Elasticity uses percentage changes

Use midpoint when two endpoints are supplied.

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.

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.

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.

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.

Elasticity also predicts 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.

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 and encourages confusion with slope, which uses units and can vary along a linear demand curve.

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.

For a point elasticity from equations, 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.

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. A straight-line demand curve 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.