equal $1,000 × (1 − 1/6.00), or $833. As demand becomes more elastic, marginal revenue and price become more alike. Unless the elasticity becomes infinite, though, marginal revenue will be less than price.

11.6 Not-for-Profit Organizations

The strategies of not-for-profit organizations may differ from those of for- profit organizations because of more severe agency problems, differences in goals, and differences in costs. These forces have multiple effects.

11.6.1 Agency Problems All organizations have agency problems. Agency problems are conflicts between the interests of managers (the agents) and the goals of other stake- holders. For example, a higher salary benefits a manager, but it benefits stakeholders only if it enhances performance or keeps the manager from leaving (when a comparable replacement could not be attracted for less). Not-for-profit firms face three added challenges. They cannot turn manag- ers into owners by requiring them to own company stock (which helps to align the interests of managers and other owners). In addition, no one owns the organization, so no one may be policing the behavior of its managers to ensure that they are serving stakeholders well. Furthermore, assessing the performance of managers in not-for-profit organizations is a challenge. A not-for-profit organization may earn less than a for-profit competitor for many reasons. Is it earning less because of its focus on other goals, because of management’s incompetence, or because the firm’s managers are using the firm’s resources to live well? Often the cause is difficult to pinpoint.

11.6.2 Differences in Goals Goals other than profits can influence an organization’s behavior, though they need not. Not-for-profit firms gain benefits from the pursuit of goals other than profit. Managers should consider how their decisions affect the benefits derived from these other goals. To best realize its goals, a not-for-profit

agency An arrangement in which one person (the agent) takes actions on behalf of another (the principal).

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Economics for Healthcare Managers178

organization should strive to make marginal revenue plus marginal benefit equal to marginal cost. Marginal benefit is the net nonfinancial gain to the firm from expanding a line of business. Three cases are possible:

1. If the marginal benefit is greater than 0, the not-for-profit will produce more than a for-profit.

2. If the marginal benefit equals 0, the not-for-profit will produce as much as a for-profit.

3. If the marginal benefit is less than 0, the not-for-profit will produce less than a for-profit.

A further complication is that the marginal benefit may depend on other income. A struggling not-for-profit may act like a for-profit, but a highly profitable not-for-profit may not.

11.6.3 Differences in Costs Not-for-profit organizations’ costs also may differ. First, the not-for-profit may not have to pay taxes (especially property taxes), which tends to make the not-for-profit’s average costs lower. On the other hand, the not-for-profit firm’s greater agency problems may result in less efficiency and higher aver- age and marginal costs.

The fundamental problem is that we cannot predict how not-for-profit organizations will differ from for-profit firms. This lack of forecast is frustrat- ing for analysts and raises a question for policymakers: If we do not know how not-for-profit organizations benefit the community, why are they given tax breaks?

Tax Exemptions for Not-for-Profit Hospitals

Not-for-profit hospitals enjoy federal, state, and local tax exemptions, but they face challenges from governments in both courtrooms and statehouses (Santos 2016). Contemporary hospitals differ markedly from those that existed at the turn of the twentieth century, which were truly charitable institutions. They were supported almost entirely by donations and largely staffed by volunteers. Thus, it can be argued that tax exemption for not-for-profit hospitals is a historical relic. When the income tax started in 1894, there was no Medicare, no Medicaid,

Case 11.2

(continued)

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Chapter 11: Maximizing Prof i ts 179

and no insurance. Most people with money got care at home. The role of hospitals was to care for the poor.

These days, hospitals serve paying customers, and for-profits, which pay income and property taxes, provide about as much uncom- pensated care as not-for-profits (Valdovinos, Le, and Hsia 2015). (Not- for-profits do appear to offer more charity care—1.9 percent of total expenses—than for-profits, at 1.4 percent.) Not surprisingly, not-for- profits’ de facto tax-exempt status has come into question.

The case of Provena Covenant Medical Center illustrates this. After a lengthy court battle, in 2010 the Supreme Court of Illinois upheld the Illinois Department of Revenue’s denial of an application for exemp- tion in 2002, finding that Provena was not a charitable institution and the property was not used for charitable purposes (Santos 2016). Two factors influenced the decision. First, of the hospital’s $118 million in total revenue, more than 96 percent came from patient and insurer payments, and less than $10,000 came from charitable donations. Second, Provena Covenant Medical Center did not actively promote its charity care program. The hospital routinely billed indigent patients and forced them to apply for discounts under the terms of the financial assistance program. In short, Provena Covenant Medical Center did not appear to be a charity.

In recent years, increasing numbers of localities have asked not- for-profits to make payments in lieu of taxes. For example, Boston received $32.4 million of these payments in 2017 (City of Boston 2018). Such arrangements are becoming more common as localities seek to cover the cost of services. Furthermore, many health systems look no more like charities than Provena Covenant Medical Center did.

One response to this situation was the changes in the community benefit standard specified by the Affordable Care Act (ACA). First, hospitals must prepare a community health needs assessment every three years. This report identifies the major health challenges fac- ing that community and lays out a plan for the hospital to address them in the coming years. Second, hospitals must create a financial assistance plan that explains the criteria for offering financial assis- tance and must make the plan freely accessible to the public. Third, hospitals cannot charge patients that qualify for assistance more than they charge insured patients. Fourth, hospitals must make reasonable

Case 11.2 (continued)

(continued)

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Economics for Healthcare Managers180

11.7 Conclusion

Even managers of not-for-profit organizations need to know how to maxi- mize profits. They must identify appropriate product lines, price and promote those product lines to realize an adequate return on investment, and produce those product lines efficiently. Most healthcare organizations are less profit- able than they could be because they are less efficient than they could be. Leadership must be effective for efficiency to increase. Cost reductions and quality improvements are easier to talk about than to realize, especially where clinical plans (i.e., physician practices) must change to improve efficiency.

efforts to establish that a patient is not eligible for assistance before initiating extraordinary collec- tion actions. However, the ACA did not specify the

terms of financial assistance plans. This issue is not likely to go away. In states that expanded Medic-

aid after 2014, uncompensated care fell from 3.9 percent to 2.3 percent (Dranove, Garthwaite, and Ody 2017). It fell only 0.12 percent in states that did not expand Medicaid. As more and more people gain health insurance, the case for tax-exempt status gets harder to make.

Discussion Questions • How much community benefit do not-for-profit hospitals provide?

• How much community benefit do for-profit hospitals provide?

• Why does using list prices tend to inflate estimates of community benefit?

• Are there other important differences between not-for-profit and for-profit hospitals?

• Would local governments be better off if they taxed hospitals and paid for charity care?

• Is tax exemption a good way to encourage private organizations to serve the public interest?

• Can you find examples of controversies about hospitals’ tax-exempt status?

• Can you find examples of payments in lieu of taxes?

• Does tax exemption for not-for-profit hospitals still make sense?

• Can you propose an alternative to tax exemption?

Case 11.2 (continued)

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Chapter 11: Maximizing Prof i ts 181

Decisions to expand or contract should be based on incremental costs and revenues. Few healthcare managers know what their costs are, so they often have difficulty forecasting revenues and estimating costs to be able to make these decisions.

Not-for-profit organizations may or may not resemble for-profit orga- nizations. In some cases, their goals and performance are similar. Managers need to understand why the goals of not-for-profit organizations are worthy of tax preferences and be able to make that case to donors and regulators.

Exercises

11.1 A clinic has $1 million in revenues and $950,000 in costs. What is its operating margin?

11.2 The owners of the clinic in exercise 11.1 invested $400,000. What is the return on investment? Is it adequate?

11.3 A laboratory has $4.2 million in revenues and $3.85 million in costs. What is its operating margin?

11.4 The owners of the laboratory in exercise 11.3 invested $6 million. What is the return on investment?

11.5 View selected interest rates on the website of the Board of Governors of the Federal Reserve System (www.federalreserve. gov/releases/h15/). What is the current annual yield for one-year Treasury securities?

11.6 Go to the Yahoo! Finance website (finance.yahoo.com), and look up the operating margin and return on equity for Community Health Systems (symbol CYH). How does it compare to Pfizer (PFE), Amgen (AMGN), Laboratory Corporation of America (LH), and Tenet Healthcare Corporation (THC)?

11.7 A not-for-profit hospital realizes a 3 percent return on its $200,000 investment in its home health unit. Its current revenue after discounts and allowances is $382,000. Administrative costs are $119,000, clinical personnel costs are $210,000, and supply costs are $47,000. Providing home health care is not a core goal of the hospital, and it will sell the home health unit if it cannot realize a return of at least 12 percent. A process improvement team has recommended changes to the home health unit’s billing processes. The team has concluded that these changes could reduce costs by $20,000 and increase revenues by $5,000. Analyze the data that follow and assess whether the changes would make the home health unit profitable enough to keep.

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Economics for Healthcare Managers182

Old New

Revenue $382,000 $387,000

Cost $376,000 $356,000

Profit $6,000 $31,000

Return on investment 3% 16%

11.8 The table shows cost and revenue data for a clinic. Calculate the clinic’s marginal cost, marginal revenue, and profits at each volume. Which price maximizes its profits?

Surgeries 250 300 350 400 450

Price $2,000 $1,920 $1,800 $1,675 $1,550

Revenue $500,000 $576,000 $630,000 $670,000 $697,500

Cost $516,000 $538,500 $563,500 $591,000 $621,000

11.9 The table shows cost and revenue data for a clinic. Calculate the clinic’s marginal cost, marginal revenue, and profits at each volume. Which price maximizes its profits?

Surgeries 250 300 350 400 450

Price $200 $210 $220 $230 $240

Revenue $50,000 $63,000 $77,000 $92,000 $108,000

Cost $49,000 $61,000 $74,750 $90,500 $108,250

11.10 The price–quantity relationship has been estimated for a new prostate cancer blood test: Q = 4,000 − (20 × P). Use a spreadsheet to calculate the quantity demanded and total spending for prices ranging from $200 to $0, using $50 increments. For each $50 drop in price, calculate the change in revenue, the change in volume, and the additional revenue per unit. (Call the additional revenue per unit marginal revenue.)

11.11 The table shows output and cost data. Calculate the average total cost, average fixed cost, average variable cost, and marginal cost

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Chapter 11: Maximizing Prof i ts 183

schedules. If the market price were $500, should the firm shut down in the short run? In the long run?

11.12 A clinic’s average and marginal cost per case is $400. It charges $600 per case and serves 1,000 customers. Its marketing team predicts that it will expand its sales to 1,250 customers if it cuts its price to $550. How do profits change if it cuts prices? What is the firm’s marginal revenue? Why is marginal revenue not equal to $550?

11.13 A clinic’s average and marginal cost per case is $400. It charges $600 per case and serves 1,000 customers. Its marketing team predicts that it will expand its sales to 1,250 if it signs a contract for a price of $550 with a local health maintenance organization. How do profits change if it signs the contract? What is the firm’s marginal revenue? Why is its marginal revenue different from the marginal revenue in the previous exercise?

11.14 Why would a for-profit organization that incurs losses choose to operate?

11.15 Why would a profitable for-profit organization choose to exit a line of business?

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Quantity 0 5 10 15 20 25 30 35

Total cost $20,000 $20,500 $20,975 $21,425 $21,850 $22,300 $22,775 $23,275

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