Price Elasticity: Percentage Changes, Midpoint and Revenue

Use midpoint for two endpoints unless another method is specified.

Choose a Percentage-Response Coefficient

E_d=%Δ Q_d/%Δ P and E_s=%Δ Q_s/%Δ P. Cross-price elasticity changes the numerator to demand for X and denominator to price of Y. Income elasticity changes the denominator to income. The sign identifies substitutes, complements, normal goods, or inferior goods. The magnitude of own-price elasticity classifies responsiveness.

The midpoint percentage change is (new-old)/[(new+old)/2]. Keep signs through calculation, then use absolute value only when classifying price elasticity of demand.

Elasticity measures responsiveness independently of the units used to measure price and quantity. Dividing raw changes would make a result depend on whether output is counted in individual items or thousands. Percentage changes solve that problem. For demand, E_d=(%Δ Q_d)/(%Δ P). Its sign is normally negative, while classification commonly uses the absolute value.

Use the Same Midpoint Bases in Either Direction

When a question gives two endpoints and no base is privileged, use the midpoint method. If price rises from $8 to $12 and quantity falls from 60 to 40, the price change is 4/10=40% and the quantity change is -20/50=-40%. Elasticity is -1, or unit elastic in magnitude. Using 8 as the price base and 60 as the quantity base would produce a different answer depending on direction.

Interpret the Sign and Size

Connect Elasticity to Total Revenue

Total revenue supplies a powerful check. Along a demand curve, if demand is elastic, a price decrease raises TR because the quantity percentage gain dominates. If demand is inelastic, the same price decrease lowers TR. At unit elasticity, the two percentage effects offset locally. This relationship concerns revenue, not profit. Cost may change as output changes.

Explain Why Responsiveness Differs

Determinants explain why coefficients differ. Demand is generally more elastic with close substitutes, a narrower product definition, a larger budget share, luxury status, and more time to adjust. Supply is more elastic when firms have spare capacity, storable inventory, mobile inputs, and a longer adjustment horizon. These are tendencies, not arithmetic substitutes for data.

Relate Elasticity to the Tax Burden

In the basic competitive per-unit-tax model, elasticity helps predict tax incidence. The less elastic side changes quantity less and bears more of the economic burden, regardless of which side legally remits the tax. Perfectly inelastic demand can bear the entire burden in the basic model. Perfectly elastic demand cannot tolerate a price increase.

Name the Response Before Dividing

Always state the interpretation: “An elasticity magnitude of 1.5 means quantity demanded changes by about 1.5 percent for a 1-percent price change around this point.” A bare 1.5 is incomplete. Slope uses units and remains constant on a straight demand line; elasticity can vary along that same line.

Use the wording of the question to select the correct coefficient. If the numerator is a change in quantity demanded of one good and the denominator is that good’s own price, calculate own-price demand elasticity. If the denominator is income, calculate income elasticity. If it is another good’s price, calculate cross-price elasticity. A problem may supply several percentage changes precisely to test this choice. Label the numerator and denominator before dividing, and preserve the sign until you have interpreted the relationship.

Calculate Point Elasticity from an Equation

For point elasticity at positive price and quantity, differentiate or use the given slope and multiply by the level ratio: E_d=(dQ/dP)(P/Q). The slope component alone is not elasticity. For example, if Q=100-2P, then dQ/dP=-2, but elasticity changes with the point because P/Q changes. At P=20, Q=60 and E_d=-2(20/60)=-2/3, so demand is inelastic there. At P=40, Q=20 and E_d=-4, so it is elastic even though the line’s slope is unchanged.

Distinguish Curve Shape, Slope and Elasticity

Extreme cases are best understood through behavior. Perfectly inelastic demand is vertical: quantity does not respond, so the elasticity magnitude is zero. Perfectly elastic demand is horizontal: even a tiny price increase causes buyers to leave the seller, so the magnitude is effectively infinite. These endpoints help check graphs, but most economics exam questions concern finite responses and ask you to compare magnitudes rather than memorize labels alone.

Do not confuse elasticity with the slope of a line. Slope is Δ P/Δ Q or Δ Q/Δ P with physical units, depending on graph convention. Elasticity uses percentage changes and is unit-free. An ordinary downward-sloping straight demand line with positive price and quantity intercepts has constant slope but changing elasticity: it is elastic near the high-price, low-quantity end and inelastic near the low-price, high-quantity end. At the midpoint it is unit elastic. This distinction explains why one visual line can support different total-revenue responses at different points.

Check the Method and the Market Assumptions

OpenStax’s elasticity calculation section explains the midpoint method and the usual magnitude-based classification of own-price demand. If a question already supplies percentage changes, use their stated common basis rather than silently replacing them with raw price or quantity changes.

The extreme-case and constant-elasticity section distinguishes vertical, horizontal and constant-unit-elastic relationships. A demand curve that is unit elastic everywhere is curved; it is different from a straight demand line that is unit elastic at one point.

The income and cross-price definitions change the denominator to the relevant determinant. Hold other determinants fixed when interpreting a response. The pricing and tax-incidence section connects elasticity to revenue and burden-sharing under the stated model; neither calculation by itself gives profit.

Keep Income and Cross-Price Responses Separate

Consider two independent hypothetical changes for city shuttle rides, with other determinants held fixed in each. An 8% income increase reduces rides by 4%. In a separate comparison, a 10% increase in parking prices raises shuttle rides by 6%. Which coefficients do these data identify?

Try Three Elasticity and Revenue Questions

Connect Responsiveness to Market Changes

Check units and economic interpretations, distinguish movements along demand from shifts, and separate revenue from profit. Continue through the CLEP Microeconomics learning hub.