Introduction: Why One Number Runs the World
In 2014, Mexico introduced a one-peso-per-litre excise tax on sugar-sweetened beverages. Public health officials predicted a collapse in soda consumption. The beverage industry predicted almost none. Both sides were arguing, whether they said so or not, about a single number: the price elasticity of demand.
Elasticity is the most practically important concept in microeconomics, and the most frequently mishandled in AP and Cambridge A-Level exams. It is not a curve. It is not a graph. It is not a slope. It is a ratio of percentage changes — and understanding what that ratio actually measures separates students who memorise formulas from students who understand markets.
Price Elasticity of Demand (PED) — a unit-free measure of the responsiveness of quantity demanded to a change in price, expressed as the ratio of the percentage change in quantity to the percentage change in price.
1. What Price Elasticity of Demand Actually Measures
The concept originates with Alfred Marshall’s Principles of Economics (1890), where he introduced “elasticity of demand” as a way of describing how much a market yields under the pressure of a price change. Marshall’s insight was that the absolute change in quantity tells you almost nothing without knowing the scale of the market. A fall of 1,000 units means one thing for a corner shop and something entirely different for Amazon. Percentages make markets comparable.
The sign problem that costs students marks
Because demand curves slope downward, PED is almost always negative. Price rises, quantity falls. Yet economists routinely quote elasticities as positive numbers.
The convention is to take the absolute value. An elasticity reported as “0.4” for gasoline means the true value is −0.4.
Examiners accept either sign convention provided you are consistent and state which you are using. What loses marks is switching mid-answer, or writing “an elasticity of −0.4, which is inelastic because it is less than one” without noting you mean less than one in magnitude. Write “|PED| < 1” and the ambiguity disappears.
Classifying elasticity
| Value of |PED| | Classification | Interpretation | Real Example |
|---|---|---|---|
| 0 | Perfectly inelastic | Quantity does not respond at all | Insulin, short run |
| 0 < |PED| < 1 | Inelastic | Quantity responds proportionally less than price | Gasoline (≈0.3), cigarettes (≈0.4) |
| = 1 | Unit elastic | Quantity responds proportionally the same | Theoretical benchmark; TR is maximised |
| > 1 | Elastic | Quantity responds proportionally more | Restaurant meals, individual soda brands |
| ∞ | Perfectly elastic | Any price rise collapses demand to zero | Individual firm in perfect competition |
2. The Mathematics: Point and Arc Elasticity
Point elasticity
This decomposition explains a fact that confuses almost every student on first encounter: a straight-line demand curve does not have constant elasticity.
The term dQ/dP — the reciprocal of the slope — is constant along a linear demand curve. But P/Q is not. At high prices and low quantities, P/Q is large, so elasticity is large. At low prices and high quantities, P/Q is small, so elasticity is small.
On any downward-sloping straight-line demand curve, demand is elastic in the upper half, unit elastic exactly at the midpoint, and inelastic in the lower half. A steep curve is not “an inelastic curve” — it is a curve with an elastic region and an inelastic region, like every other.
Worked example
Let Q = 100 − 2P, so dQ/dP = −2.
| Price | Quantity | PED = −2 × (P/Q) | Classification | Total Revenue |
|---|---|---|---|---|
| 40 | 20 | −4.00 | Highly elastic | 800 |
| 30 | 40 | −1.50 | Elastic | 1,200 |
| 25 | 50 | −1.00 | Unit elastic | 1,250 (max) |
| 20 | 60 | −0.67 | Inelastic | 1,200 |
| 10 | 80 | −0.25 | Highly inelastic | 800 |
Total revenue peaks precisely at the unit-elastic midpoint. This is not coincidence — it is the mathematical link between elasticity and revenue.
Arc elasticity and the midpoint formula
When you have only two discrete price-quantity observations, point elasticity is ambiguous: do you use the starting price or the ending price as your base? The midpoint formula resolves this by averaging.
The midpoint formula gives the same answer whether you move from A to B or from B to A. Cambridge A-Level papers frequently supply two data points and expect the midpoint method. AP more commonly accepts either. Read the question.
3. Elasticity and Total Revenue
The relationship between elasticity and total revenue is the reason firms care about this concept at all.
- If demand is elastic (|PED| > 1), a price cut raises total revenue.
- If demand is inelastic (|PED| < 1), a price rise raises total revenue.
- If unit elastic, revenue is unchanged and is at its maximum.
Notice what MR = P(1 + 1/PED) implies. If |PED| < 1, then 1/PED < −1, and MR is negative.
A profit-maximising firm sets MR = MC, and marginal cost is never negative. Therefore no profit-maximising firm ever operates on the inelastic portion of its demand curve. A monopolist finding itself there can always raise price, sell less, spend less on production, and earn more — and will do so until it reaches the elastic region.
4. What Determines Elasticity? The Five Drivers
(a) Availability of close substitutes
The single most powerful determinant. Demand for Coca-Cola is elastic because Pepsi exists. Demand for carbonated soft drinks as a category is far less elastic, because the category as a whole has weaker substitutes. This distinction between brand-level and category-level elasticity is central to competition policy and to soda tax design — and it is the reason a soda tax works at all.
(b) Necessity versus luxury
Insulin is a necessity; a Caribbean cruise is not. Necessities exhibit inelastic demand because consumers reduce almost everything else before they reduce them.
(c) Share of income spent on the good
Salt costs a trivial fraction of a household budget. A doubling of the price of salt is barely noticed. A doubling of the price of rent is catastrophic. Goods absorbing a larger income share tend to have more elastic demand.
(d) Time horizon
The most consistently underrated determinant. In the short run, a driver facing higher petrol prices cannot change their car, their job, or their commute. In the long run, they can do all three.
Havranek, Irsova & Janda (2012), Energy Economics 34(1)
The authors conducted a meta-analysis of dozens of published gasoline demand studies. Their contribution was methodological: they corrected for publication bias — the tendency of journals to publish results that are statistically significant and of the expected sign.
What they found: after correction, the short-run price elasticity of gasoline demand is meaningfully closer to zero than the headline literature suggests. Long-run elasticities are substantially larger, but still smaller than commonly assumed.
Why it matters: if gasoline demand is more inelastic than believed, fuel taxes raise more revenue than expected and reduce emissions less than expected. The same policy is simultaneously a better fiscal instrument and a worse environmental one. This is a direct, quantitative policy implication of a parameter estimate.
(e) Definition of the market
The narrower the market, the more elastic the demand. Demand for “food” is nearly perfectly inelastic. Demand for “organic Fuji apples from one specific supermarket” is enormously elastic.
Q: A firm reports that a 10% price rise reduced its sales by 25%. Should it have raised the price?
A: |PED| = 25/10 = 2.5, elastic. Total revenue fell (0.9 × 0.75 = 0.675, a 32.5% decline). It should not have raised price — and if it is a profit-maximiser it was probably pricing correctly before.
5. Case Study One: Mexico’s Sugar Tax (2014–Present)
The policy: A one-peso-per-litre excise tax on sugar-sweetened beverages, roughly a 10% price increase. The first national soda tax of its scale.
The study: Colchero, Popkin, Rivera & Ng (2016), BMJ 352:h6704. Store purchase data across 53 Mexican cities, compared against a modelled counterfactual.
The finding: Purchases of taxed beverages fell relative to the counterfactual, with the decline growing over time — modest in early months, substantially larger by December 2014. Purchases of untaxed beverages, chiefly bottled water, rose.
Implied elasticity: roughly −0.6 for the first year, steeper thereafter. Inelastic.
Two consequences follow immediately, and they are the ones examiners want:
- The tax raises substantial revenue. Because quantity falls proportionally less than price rises, the tax base holds up.
- The consumption reduction is real but moderate. If policymakers expected soda consumption to halve, they misunderstood the elasticity.
Dubois, Griffith & O’Connell (2020), “How Well Targeted Are Soda Taxes?”, American Economic Review 110(11)
This paper is the most important refinement of the soda tax literature, and it complicates the textbook Pigouvian story considerably.
The argument: The welfare case for a soda tax requires that the people who reduce consumption most are the people whose consumption is most harmful. The authors show this need not hold. Price responsiveness and marginal health harm are separate characteristics of a household, and their correlation is an empirical question, not a theoretical guarantee.
Their finding: pass-through of the tax to consumers is incomplete and varies by retailer, and the households consuming the most sugar are not reliably the most price-responsive.
Why it matters: the standard Pigouvian formula (set the tax equal to marginal external damage) implicitly assumes a representative consumer. With heterogeneous consumers, the optimal tax depends on the joint distribution of elasticity and harm — an informational requirement no regulator has ever met.
6. Case Study Two: The UK Soft Drinks Industry Levy
The policy: Rather than taxing volume, the UK taxed sugar content above thresholds — a lower band above 5g/100ml, a higher band above 8g/100ml. Announced in 2016, implemented in 2018.
The study: Scarborough et al. (2020), PLOS Medicine 17(2):e1003025.
The finding: The dominant effect was not a fall in the quantity of drinks purchased. Consumers kept buying roughly as many bottles. The fall came in the sugar content of those drinks. Manufacturers reformulated en masse to drop below the thresholds. Total sugar purchased from soft drinks fell substantially even though volume barely moved.
The mechanism: supply-side response, not demand-side response.
When demand is inelastic, a tax on the quantity of a good is a blunt instrument. But a tax on the harmful attribute of the good bypasses the elasticity problem entirely, by inducing reformulation on the supply side.
A student who writes “demand for soft drinks is inelastic, therefore a tax will not reduce sugar consumption much” has produced a correct application of elasticity theory and an incorrect prediction about the world. That gap is exactly where evaluation marks live.
7. Case Study Three: Uber, Surge Pricing, and Big-Data Elasticity
The problem: Classical elasticity estimation is hard because you rarely observe price variation that is exogenous — unrelated to demand conditions. Prices usually move because demand moved.
The study: Cohen, Hahn, Hall, Levitt & Metcalfe (2016), NBER Working Paper 22627.
The design: Uber’s surge multiplier jumps discontinuously at an algorithmic threshold. Riders arriving just below and just above that threshold are essentially identical in every respect — except the price they face. This is a regression discontinuity design: causal identification, not correlation.
The finding: price elasticity of demand for UberX in the neighbourhood of −0.5. Inelastic. The authors used the traced-out demand curve to compute consumer surplus.
The methodological lesson is as important as the number. Elasticity estimates from the 2010s onward are vastly more credible than those from the 1970s, because the field learned to hunt for accidental randomisation rather than to assume it away.
8. Elasticity and Tax Incidence: Who Actually Pays?
This is the highest-yield application in both syllabi.
Tax Incidence — the distribution of the economic burden of a tax between buyers and sellers, which depends on relative elasticities rather than on who is legally required to remit the tax.
The burden falls more heavily on whichever side of the market is less elastic. Intuitively: the inelastic side cannot escape. If demand is perfectly inelastic, consumers bear the entire tax. If perfectly elastic, producers bear all of it. Cigarette taxes fall overwhelmingly on smokers precisely because nicotine demand is inelastic.
Chetty, Looney & Kroft (2009), “Salience and Taxation”, American Economic Review 99(4)
The experiment: The authors ran a field experiment in a grocery store, posting tax-inclusive prices on some products and leaving others with tax added only at the register. They also exploited variation in alcohol excise taxes (included in the shelf price) versus sales taxes (added at checkout).
The finding: Consumers respond substantially less to taxes that are not visible on the shelf tag. The same tax, differently displayed, produces a different behavioural response.
Why it matters: effective elasticity is partly a function of how a price is presented, not merely what it is. This is one of the earliest rigorous demonstrations that a parameter economists treated as structural is partly psychological. It reshaped public economics, and it means that a government can change the behavioural bite of a tax without changing its rate.
9. The Empirical Landscape: What Do We Actually Know?
Andreyeva, Long and Brownell (2010), in a systematic review in the American Journal of Public Health, synthesised the food demand literature. Their headline finding is that food price elasticities cluster in the inelastic range across virtually every category — but with meaningful variation. Soft drinks and food away from home sit toward the elastic end; eggs and staple cereals sit near the inelastic extreme.
Three broad regularities emerge from the modern literature:
- Category-level demand is nearly always inelastic; brand-level demand is nearly always elastic. This gap can span an order of magnitude.
- Long-run elasticities typically exceed short-run elasticities by a factor of two to four for durable-dependent goods such as fuel, energy and housing.
- Published elasticity estimates suffer from publication bias. Funnel-plot corrections consistently shrink estimated elasticities toward zero.
The theoretical framework underlying rigorous demand estimation is Deaton and Muellbauer’s Almost Ideal Demand System (American Economic Review, 1980), which remains the workhorse specification for estimating systems of own- and cross-price elasticities that are consistent with consumer theory — that is, which satisfy adding-up, homogeneity and Slutsky symmetry.
10. Beyond Price: The Other Elasticities
Income Elasticity of Demand (YED) = %ΔQ ÷ %ΔIncome. Positive for normal goods, negative for inferior goods, greater than one for luxuries.
Cross-Price Elasticity of Demand (XED) = %ΔQ of good A ÷ %ΔP of good B. Positive for substitutes, negative for complements. Competition authorities use XED to define the boundaries of a relevant market in merger cases.
Price Elasticity of Supply (PES) = %ΔQ supplied ÷ %ΔP. Depends on spare capacity, stock levels, factor mobility, and — again — time.
11. Exam Technique
- Know that a linear demand curve has varying elasticity; identify the unit-elastic midpoint.
- State and apply the total revenue test in one sentence.
- Connect elasticity to tax incidence with a labelled diagram showing the split of the tax wedge.
- Remember MR = P(1 + 1/PED) and its implication for monopoly pricing.
- Evaluation questions rarely reward the mechanical answer. For “Discuss whether a tax on sugary drinks will reduce obesity,” the elasticity point is your analysis. The reformulation channel, regressivity, substitution to untaxed sugar sources, and cross-border shopping are your evaluation.
- Always distinguish short run from long run explicitly.
- Cite a real example. Examiners consistently reward Mexico, the UK levy, or tobacco taxation over hypothetical numbers.
- Confusing elasticity with the slope of the demand curve. They are different objects.
- Calling a steep demand curve “inelastic” without reference to a point on the curve.
- Asserting that inelastic demand means “quantity does not change.” It means quantity changes proportionally less.
- Computing tax incidence using PED alone. The formula requires both PED and PES.
- Applying the point formula to two discrete observations without stating which base price you used.
Summary
Price elasticity of demand converts a qualitative claim — “people buy less when prices rise” — into a quantitative one that policy can act on. Its value determines whether a tax raises revenue or changes behaviour, whether a firm should cut prices or raise them, and who ultimately bears the cost of regulation.
The last decade of research has done two things to the concept. It has made estimation vastly more credible, through natural experiments and regression discontinuity designs. And it has complicated the concept, by showing that elasticity is not a fixed physical constant of a good but a parameter that depends on framing, salience, time horizon, and the availability of supply-side responses that classical analysis never contemplated.
Exercise 1 — Which Tax Design Is Superior?
The Mexican soda tax reduced beverage purchases by roughly 6% in its first year, implying inelastic demand. The UK levy barely reduced purchase volume at all, yet cut sugar consumption substantially through reformulation. Both are called “successful.”
Construct an argument for which policy design is superior, and specify precisely what empirical information you would need in order to settle the question. In your answer, consider whether “success” should be measured in sugar consumed, revenue raised, or welfare — and whether these three criteria can conflict.
📄 Read: Dubois, P., Griffith, R., & O’Connell, M. (2020). “How Well Targeted Are Soda Taxes?” American Economic Review, 110(11), 3661–3704. Pay particular attention to their treatment of heterogeneity in price responsiveness across households, and to their decomposition of the tax’s welfare effect into a corrective component and a distortionary component.
Exercise 2 — Is Elasticity a Property of the Good, or of the Choice Architecture?
Chetty, Looney and Kroft showed that consumers respond less to taxes that are not displayed prominently. If effective elasticity depends on how a price is presented, then a government could increase the behavioural impact of a tax without changing its rate, simply by changing its display.
Is elasticity, then, a property of the good, a property of the consumer, or a property of the choice architecture? What does your answer imply for the standard welfare analysis of taxation, which treats elasticity as an exogenous parameter — and for whether the “correct” elasticity for policy purposes is the one we observe or the one that would obtain under full attention?
📄 Read: Chetty, R., Looney, A., & Kroft, K. (2009). “Salience and Taxation: Theory and Evidence.” American Economic Review, 99(4), 1145–1177.
References
- Andreyeva, T., Long, M. W., & Brownell, K. D. (2010). The Impact of Food Prices on Consumption: A Systematic Review of Research on the Price Elasticity of Demand for Food. American Journal of Public Health, 100(2), 216–222.
- Chetty, R., Looney, A., & Kroft, K. (2009). Salience and Taxation: Theory and Evidence. American Economic Review, 99(4), 1145–1177.
- Cohen, P., Hahn, R., Hall, J., Levitt, S., & Metcalfe, R. (2016). Using Big Data to Estimate Consumer Surplus: The Case of Uber. NBER Working Paper No. 22627.
- Colchero, M. A., Popkin, B. M., Rivera, J. A., & Ng, S. W. (2016). Beverage purchases from stores in Mexico under the excise tax on sugar sweetened beverages: observational study. BMJ, 352, h6704.
- Deaton, A., & Muellbauer, J. (1980). An Almost Ideal Demand System. American Economic Review, 70(3), 312–326.
- Dubois, P., Griffith, R., & O’Connell, M. (2020). How Well Targeted Are Soda Taxes? American Economic Review, 110(11), 3661–3704.
- Havranek, T., Irsova, Z., & Janda, K. (2012). Demand for gasoline is more price-inelastic than commonly thought. Energy Economics, 34(1), 201–207.
- Marshall, A. (1890). Principles of Economics. London: Macmillan.
- Scarborough, P., Adhikari, V., Harrington, R. A., et al. (2020). Impact of the announcement and implementation of the UK Soft Drinks Industry Levy on sugar content, price, product size and number of available soft drinks in the UK, 2015–18. PLOS Medicine, 17(2), e1003025.