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Elasticity in Markets: Demand, Revenue, and Policy

A structured guide to measuring responsiveness in markets, calculating major elasticity measures, interpreting revenue effects, and applying elasticity to business decisions and public policy.

Measuring Responsiveness

compares percentage changes, so it measures proportional responsiveness rather than changes in raw units. This makes it possible to compare consumer or producer reactions across products and markets of different sizes.

Elasticity=% change in one variable% change in another variable\text{Elasticity}=\frac{\%\text{ change in one variable}}{\%\text{ change in another variable}}

Interpret the result as follows:

  • Elastic: Quantity changes by a greater percentage than the related variable.

  • Inelastic: Quantity changes by a smaller percentage than the related variable.

  • : Quantity and the related variable change by the same percentage.

  • Perfectly inelastic: Quantity does not change when the related variable changes; the curve is vertical.

  • Perfectly elastic: A very small change in the related variable produces a very large quantity response; the curve is horizontal.

is not the same as slope. Slope uses the units shown on a graph’s axes, whereas uses percentage changes. A straight-line demand curve can therefore have a constant slope but different values at different points.

Takeaway: Focus on proportional responsiveness. A larger numerical change is not automatically a more elastic response unless it is larger relative to the relevant percentage change.

describes how quantity demanded responds to a change in the good’s own price:

Ed=%ΔQd%ΔPE_d=\frac{\%\Delta Q_d}{\%\Delta P}

Demand is usually negative because price and quantity demanded move in opposite directions. Classification normally uses the absolute value:

  • If ∣Ed∣>1|E_d|>1, demand is elastic.

  • If ∣Ed∣<1|E_d|<1, demand is inelastic.

  • If ∣Ed∣=1|E_d|=1, demand is .

  • If Ed=0E_d=0, demand is perfectly inelastic.

  • If is extremely large or infinite, demand is perfectly elastic.

For example, if Ed=−2.0E_d=-2.0, a 1%1\% price increase is associated with an approximately 2%2\% decrease in quantity demanded. A 10%10\% price increase would imply an approximate 20%20\% quantity decrease for a sufficiently small change or a stable interval.

The main determinants of demand are:

  1. Availability of substitutes: More easily available alternatives make demand more elastic.

  2. Necessity versus luxury: Necessities tend to have more inelastic demand; luxuries tend to have more elastic demand.

  3. Budget share: Goods that take a large share of a consumer’s budget tend to have more elastic demand.

  4. Time: Demand often becomes more elastic as consumers gain time to adjust.

  5. Market definition: Demand for a narrowly defined product or brand is usually more elastic than demand for a broad category.

Takeaway: To predict , ask how easily buyers can change what, how much, or when they purchase.

Calculating with the

Use the when comparing two observations. It prevents the calculated percentage change from depending on which observation is treated as the starting point.

For quantity and price:

%ΔQ=Q2−Q1(Q2+Q1)/2×100\%\Delta Q=\frac{Q_2-Q_1}{(Q_2+Q_1)/2}\times 100
%ΔP=P2−P1(P2+P1)/2×100\%\Delta P=\frac{P_2-P_1}{(P_2+P_1)/2}\times 100

Then divide the quantity percentage change by the price percentage change.

Example: A coffee shop raises price from $4\$4 to $5\$5, while quantity demanded falls from 100100 cups to 8080 cups.

  1. Quantity changes by

80−100(80+100)/2=−2090≈−0.2222\frac{80-100}{(80+100)/2}=\frac{-20}{90}\approx -0.2222

or approximately −22.22%-22.22\%.

  1. Price changes by

5−4(5+4)/2=14.5≈0.2222\frac{5-4}{(5+4)/2}=\frac{1}{4.5}\approx 0.2222

or approximately 22.22%22.22\%.

  1. is

Ed=−22.22%22.22%=−1.00E_d=\frac{-22.22\%}{22.22\%}=-1.00

Demand is over this interval.

A reliable calculation sequence is:

  1. Identify old and new prices.

  2. Identify old and new quantities.

  3. Use the midpoint for each variable.

  4. Calculate both percentage changes.

  5. Divide quantity responsiveness by price responsiveness.

  6. Use the absolute value for classification, but retain the negative sign when interpreting the usual demand relationship.

Supply uses the same method, but quantity supplied is normally positively related to price:

Es=%ΔQs%ΔPE_s=\frac{\%\Delta Q_s}{\%\Delta P}

Supply is often more inelastic in the short run and more elastic in the long run. Spare capacity, mobile resources, inventories, and fewer production constraints make supply more responsive.

and

equals price multiplied by quantity sold:

TR=P×QTR=P\times Q

The connection between price changes and revenue follows from demand :

  • Elastic demand: A price increase decreases ; a price decrease increases .

  • Inelastic demand: A price increase increases ; a price decrease decreases .

  • Unit-elastic demand: A price change leaves approximately unchanged.

Suppose a venue sells 1,0001{,}000 tickets at $30\$30:

TR1=1,000×$30=$30,000TR_1=1{,}000\times \$30=\$30{,}000

If the price rises to $33\$33 and sales fall to 950950 tickets:

TR2=950×$33=$31,350TR_2=950\times \$33=\$31{,}350

Revenue rises even though fewer tickets are sold. The demand response was inelastic over this interval because the percentage decrease in quantity was smaller than the percentage increase in price.

For a linear demand curve, revenue is generally highest near the point where demand is . A firm should therefore consider both the current price and quantity and the of demand before changing price.

Takeaway: When demand is elastic, lowering price tends to raise revenue; when demand is inelastic, raising price tends to raise revenue.

Income and Related-Good Elasticities

Two additional measures connect demand to income and to prices of related goods.

Income response

is

EY=%ΔQd%ΔYE_Y=\frac{\%\Delta Q_d}{\%\Delta Y}

If income rises by 5%5\% and restaurant demand rises by 10%10\%, then

EY=10%5%=2E_Y=\frac{10\%}{5\%}=2

Restaurant meals are a normal, income-elastic good in this example. If income rises by 5%5\% while demand for an inexpensive generic product falls by 2%2\%, then

EY=−2%5%=−0.4E_Y=\frac{-2\%}{5\%}=-0.4

The product is an inferior good.

Response to a related good’s price

is

EAB=%ΔQA%ΔPBE_{AB}=\frac{\%\Delta Q_A}{\%\Delta P_B}

A positive result indicates substitutes. For example, if coffee’s price rises by 10%10\% and tea demand rises by 4%4\%,

Etea,coffee=4%10%=0.4E_{tea,coffee}=\frac{4\%}{10\%}=0.4

A negative result indicates complements. If smartphone prices rise by 8%8\% and phone-case demand falls by 4%4\%,

Ecases,smartphones=−4%8%=−0.5E_{cases,smartphones}=\frac{-4\%}{8\%}=-0.5

These measures help businesses forecast sales during expansions or recessions, identify competitors, and evaluate related-product strategies such as bundling.

Takeaway: Income identifies how demand changes with purchasing power; cross-price identifies relationships among goods.

in Public Policy and Markets

explains how markets respond to taxes, subsidies, and price controls.

Taxes

A per-unit tax creates a wedge between the price paid by buyers and the price received by sellers. The less elastic side generally bears the larger share of the economic burden. If demand is relatively inelastic and supply is relatively elastic, consumers bear most of the burden. If supply is relatively inelastic and demand is relatively elastic, producers bear more.

Tax revenue is calculated as

Tax revenue=tax per unit×quantity sold after the tax\text{Tax revenue}=\text{tax per unit}\times\text{quantity sold after the tax}

A product with inelastic demand may generate substantial revenue because quantity falls relatively little, although revenue also depends on the tax size and the resulting quantity reduction. The legal assignment of the tax does not by itself determine its economic incidence.

Subsidies

A subsidy lowers the effective cost of buying or producing a good. Depending on elasticities, its benefit may appear as a lower consumer price, a higher producer price, or a larger quantity exchanged. The less elastic side generally receives more of the economic benefit because it changes behavior less in response to price changes.

Price controls

A binding price ceiling below equilibrium creates a shortage because quantity demanded exceeds quantity supplied. A binding price floor above equilibrium creates a surplus because quantity supplied exceeds quantity demanded. affects the size of these unintended quantity responses: more elastic demand or supply generally produces a larger response to the controlled price.

Graphing checklist

  • Put price, wage, or another price variable on the vertical axis and quantity on the horizontal axis.

  • Draw ordinary demand downward sloping and supply upward sloping unless a special case is specified.

  • Mark the original equilibrium when analyzing a market change.

  • Distinguish a movement along a curve from a shift of a curve.

  • A change in the good’s own price causes movement along a curve.

  • Changes in income, tastes, related-good prices, input costs, technology, or taxes shift a curve.

  • For a tax, show the gap between the buyer price and the seller price.

  • Use steepness as a visual clue, but calculate when precision is required.

Takeaway: predicts not only quantity responses but also who gains, who bears costs, and how strongly policy changes affect market outcomes.