Calculating and Interpreting Elasticity

Using the starting value as denominator gives different answers for increases and decreases. The midpoint method uses the average of both values:

$\%\Delta Q=\frac{Q_2-Q_1}{(Q_1+Q_2)/2}\times100\%$

Calculate price change similarly, then divide the absolute quantity percentage change by the price percentage change.

A complete worked calculation

Let price rise from 20 to 30 and quantity fall from 100 to 60. Average price is 25 and average quantity is 80:

$\%\Delta P=\frac{10}{25}\times100\%=40\%,\qquad \%\Delta Q_d=\frac{-40}{80}\times100\%=-50\%$

Thus $E_d=|-50\%/40\%|=1.25$, elastic over this interval. Reversing direction gives the same averages and result.

A complete interpretation names the value, classification, and context: “Between prices 20 and 30, a 1% price change is associated with about a 1.25% opposite quantity change.” Common errors are inconsistent bases, forgetting absolute value, writing 125 instead of 1.25, equating slope with elasticity, or claiming causality from uncontrolled observations.

If price rises from 8 to 12 while quantity falls from 60 to 40, both midpoint changes are 40%, so elasticity is 1. An interpretation should name the object, direction, and relative size: “Demand is unit elastic over this interval; quantity changes by the same percentage as price.”

Demand elasticity is normally reported in absolute value. The negative sign records the law of demand, not a negative degree of responsiveness.