Elastic Demand

Elastic Demand in Health Taxes and Medicine Pricing

Elastic demand is the case in which buyers cut the quantity they buy by a larger percentage than the price rises, so the own-price elasticity lies below minus one. In health economics the case matters because it reverses the link between price and spending seen under inelastic demand, so a higher tax, charge or list price lowers total spending on the product while cutting use sharply. Evidence on medical care as a whole points the other way, towards inelastic demand, and the elastic case arises mainly for products with close substitutes or outside options, such as sugar-sweetened beverages, and for medicines sold in low-income markets. The general measure and its estimation sit on the price elasticity of demand page, and the elastic case matters most for the revenue from health taxes and for the pricing of medicines.

The revenue test that separates elastic from inelastic demand

Elasticity is usually classified by its absolute value. Shapiro, MacDonald and Greenlaw, in the OpenStax microeconomics text, describe an elastic demand as one with an elasticity greater than one, indicating high responsiveness to price. The practical test is what happens to spending when price changes.

$$\frac{dR}{dP} = Q\,(1 + \varepsilon)$$

where $R = P \times Q$ is total revenue to sellers, which equals total spending by buyers, $P$ is the price buyers pay, $Q$ is the quantity demanded, and $\varepsilon = (dQ/dP)(P/Q)$ is the own-price elasticity, which is negative for an ordinary downward-sloping demand curve.

When $\varepsilon$ is below minus one the bracket is negative, so a price rise lowers revenue and a price cut raises it. At exactly minus one revenue does not change, and between minus one and zero a price rise raises revenue. The same point can be written as marginal revenue.

$$MR = P\left(1 + \frac{1}{\varepsilon}\right)$$

where $MR$ is the change in total revenue from selling one more unit, and $P$ and $\varepsilon$ are as above. Marginal revenue is positive only where demand is elastic. A seller with pricing power and positive marginal cost therefore never chooses a point on the inelastic part of its demand curve, because a higher price there would raise revenue and lower costs at the same time.

Elasticity also changes along most demand curves. For a straight-line demand curve $Q = a-bP$, the elasticity is $-bP/Q$, so demand is elastic at prices above $a/(2b)$ and inelastic below it. A product can therefore be in the elastic range at one price and in the inelastic range at another.

What makes demand for a health product elastic

The OpenStax text lists luxury goods, items that take a large share of income and goods with many substitutes as likely to have highly elastic demand, and gives life-saving drugs as an example of a necessity with no close substitute and highly inelastic demand. It also notes that elasticities are often lower in the short run than in the long run, since buyers need time to change habits or find alternatives.

In health care these conditions separate the market for a whole class of care from the market facing one supplier. Demand for treatment of a condition can be inelastic while demand for one brand among several therapeutically equivalent products is elastic, because a prescriber, pharmacist or patient can switch when one price rises, which the cross-price elasticity measures. Income matters too. Danzon and Towse, writing on medicine pricing, note that a patent-holder may rationally set prices near marginal cost in low-income markets where demand is highly price elastic.

Insurance works in the opposite direction. Danzon, Towse and Mestre-Ferrandiz argue that insurance undermines patients' price sensitivity, potentially leading to prices above second-best efficient levels. Under cost sharing with a fixed copayment the patient bears none of a change in the list price, so the demand a manufacturer faces can be far less elastic than it would be if patients paid the full price.

Evidence on where demand in health is elastic and where it is not

The best-known evidence on medical care itself does not show elastic demand. Aron-Dine, Einav and Finkelstein, revisiting the RAND Health Insurance Experiment, describe the famous RAND estimate that the elasticity of medical spending with respect to its out-of-pocket price is minus 0.2. Their simple alternative summaries of the experimental results give price elasticities between minus 0.04 and minus 0.6, all inside the inelastic range. Cost sharing still reduces use, but medical spending falls proportionally less than the patient's price rises.

Tobacco is also inelastic overall. The IARC Handbook on tax and price policies for tobacco control, published in 2011, describes tobacco products as exhibiting relatively inelastic demand and states that the inelasticity of demand and the relatively low share of tax in price in most countries mean that significant tax increases will generate significant increases in government revenue. The same volume reports that cigarette demand in developing countries is more elastic than in developed countries, as Warner predicted in 1990 on the grounds that cigarettes are less affordable where incomes are lower.

Sugar-sweetened beverages are the clearest health example of elastic demand. A systematic review and meta-analysis by Andreyeva and colleagues, covering 86 studies with 62 in the meta-analysis, estimated a price elasticity for sales of taxed beverages of minus 1.59 (95% CI minus 2.11 to minus 1.08), with a prediction interval of minus 3.94 to 0.75 and very high heterogeneity. The estimate was minus 1.39 in the subgroup of high-quality studies. The authors also found cross-border shopping in most studies of local-level taxes, and the pooled elasticity for consumption, as distinct from sales, was not statistically significant. A sales elasticity above one in absolute value may partly reflect buyers moving their purchases elsewhere, which is one of the outside options that make demand elastic.

Health taxes on products with elastic demand

For a given tax, elastic demand gives a larger fall in consumption and a smaller tax take than inelastic demand. The IARC Handbook puts the revenue side in terms of the Ramsey rule for efficient consumption taxes, saying that because of the relative inelasticity of demand tobacco taxes can generate considerable revenues while creating fewer distortions than taxes on goods with more elastic demand. A tax designed to change behaviour, such as a Pigouvian tax on a harmful product, works best where demand responds, so the health case and the revenue case point in different directions.

Elasticity also shapes who bears a tax. The OpenStax text explains that the tax burden falls on the more inelastic side of the market, so when demand is more elastic than supply, producers bear more of it and the price buyers pay rises by less than the tax. Andreyeva and colleagues found an average pass-through of 82 per cent for sugar-sweetened beverage taxes, which they read as undershifting, and a 15 per cent average fall in sales, which they link to many taxes having been small and incompletely passed through.

Pricing medicines when buyers are price sensitive

A firm with market power sets price where marginal revenue equals marginal cost. Rearranging the marginal revenue formula gives the markup rule that Danzon and Towse state for profit-maximising pricing in each market.

$$\frac{P_j-c_j}{P_j} = \frac{1}{|\varepsilon_j|}$$

where $P_j$ is the price in market $j$, $c_j$ is the marginal cost of supplying that market, $|\varepsilon_j|$ is the absolute value of the own-price elasticity there, and the left-hand side is the Lerner index, the markup as a share of price. The rule only has a solution with $P_j > c_j$ when $|\varepsilon_j|$ exceeds one.

Danzon and Towse describe Ramsey pricing, in which markups vary across market segments in inverse relation to their demand elasticities, as the second-best efficient way of paying for the joint costs of pharmaceutical research and development. Markets with more elastic demand get lower markups, and assuming elasticities are related to income, the pattern would also be consistent with standard norms of equity. They add that if price differences cannot be sustained because of parallel trade and external referencing, manufacturers will tend to charge a single price between the differentiated prices, which links elastic demand in poorer markets to external reference pricing in richer ones.

Worked example with a drinks tax and a medicine sold in two markets

All numbers in this example are illustrative. The first part compares a tax on a product with elastic demand and one with inelastic demand, and the second applies the markup rule to a medicine.

1. Set up the tax. A drink sells at GBP 1.00 per litre with sales of 100 million litres a year. A tax of GBP 0.20 per litre is assumed to pass through in full, so buyers pay GBP 1.20, a 20 per cent rise. Demand is taken to have constant elasticity over this range.

$$Q_1 = Q_0 \left(\frac{P_1}{P_0}\right)^{\varepsilon}$$

where $Q_0$ and $Q_1$ are sales before and after the tax, $P_0$ and $P_1$ are the prices buyers pay before and after, and $\varepsilon$ is the constant own-price elasticity.

2. Elastic case, elasticity minus 1.5. Since 1.2 raised to the power 1.5 is 1.3145, sales fall to 100 / 1.3145 = 76.07 million litres, a fall of 23.9 per cent. Buyers' spending falls to 1.20 × 76.07 = GBP 91.29 million, below the GBP 100 million before the tax, and tax revenue is 0.20 × 76.07 = GBP 15.21 million.

3. Inelastic case, elasticity minus 0.5. Since 1.2 raised to the power 0.5 is 1.0954, sales fall to 100 / 1.0954 = 91.29 million litres, a fall of 8.7 per cent. Buyers' spending rises to 1.20 × 91.29 = GBP 109.54 million, and tax revenue is 0.20 × 91.29 = GBP 18.26 million.

4. Compare the two. The elastic product loses nearly three times as much volume (23.9 against 8.7 per cent) and yields GBP 3.05 million less tax. A first-order approximation, 1.5 × 20 per cent, would predict a 30 per cent fall in the elastic case instead of 23.9 per cent, which is why the constant-elasticity form is used for a change this large.

5. Price a medicine in two markets. A manufacturer's marginal cost is GBP 10 per pack. Rearranging the markup rule gives $P = c\,|\varepsilon| / (|\varepsilon|-1)$. In a high-income market with elasticity minus 1.25 the price is 10 × 1.25 / 0.25 = GBP 50, a markup of 80 per cent of price. In a low-income market with elasticity minus 4 the price is 10 × 4 / 3 = GBP 13.33, a markup of 25 per cent.

6. Interpretation. Elastic demand turned the tax into a strong lever on consumption and a weaker source of revenue, and turned the low-income market into one where the profit-maximising price sits close to cost. In a market with elasticity minus 0.8 the rule has no solution, because at a constant elasticity every price rise would raise revenue and lower cost, so no profit-maximising price exists.

Using elastic-demand estimates in budget impact and evaluation

An elasticity enters budget impact analysis and policy models as a forecast of use and revenue. The revenue test applies to spending by whoever faces the price, so a patient-price elasticity says how patients' payments change, not how the payer's or the health system's spending changes. The analysis also has to state the price range, because an elasticity estimated for small changes may not hold for a large tax or a new price tier, and should carry the uncertainty of the estimate into sensitivity analysis.

Tax revenue raised by a health tax is a transfer between buyers and government, so it cancels out from a societal perspective, while the change in consumption carries the health effects. A smaller tax take under elastic demand therefore reflects the larger change in behaviour that a corrective tax aims for.

Common misreadings of elastic demand in health

Several errors recur when the term is used in health policy. Most come from carrying a textbook label into settings where insurance, substitutes or the data change what the elasticity measures.

1. Calling medical care elastic because cost sharing reduces use. A fall in use after a charge rises shows that demand slopes downward, and the RAND-based estimates all sit inside the inelastic range.
2. Treating a sales elasticity as a health response. The sugar-sweetened beverage estimate above one comes from sales data that include cross-border shopping, and the consumption estimates were not statistically significant.
3. Taking market elasticity as brand elasticity. Demand for one product among close substitutes is more elastic than demand for the class.

Reading elasticity from slope, and assuming one elasticity holds at every price, are general errors covered on the price elasticity of demand page.

Sources

• Andreyeva T, Marple K, Marinello S, Moore TE, Powell LM. Outcomes following taxation of sugar-sweetened beverages: a systematic review and meta-analysis. JAMA Network Open. 2022;5(6):e2215276. doi:10.1001/jamanetworkopen.2022.15276. https://pmc.ncbi.nlm.nih.gov/articles/PMC9161017/
• Aron-Dine A, Einav L, Finkelstein A. The RAND Health Insurance Experiment, three decades later. Journal of Economic Perspectives. 2013;27(1):197-222. doi:10.1257/jep.27.1.197. https://pmc.ncbi.nlm.nih.gov/articles/PMC3943162/
• Danzon PM, Towse A. Differential pricing for pharmaceuticals: reconciling access, R&D and patents. International Journal of Health Care Finance and Economics. 2003;3(3):183-205. https://faculty.wharton.upenn.edu/wp-content/uploads/2014/10/differential-pricing_3.pdf
• Danzon PM, Towse AK, Mestre-Ferrandiz J. Value-based differential pricing: efficient prices for drugs in a global context. NBER Working Paper 18593. Cambridge, MA: National Bureau of Economic Research; 2012. doi:10.3386/w18593. https://www.nber.org/papers/w18593
• International Agency for Research on Cancer. Effectiveness of Tax and Price Policies for Tobacco Control. IARC Handbooks of Cancer Prevention, Volume 14. Lyon: IARC; 2011. https://publications.iarc.who.int/384
• Shapiro D, MacDonald D, Greenlaw SA. Principles of Microeconomics. 3rd ed. Houston: OpenStax; 2022. Chapter 5. https://openstax.org/books/principles-microeconomics-3e/pages/5-3-elasticity-and-pricing