Why is price elasticity of demand negative but reported as positive

The price elasticity of demand (PED) is defined as the percentage change in quantity demanded divided by the percentage change in price: $\varepsilon = \frac{\%\Delta Q}{\%\Delta P}$. Since the law of demand states that quantity falls when price rises, $\%\Delta Q$ and $\%\Delta P$ have opposite signs, making $\varepsilon$ negative. Economists care about how responsive demand is, not the direction, so they report the absolute value.

Why the formula gives a negative sign

When price increases by 10 % and quantity falls by 20 %, the calculation is $\varepsilon = \frac{-20\%}{+10\%} = -2$. The negative sign tells you that the relationship is inverse, but the magnitude 2 tells you that a 1 % price rise cuts demand by 2 %. In most analyses the direction is already known, so the sign is dropped.

Key points to remember

• Demand falls when price rises, giving opposite‑sign percentage changes
• Elasticity measures magnitude of response
• Reporting uses the absolute value to simplify comparison

How to report elasticity as a positive number

1. 1Compute the raw elasticity using the percentage‑change formula
2. 2Take the absolute value of the result
3. 3State the value without a sign, e.g., "elasticity = 2"

Sample calculations

Worked example: Suppose a coffee shop raises the price of a latte from $3.00 to $3.30, a 10 % increase. Sales drop from 200 cups per day to 160 cups, a 20 % decrease. The raw elasticity is $\varepsilon = \frac{-20\%}{+10\%} = -2$. Taking the absolute value gives a reported elasticity of 2, indicating that demand is relatively elastic.