Income Elasticity of Demand

Income Elasticity of Demand for Health Care

Income elasticity of demand tells how far the use of a good or service, or real spending on it, moves when income changes while prices stay fixed. In health economics the measure shows whether richer people and richer countries buy proportionally more health care, and so whether health spending takes a growing or shrinking share of income as incomes rise. The answer depends on the level of analysis, since insured individuals respond little to their own income while national spending tracks national income far more closely. The UK Office for Budget Responsibility (OBR) builds an income elasticity of 0.8 into its long-term health spending projections, and the measure also guides tobacco tax design.

Measuring how demand moves with income

The measure compares proportional changes, so the result has no units and can be compared across services counted in visits or pounds. For a smooth demand function the point elasticity is written as follows.

$$\eta = \frac{\partial Q}{\partial Y}\,\frac{Y}{Q} = \frac{\partial \ln Q}{\partial \ln Y}$$

where $\eta$ is the income elasticity of demand, $Q$ is the quantity demanded per person (or real spending per person), $Y$ is income per person, and the price of the good, the prices of other goods and preferences are held constant.

With only two observations, analysts usually take an arc elasticity, and the midpoint version gives the same answer whichever observation is treated as the start.

$$\eta_{arc} = \frac{(Q_2 - Q_1)/[(Q_1 + Q_2)/2]}{(Y_2 - Y_1)/[(Y_1 + Y_2)/2]}$$

where $Q_1$ and $Q_2$ are the quantities demanded at incomes $Y_1$ and $Y_2$. The OpenStax text describes the effect of a rise in income on a normal good as a rightward shift of the demand curve, with a larger shift the higher the elasticity. Income elasticity therefore measures a shift of demand, while the price elasticity of demand measures movement along the curve.

Studies of national health spending use real expenditure as $Q$. Costa-Font, Gemmill and Rubert, in their 2009 working paper, define the elasticity as the percentage change in health expenditures associated with a one per cent change in income. A spending elasticity mixes more services with dearer or better ones, so the result differs from an elasticity of visits.

Normal goods, inferior goods, necessities and luxuries

The sign and size of the elasticity sort goods into groups. The OpenStax text calls goods with a positive income elasticity normal goods and those with a negative one inferior goods. Costa-Font and colleagues add the split that drives the health care debate, with an elasticity below one marking a necessity and one above one marking a luxury.

The last column follows directly from the definition. If the price is fixed, the share of income spent on the good changes with income as shown below.

$$s = \frac{pQ}{Y}, \qquad \frac{\partial \ln s}{\partial \ln Y} = \eta - 1$$

where $s$ is the budget share, $p$ is the price and the other symbols are as above. The share rises only when the elasticity exceeds one. The OBR notes that with an elasticity below one, and leaving aside demography and other cost pressures, health spending would fall as a share of GDP. Because a household's spending shares must add up to the whole budget, the share-weighted average of the income elasticities of all goods equals one, so some goods must be necessities if others are luxuries.

The classification can change over time. The 2021 WHO technical manual on tobacco tax policy and administration reports that cigarettes have become an inferior good in the United States after being a normal one, while in many low and middle income countries tobacco use still increases with incomes. The manual concludes that taxes must raise real prices faster than real incomes if tobacco is to become less affordable, which ties the income elasticity to the design of a Pigouvian tax and to affordability.

Why individuals and nations give different answers

Much of the wide range of estimates comes from the level at which demand is measured. Getzen, in a 2000 paper, argues that health care is both a necessity and a luxury because the elasticity varies with the level of analysis. He reports that under insurance individual elasticities are typically near zero, while national elasticities are commonly above one. He attributes the apparent contradiction to studies that fail to separate variation within groups from variation between groups.

The pattern is clearest in a tax-financed or fully insured system. A patient's own income has little bearing on whether a hip replacement is covered, but national income sets the budget for the whole health system. Health insurance and public finance therefore weaken the link for individuals without removing it for nations.

The national figures themselves have been challenged. Costa-Font, Gemmill and Rubert tested the luxury good hypothesis, that the income elasticity exceeds one, by meta-regression, and reported in 2011 that publication bias exists and that the corrected estimates range from 0.4 to 0.8, which cast serious doubt on the hypothesis. Acemoglu, Finkelstein and Notowidigdo instrumented local area income in the Southern United States with global oil price changes between 1970 and 1990 interacted with local oil reserves. Their central estimate was 0.7, with an upper 95% confidence limit of 1.1, and they judged rising income unlikely to be a major driver of the rising health share of GDP, which the health spending as GDP share page covers.

Estimating an income elasticity from data

Most estimates come from a regression of the log of use or spending on the log of income. In the constant elasticity form the income coefficient is the elasticity itself.

$$\ln Q_i = \alpha + \eta \ln Y_i + \gamma' X_i + \varepsilon_i$$

where $Q_i$ is use or real spending for unit $i$ (a person, region or country), $Y_i$ is income, $X_i$ holds other determinants such as prices, insurance and health status, $\alpha$ and $\gamma$ are coefficients to be estimated, and $\varepsilon_i$ is the error term. A spreadsheet LINEST of LN(quantity) on LN(income) gives the estimate without controls.

Several choices move the estimate, starting with whether income is measured for one year or over a longer period. Many people use no care in a given year, and a log cannot be taken of zero, so analysts often model whether any care is used separately from how much. Omitting health status is a further problem, because illness can lower income and raise use of care at the same time. At the national level the OBR notes that health spending can also affect economic growth, which is why studies such as that of Acemoglu and colleagues rely on an instrumental variable for income rather than ordinary regression analysis alone.

Income effects in UK health spending projections

Fiscal projections use the income elasticity to turn assumed GDP growth into growth in health spending. In its July 2026 Fiscal risks and sustainability report the OBR keeps the assumptions of its detailed 2024 analysis, and its full decomposition of health spending growth is set out on the actuarial projection page. Income effects add 1.2 percentage points of annual real growth, based on an income elasticity of 0.8 that the OBR describes as in line with international evidence. The 2024 report tested elasticities of 0.5 and 1 against the baseline of around 0.8, and found health spending in 2073-74 lower by 3.3 per cent of GDP in the low case and higher by 2.2 per cent of GDP in the high case.

Worked example with dental visits and a twenty-year projection

All figures in this example are illustrative. A household survey compares adults in two income bands who pay the same GBP 60 for a private dental check-up and are assumed alike in age, health and cover. Mean household income is GBP 30,000 in the lower band and GBP 36,000 in the higher band, and private check-ups per adult per year are 1.50 and 1.68.

1. Simple percentage changes. Income is 20% higher (6,000 / 30,000 = 0.20) and visits are 12% higher (0.18 / 1.50 = 0.12), so the elasticity is 0.12 / 0.20 = 0.60.

2. Midpoint arc elasticity. The quantity change over the mean quantity is 0.18 / 1.59 = 0.1132, and the income change over the mean income is 6,000 / 33,000 = 0.1818, so $\eta_{arc}$ = 0.1132 / 0.1818 = 0.623.

3. Classify and check the budget share. An elasticity of about 0.62 marks dental check-ups as a normal good and a necessity in this sample. Spending per adult is 60 × 1.50 = GBP 90 in the lower band and 60 × 1.68 = GBP 100.80 in the higher band, which is 0.300% and 0.280% of income, so the share falls as income rises, as the formula for $s$ requires.

4. Project national spending. A country spends 10% of GDP on health, and real GDP per person grows by 2% a year for 20 years, with demography and other pressures set aside. With an elasticity of 0.8, health spending grows by 1.597% a year (1.02 to the power 0.8). After 20 years income has grown by a factor of 1.02 to the power 20, or 1.4859, and health spending by a factor of 1.02 to the power 16 (20 × 0.8), or 1.3728. The share becomes 10 × 1.3728 / 1.4859 = 9.24% of GDP. With an elasticity of 1.0 the share stays at 10%, and with 1.2 spending grows by a factor of 1.02 to the power 24, or 1.6084, so the share becomes 10 × 1.6084 / 1.4859 = 10.82%.

5. Interpretation. The survey estimate describes households facing a private price and says nothing about how a tax-financed service would grow with national income. The gap between 9.24% and 10.82% of GDP after 20 years shows why fiscal projections test more than one elasticity.

Related elasticities and measures

Income elasticity is one of three standard demand elasticities. Own-price responses sit on the price elasticity, elastic demand and inelastic demand pages, and responses to another product's price under cross-price elasticity.

A different income elasticity appears in benefit transfer. The income elasticity of the value of statistical life measures how willingness to pay for small risk reductions changes with income, not how much of a good is bought. Robinson, Hammitt and O'Keeffe report in a 2019 paper that comparisons among high-income populations often find the elasticity below one and comparisons across large income differences often find it above one.

The income elasticity of use is also distinct from income-related inequity in use, which is judged against need under horizontal equity and summarised by measures such as the concentration index.

Common misreadings and limits

The labels attached to elasticity values are technical terms. Several errors recur when they reach health policy writing.

1. Reading luxury as optional care. A luxury in this sense is any good whose demand rises faster than income, which can include effective treatment.
2. Moving between levels. An individual estimate near zero says little about national spending growth, and the reverse holds too.
3. Treating a before-and-after change as the elasticity. Prices, insurance terms and technology often change along with income, so a raw ratio of percentage changes is not a ceteris paribus estimate.
4. Assuming the value is fixed. The WHO manual reports that the income elasticity of tobacco demand varies across time, countries and demographic groups, and the OBR's 2024 report notes that most studies find health elasticities fall as countries grow richer.
5. Ignoring publication bias. Costa-Font and colleagues note that the general finding in earlier work was an elasticity above one, yet their correction for publication bias brings the estimate to between 0.4 and 0.8.

Sources

• Acemoglu D, Finkelstein A, Notowidigdo MJ. Income and health spending: evidence from oil price shocks. Review of Economics and Statistics. 2013;95(4):1079-1095. NBER Working Paper 14744, revised December 2011. https://www.nber.org/papers/w14744
• Costa-Font J, Gemmill M, Rubert G. Biases in the healthcare luxury good hypothesis?: a meta-regression analysis. Journal of the Royal Statistical Society Series A. 2011;174(1):95-107. https://doi.org/10.1111/j.1467-985X.2010.00653.x
• Costa-Font J, Gemmill M, Rubert G. Re-visiting the health care luxury good hypothesis: aggregation, precision, and publication biases? HEDG Working Paper 09/02, University of York; January 2009. https://www.york.ac.uk/media/economics/documents/herc/wp/09_02.pdf
• Getzen TE. Health care is an individual necessity and a national luxury: applying multilevel decision models to the analysis of health care expenditures. Journal of Health Economics. 2000;19(2):259-270. https://doi.org/10.1016/S0167-6296(99)00032-6
• Greenlaw SA, Shapiro D, MacDonald D. Principles of Economics 3e. OpenStax; 2022. Section 5.4. https://openstax.org/books/principles-economics-3e/pages/5-4-elasticity-in-areas-other-than-price
• Office for Budget Responsibility. Fiscal risks and sustainability. CP 1142; September 2024. Paragraphs 3.22, 3.23 and 3.41. https://obr.uk/docs/dlm_uploads/Fiscal-risks-and-sustainability-report-September-2024-1.pdf
• Office for Budget Responsibility. Fiscal risks and sustainability. July 2026. Paragraph 3.15. https://assets.publishing.service.gov.uk/media/6a4cb4c74889d85e75ab40e0/E03599617_OBR_FRS_2026_Accessible.pdf
• Robinson LA, Hammitt JK, O'Keeffe L. Valuing mortality risk reductions in global benefit-cost analysis. Journal of Benefit-Cost Analysis. 2019;10(S1):15-50. https://doi.org/10.1017/bca.2018.26
• World Health Organization. WHO technical manual on tobacco tax policy and administration. Geneva: World Health Organization; 2021. https://iris.who.int/server/api/core/bitstreams/89e10697-e083-47ca-8b96-3bb009158296/content