Distinguish elasticity from slope and from a percentage change

These three ideas answer different questions.

Slope uses changes in the original units, such as dollars per ticket. Elasticity uses percentage changes and therefore has no unit. A 20 percent increase in quantity is not an elasticity until it is divided by the percentage change in the causal variable. If quantity rises 20 percent after price falls 10 percent, the price-elasticity magnitude is 2, not 20 and not 10.

Write the three calculations separately: slope=(Δ P)/(Δ Q), %Δ Q=(Δ Q)/(base Q)×100, E=(%Δ Q)/(%Δ P). They can use the same endpoints but answer different questions. Slope describes the graph’s numerical rate in axis units. Percentage change describes one variable relative to a base. Elasticity compares two relative changes.

The distinction matters because changing units changes slope but does not change elasticity. Measuring quantity in individual bottles instead of cases makes a demand curve’s numerical slope look different, yet buyer responsiveness is unchanged. On a straight-line demand curve, slope is constant while elasticity varies because the same absolute changes represent different percentages at different points. Near the high-price, low-quantity end, a quantity change is large relative to quantity, so demand is elastic. Near the low-price, high-quantity end, the same change is small relative to quantity, so demand is inelastic.

Suppose a curve’s quantity unit changes from cases to bottles, with 12 bottles per case. A change of one case becomes 12 bottles, so a slope stated as dollars per case becomes one-twelfth as many dollars per bottle. The buyers’ behavior did not change. Both percentage quantity changes use proportional bases and therefore give the same elasticity.

Visual steepness can also be altered by stretching an axis. The same data can look steep on a narrow quantity scale and flat on a wide one. Only a special comparison with identical axis units and scales permits a visual slope judgment, and even then slope is not elasticity. Use numbers or stated responsiveness.

Three correct numbers with different meanings

Price falls from $50 to $45 and quantity rises from 100 to 120. The raw quantity change is 20 units. Its midpoint percentage change is 20/110≈18.2%. The price change magnitude is 5/47.5≈10.5%, so elasticity is about 1.73. Choosing 20, 18.2, or 1.73 depends on whether the stem asks for a change, a percentage change, or elasticity.

Along a straight-line demand curve, the midpoint is unit elastic and total revenue is maximized there. Above it, demand is elastic. Lowering price raises revenue. Below it, demand is inelastic. Lowering price reduces revenue. This result connects elasticity, linear geometry, and revenue without treating slope as the classification.

When choices are numerical, inspect units. A slope may be dollars per unit. A percentage change carries percent. Elasticity is unit-free. An option with the wrong unit answers a different question even if it came from the same two data points.

Use one final diagnostic before choosing: ask what the denominator represents. A slope divides one change in original units by another. A percentage change divides by a reference level. An elasticity divides one percentage response by another percentage change. Writing that denominator in words usually exposes an option that used the right numbers for the wrong calculation.

Avoid the necessity shortcut

Necessities tend to have inelastic demand, but elasticity depends on available substitutes, market definition, time, and budget share. Use the full evidence in the stem rather than one label.