# RobertLee_2019_Chapter8Elasticities_EconomicsForHealthcar.pdf

CHAPTER

125

8ELASTICITIES

Learning Objectives

After reading this chapter, students will be able to

• describe economic relationships with elasticities,• use elasticity terms appropriately,• apply elasticities to make simple forecasts, and• calculate an elasticity.

Key Concepts

• Elasticities measure the association between the quantity demanded and related factors.

• Elasticities are ratios of percentage changes, so they are scale free.• Income, price, and cross-price elasticities are used most often.• Income elasticities are usually positive but small.• Price elasticities are usually negative.• Cross-price elasticities may be positive or negative.• Managers can use elasticities to forecast sales and revenues.

8.1 Introduction

Elasticities are valuable tools for managers. Armed only with basic marketing data and reasonable elasticity estimates, managers can make sales, revenue, and marginal revenue forecasts. In addition, elasticities are ideal for analyz-ing “what if” questions. What will happen to revenues if we raise prices by 2 percent? What will happen to our sales if the price of a substitute drops by 3 percent?

Elasticities reduce confusion in descriptions. For example, suppose the price of a 500-tablet bottle of generic ibuprofen rose from \$7.50 to \$8.00. Someone seeking to downplay the size of this increase (or someone whose focus was on the cost per tablet) would say that the price rose from 1.5 cents

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Economics for Healthcare Managers126

to 1.6 cents per tablet. Describing this change in percentage terms would eliminate any confusion about price per bottle or price per tablet, but a potential source of confusion remains.

To avoid confusion in calculating percentages, economists recommend being explicit about the values used to calculate percentage changes. For example, one might say that the price increase to \$8.00 represents a 6.67 percent increase from the starting value of \$7.50.

8.2 Elasticities

An elasticity measures the association between the quantity demanded and related factors. For example, Chen, Okunade, and Lubiani (2014) used statis-tical techniques to estimate that the income elasticity for adjusted inpatient days was 0.04. The base for this estimate is average income, so an income 1 percent above the average is associated with an average level of physician visits that is 0.04 percent above average. As we shall see, these apparently esoteric estimates can be valuable to managers.

First we need to learn a little more about elasticities. Economists rou-tinely calculate three demand elasticities:

1. income elasticities, which quantify the association between the quantity demanded and consumer income;

2. price elasticities, which quantify the association between the quantity demanded and the product’s price; and

3. cross-price elasticities, which quantify the association between the quantity demanded and the prices of a substitute or complement.

Elasticities are ratios of percentage changes. For example, the income elasticity of demand for visits would equal the ratio of the percentage change in visits (dQ/Q) associated with a given percentage change in income (dY/Y). (The mathematical terms dQ and dY identify small changes in consumption and income.) So, the formula for an income elasticity would be (dQ/Q)/(dY/Y). The formula for a price elasticity would be (dQ/Q)/(dP/P), and the formula for cross-price elasticity would be (dQ/Q)/(dR/R). (A cross-price elasticity measures the response of demand to changes in the price of a substitute or complement, so R is the price of a related product. Substitutes have positive cross-price elasticities. Complements have negative cross-price elasticities.)

Now recall that Chen, Okunade, and Lubiani (2014) estimated that the income elasticity for physician visits is 0.04. This implies that 0.04 = (dQ/Q)/(dY/Y). Suppose we want to know how much higher than average

income elasticity The percentage change in the quantity demanded divided by the percentage change in income. For example, if visits are 0.04 percent higher for consumers with incomes that are 1 percent higher, the income elasticity is 0.0004/0.010, which equals 0.04.

substitute A product used instead of another product.

complement A product used in conjunction with another product.

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Chapter 8: Elast ic i t ies 127

the number of visits per person would be in an area where the average income is 2 percent higher than the national average. Because we are considering a case in which dY/Y = 0.02, we multiply both sides of the equation by 0.02 and find that visits should be 0.0008 (0.08%) higher in an area with income 2 percent above the national average. From the perspective of a working manager, what matters is the conclusion that visits will be only slightly higher in the wealthier area.

8.3 Income Elasticities

Consumption of most healthcare products increases with income, but only slightly. As exhibit 8.1 shows, consumption of healthcare products appears to increase more slowly than income. As a result, healthcare spending will rep-resent a smaller proportion of income among high-income consumers than among low-income consumers.

8.4 Price Elasticities of Demand

The price elasticity of demand is even more useful, because prices depend on choices managers make. Estimates of the price elasticity of demand will guide pricing and contracting decisions, as chapter 9 explores in more detail.

Managers need to be careful in using the price elasticity of demand for three reasons. First, because the price elasticity of demand is almost always negative, we need a special vocabulary to describe the responsiveness of demand to price. For example, −3.00 is a smaller number than −1.00, but −3.00 implies that demand is more responsive to changes in prices (a 1 percent rise in prices results in a 3 percent drop in sales rather than a 1 percent drop in sales). Second, changes in prices affect revenues directly and indirectly, via changes in quantity. Managers need to keep this fact in mind when using the price elasticity of demand. Third, managers need to think about two different price elasticities of demand: the overall price elasticity of demand and the price elasticity of demand for the firm’s products.

price elasticity of demand The ratio of the percentage change in sales volume associated with a percentage change in a product’s price. For example, if prices rose by 2.5 percent and the quantity demanded fell by 7.5 percent, the price elasticity would be −0.075/0.025, which equals −3.00.

Source Variable Estimate

Chen, Okunade, and Lubiani (2014) Adjusted inpatient days 0.04

Newhouse and Phelps (1976) Hospital admissions 0.02 to 0.04

Newhouse and Phelps (1976) Physician visits 0.01 to 0.04

EXHIBIT 8.1Selected Estimates of the Income Elasticity of Demand

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Economics for Healthcare Managers128

Economists usually speak of price elasticities of demand (but not other elasticities) as being elastic or inelastic. When a change in price results in a larger percentage change in the quantity demanded, the price elasticity of demand will be less than −1.00, and demand is said to be elastic. When price change results in a smaller percentage change in the quantity demanded, the price elasticity of demand will be between 0.00 and −1.00, and demand is said to be inelastic. For example, a price elasticity of −4.55 would indicate elastic demand. A price elasticity of −0.55 would indicate inelastic demand.

Inelastic demand does not mean that consumption will be unaffected by price changes. Suppose that, in forecasting the demand response to a 3.5 percent price cut, we use an elasticity of −0.20. Predicting that sales will rise by 0.7 percent (0.007 = −0.035 × −0.2), this elasticity implies that demand is inelastic but not unresponsive. Recall that a price elasticity of demand equals the ratio of the percentage change in quantity that is associated with a percentage change in price, or (dQ/Q)/(dP/P). Using this formula and our elasticity estimate gives us −0.20 = (dQ/Q)/(−0.03). After solving for the percentage change in quantity, we forecast that a 3 percent price cut will increase consumption by 0.006 (or 0.6%), which is equal to −0.20 × −0.03. Exhibit 8.2 shows that the demand for medical care is usually inelastic.

elastic A term used to describe demand when the quantity demanded changes by a larger percentage than the price. (This term is usually applied only to price elasticities of demand.)

inelasticA term used to describe demand when the quantity demanded changes by a smaller percentage than the price. (This term is usually applied only to price elasticities of demand.)

Source Variable Estimate

Ellis, Martins, and Zhu (2017) Total spending −0.44

Dunn (2016) Total spending −0.22

Ellis, Martins, and Zhu (2017) Inpatient −0.30

Ellis, Martins, and Zhu (2017) Outpatient −0.29

Ellis, Martins, and Zhu (2017) Emergency department −0.04

EXHIBIT 8.2Selected

Estimates of the Price Elasticity

of Demand

The Curious Case of Daraprim

In August 2015 Turing Pharmaceuticals raised the price of Daraprim from \$13.50 a tablet to \$750,

an increase of 5,456 percent (Over and Silverman 2015). Daraprim is the only available treatment for toxoplasmosis, a rare infection that can become deadly for patients with weakened immune systems. This

Case 8.1

(continued)

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Chapter 8: Elast ic i t ies 129

price increase means that an individual’s treat-ment could cost up to \$634,000. Daraprim’s patent expired in 1953, and it can be compounded for less

than a dollar per tablet (Langreth 2015). Two contradictory trends are evident. Generic drug prices have

been declining in the United States since at least 2010, yet multiple generic drugs have risen in price (Ornstein and Thomas 2017). The price increases generate far more attention than the price decreases, yet the structure of the market has not changed.

In the United States, pharmaceutical prices (indeed most medical prices) are based on negotiations between private insurers and suppli-ers. The US market has two features that are uncommon in other coun-tries. First, pharmacy benefit managers often act as an intermediary between insurers and suppliers. Second, the federal government plays a limited role in negotiating prices. Although the Department of Vet-erans Affairs negotiates drug prices for its beneficiaries, private firms negotiate for Medicare.

Discussion Questions• Would you expect demand for Daraprim to be elastic or inelastic? Why?

• What change in the market would make demand for Daraprim more elastic? Less?

• What would the out-of-pocket cost for Daraprim be for a patient on Medicare? Medicaid?

• What would the price elasticity be after a patient exceeded the out-of-pocket maximum?

• Why did other companies not start making versions of Daraprim?

• Did Turing Pharmaceuticals violate any laws or regulations when it raised the price?

• Could a company have raised the price of a drug like this in Canada? France? Australia?

• Companies have also raised prices for other off-patent drugs. Can you explain why?

• Can you offer examples of large price increases for off-patent drugs?

• What should the United States do about cases like that of Daraprim?

• Should the federal government negotiate pharmaceutical prices? Why? Why not?

• Should someone else negotiate pharmaceutical prices? Who? Why? Why not?

Case 8.1(continued)

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Economics for Healthcare Managers130

8.5 Other Elasticities

The cross-price elasticity of demand describes how the quantity demanded changes when the price of a related product changes. This might sound eso-teric, but it has practical implications. For example, how does use of hospital services change when the price of primary care changes? Alternatively, how does the demand for outpatient or emergency care change if drug copay-ments change? These questions are important for the design of health insur-ance plans. Unfortunately, the evidence is contradictory.

For example, among their other effects, insurance expansions reduce the out-of-pocket price for primary care. In some instances, this scenario has led to an increase in emergency department use, suggesting that primary care is a complement for emergency department care. In other cases, it has led to a reduction in emergency department use, suggesting that primary care is a substitute (Sommers and Simon 2017).

8.6 Using Elasticities

Elasticities are useful forecasting tools. With an estimate of the price elasticity of demand, a manager can quickly estimate the impact of a price cut on sales and revenues. As noted previously, managers need to use the correct elastic-ity. Most estimates of the overall price elasticity of demand fall between −0.10 and −0.40. For the market as a whole, the demand for healthcare products is typically inelastic. For individual firms, in contrast, demand is usually elastic. The reason is simple. Most healthcare products have few close substitutes, but the products of one healthcare organization represent close substitutes for the products of another.

The price elasticity of demand that individual firms face typically depends on the overall price elasticity and the firm’s market share. So, if the price elasticity of demand for hospital admissions is −0.17 and a hospital has a 12 percent share of the market, the hospital needs to anticipate that it faces a price elasticity of −0.17/0.12, or −1.42. This rule of thumb need not hold exactly, but good evidence indicates that individual firms confront elastic demand. Indeed, as we will show in chapter 9, profit-maximizing firms should set prices high enough that demand for their products is elastic.

Armed with a reasonable estimate of the price elasticity of demand, we will now predict the impact of a 5 percent price cut on volume. If the price elasticity faced by a physician firm were −2.80, a 5 percent price cut should increase the number of visits by 14 percent, which is the product of −0.05 and −2.80. (Prudent managers will recognize that their best guess about the price elasticity will not be exactly right and will repeat the calculations

cross-price elasticity of demand The ratio of the percentage change in sales volume associated with a percentage change in another product’s price. For example, if prices of the other product rose by 2.0 percent and the quantity demanded fell by 5.0 percent, the cross-price price elasticity would be −0.05/0.02, which equals −2.50.

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Chapter 8: Elast ic i t ies 131

with other values. For example, if the price elasticity is really −1.40, volume will increase by 7 percent. If the price elasticity is really −4.20, volume will increase by 21 percent.)

How much will revenues change if we cut prices by 5 percent and the price elasticity is −2.80? Obviously, because prices are reduced, revenues will rise to a lesser extent than volume does. A rough, easily calculated estimate of the change in revenues is the percentage change in prices plus the percentage change in volume. Prices will fall by 5 percent and quantity will rise by 7 to 21 percent, so revenues should rise by approximately 2 to 16 percent. Our baseline estimate is that revenues will rise by 9 percent. If costs rise by less than this percentage, profits will rise.

Should Sodas Be Taxed?

One in five adults is obese in wealthy countries around the world. Unfortunately, in the United

States, the rate is about two in five (Organisation for Economic Co-operation and Development [OECD] 2017). Major causes appear to be sweet drinks and added sugars in other products. According to the Centers for Disease Control and Prevention (2017), frequent consump-tion of sweetened beverages is associated with obesity, heart disease, kidney diseases, cavities, and other diseases.

Oddly, despite the obesity epidemic, subsidies for crops that can be refined into sugar—corn, wheat, rice, sorghum, and others—con-tinue. The subsidies reduce the prices of products containing sugars. These products include sodas, sweetened teas, and other products.

A number of local governments have enacted taxes on sweetened beverages, but no taxes have passed at the state or federal level. (France and Mexico have passed national taxes.) Paarlberg, Mozaffar-ian, and Micha (2017) argue that a 17 percent tax on sweetened bever-ages would reduce consumption by 15 percent.

Discussion Questions• What price elasticity does the estimate by Paarlberg, Mozaffarian,

and Micha (2017) imply?

• Can you find another estimate of the price elasticity of demand for sweetened drinks?

• Is the demand for sweetened drinks elastic or inelastic?

Case 8.2

(continued)

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Economics for Healthcare Managers132

8.7 Conclusion

An elasticity is the percentage change in one variable that is associated with a 1  percent change in another variable. Elasticities are simple, valuable tools that managers can use to forecast sales and revenues. Elasticities allow managers to apply the results of sophisticated economic studies to their organizations.

Three elasticities are common: income elasticities, price elasticities, and cross-price elasticities. Income elasticities measure how much demand varies with income, price elasticities measure how much demand varies with the price of the product itself, and cross-price elasticities measure how much demand varies with the prices of complements and substitutes. Of these, price elasticity is the most important because it guides pricing and contract-ing decisions.

Virtually all price elasticities of demand for healthcare products are negative, reflecting that higher prices generally reduce the quantity demanded. Overall, demand is generally inelastic, meaning that a price increase will result in a smaller percentage reduction in sales. In most cases, though, the demand for an individual organization’s products will be elastic, meaning that a price increase will result in a larger percentage reduction in sales. This difference is based on ease of substitution. Few good substitutes are available for broadly defined healthcare products, so demand is inelastic. In contrast, the products of other healthcare providers are usually good sub-stitutes for the products of a particular provider, so demand is elastic. When making decisions, managers must consider that their organization’s products face elastic demands.

• If the price of sodas rose by 5 percent, how much would sales drop?

• What are substitutes for sweetened drinks?

• Can you find an estimate of the cross-price elasticity of demand for sweetened drinks?

• Is water a substitute or complement for soda?

• In light of your answer to the previous question, should the cross-price elasticity be positive?

• Do you favor a tax on sweetened drinks? Why? Why not?

• Do you favor a tax on added sugars? Why? Why not?

• How could a health system reduce sugar consumption? Should it try?

Case 8.2(continued)

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Chapter 8: Elast ic i t ies 133

Exercises

8.1 Why are elasticities useful for managers? 8.2 Why are price elasticities of demand called “elastic” or “inelastic”

when other elasticities are not? 8.3 Why is the demand for healthcare products usually inelastic? 8.4 Why is the demand for an individual firm’s healthcare products

usually elastic? 8.5 Per capita income in the county was \$40,000, and physician visits

averaged 4.00 per person per year. Per capita income has risen to \$42,000, and physician visits have risen to 4.02 per person per year. What is the percentage change in visits? What is the percentage change in income? What is the income elasticity of demand for visits?

8.6 Average visits per week equal 640 when the copayment is \$40 and 360 when the copayment rises to \$60. Calculate the percentage change in visits, percentage change in price, and price elasticity of demand.

8.7 Sales were 4,000 at a price of \$200 but fell to 3,800 when the price was increased to \$220. Calculate the percentage change in sales, the percentage change in price, and the price elasticity of demand.

8.8 Per capita income in the county was \$45,000, and physician visits averaged 5.0 per person per year. Per capita income has risen to \$49,500. The income elasticity of demand for visits is 0.4. By what percent will visits rise? What will the average number of visits be?

8.9 The price elasticity of demand is −1.2. Is demand elastic or inelastic?

8.10 The price elasticity of demand is −0.12. Is demand elastic or inelastic?

8.11 If the income elasticity of demand is 0.2, how would the volume of services change if income rose by 10 percent?

8.12 You are a manager for a regional health system. Using an estimate of the price elasticity of demand of −0.25, calculate how much ambulatory visits will change if you raise prices by 5 percent.

8.13 If the cross-price elasticity of clinic visits with respect to pharmaceutical prices is −0.18, how much will ambulatory visits change if pharmacy prices rise by 5 percent? Are pharmaceuticals substitutes for or complements to clinic visits?

8.14 If the cross-price elasticity of clinic visits with respect to emergency department prices is 0.21, how much will ambulatory visits change

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Economics for Healthcare Managers134

if emergency department prices rise by 5 percent? Are emergency department visits substitutes for or complements to clinic visits?

8.15 If the income elasticity of demand is 0.03, how much will ambulatory visits change if incomes rise by 4 percent?

8.16 A study estimates that the price elasticity of demand for Lipitor is −1.05, but the price elasticity of demand for statins as a whole is −0.13. a. Why is demand for Lipitor more elastic than for statins as a

whole? b. What would happen to revenues if the makers of Lipitor raised

prices by 10 percent? c. What would happen to industry revenues if all manufacturers

raised prices by 10 percent?d. Why are the answers so different? Does this difference make

sense? 8.17 The price elasticity of demand for the services of Kim Jones, MD, is

−4.0. The price elasticity of demand for physicians’ services overall is −0.1.a. Why is demand so much more elastic for the services of Dr. Jones

than for the services of physicians in general?b. If Dr. Jones reduced prices by 10 percent, how much would

volume and revenue change?c. Suppose that all the physicians in the area reduced prices by 10

percent. How much would the total number of visits and revenue change?

d. Why does it make sense that your answers to questions b and c are so different?

References

Centers for Disease Control and Prevention. 2017. “Get the Facts: Sugar-Sweetened Beverages and Consumption.” Updated April 7. www.cdc.gov/nutrition/data -statistics/sugar-sweetened-beverages-intake.html.

Chen, W., A. Okunade, and G. G. Lubiani. 2014. “Quality–Quantity Decomposition of Income Elasticity of U.S. Hospital Care Expenditure Using State-Level Panel Data.” Health Economics 23 (11): 1340–52.

Dunn, A. 2016. “Health Insurance and the Demand for Medical Care: Instrumental Variable Estimates Using Health Insurer Claims Data.” Journal of Health Economics 48: 74–88.

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Ellis, R. P., B. Martins, and W. Zhu. 2017. “Health Care Demand Elasticities by Type of Service.” Journal of Health Economics 55: 232–43.

Langreth, R. 2015. “Express Scripts Covers \$1 Alternative to \$750 Pill Daraprim.” Bloomberg. Published November 30. www.bloomberg.com/news/articles /2015-12-01/express-scripts-to-cover-1-alternative-to-750-pill-daraprim.

Newhouse, J. P., and C. E. Phelps. 1976. “New Estimates of Price and Income Elasticities of Medical Care Services.” In The Role of Health Insurance in the Health Services Sector, edited by R. Rosett, 261–320. New York: Neal Watson.

Organisation for Economic Co-operation and Development (OECD). 2017. “OECD Health Statistics 2017.” Accessed August 16, 2018. www.oecd.org /els/health-systems/health-statistics.htm.

Ornstein, C., and K. Thomas. 2017. “Generic Drug Prices Are Falling, but Are Consumers Benefiting?” New York Times. Published August 8. www.nytimes.com/2017/08/08/health/generic-drugs-prices-falling.html.

Over, M., and R. Silverman. 2015. “The 5000% Price Increase and the Economic Case for Pharma Price Regulation.” Global Health Policy Blog. Published Sep-tember 23. www.cgdev.org/blog/5000-price-increase-and-economic-case -pharma-price-regulation.

Paarlberg, R., D. Mozaffarian, and R. Micha. 2017. “Viewpoint: Can U.S. Local Soda Taxes Continue to Spread?” Food Policy 71: 1–7.

Sommers, B. D., and K. Simon. 2017. “Health Insurance and Emergency Depart-ment Use—A Complex Relationship.” New England Journal of Medicine 376 (18): 1708–11.

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