Keep the sign, then classify the magnitude.
PED = percentage change in quantity demanded / percentage change in own price, ceteris paribus. Ordinary downward-sloping demand gives a negative signed PED; use its absolute value to classify responsiveness. A magnitude above one is elastic, between zero and one is inelastic, and equal to one is unit elastic. When two price-quantity observations are supplied, state how percentages are calculated. This chapter uses midpoint percentages for its two-point examples: change divided by the average of the initial and final values, multiplied by 100. If a question specifies another method or supplies percentages, follow that information.
- Formula
- PED = percentage change in quantity demanded / percentage change in own price.
- Classification
- Magnitude means the number ignoring its sign. Above 1 is elastic: the quantity percentage response is larger than the price change. Between 0 and 1 is inelastic: it is smaller. At 1, the percentages are equal.
- Method
- Use the given percentages or stated method. Our two-point examples use midpoint percentages: divide each change by the average of its old and new values, then multiply by 100.
Percentage methods
Original base
The base is the value you compare the change with. With an original base, percentage change = (new - original) / original x 100. Reversing the comparison can give a different estimate because the starting value changes.
Midpoint
The midpoint base is the average of the two values: percentage change = (new - original) / ((new + original)/2) x 100. Use the same method for quantity and price.
Interpretation
The coefficient is the elasticity number you calculate. An interval is the range between the two observations. The result describes responsiveness over that range, not a number of units or every point on the curve.
Zero denominator
No price change does not provide a finite PED from a raw ratio. Perfectly elastic demand is a theoretical limiting case, not permission to divide by zero in data.
| Magnitude | Description | Quantity response |
|---|---|---|
| 0 | Perfectly inelastic | No response |
| Between 0 and 1 | Inelastic | Less than proportionate |
| 1 | Unit elastic | Proportionate under the stated local/interval measure |
| Above 1 | Elastic | More than proportionate |
| Infinite limiting case | Perfectly elastic | Horizontal demand at the specified price in the model |
Worked example: A two-point calculation
On one unchanged demand curve, price rises from $10 to $12 and weekly quantity demanded falls from 100 to 80. Use midpoint percentages.
- The quantity change is -20 and the average quantity is 90. Percentage quantity change = (-20/90) x 100, approximately -22.22%.
- The price change is $2 and the average price is $11. Percentage price change = (2/11) x 100, approximately 18.18%.
- PED = -22.22/18.18, approximately -1.22. Its magnitude exceeds one, so demand is elastic over this interval.
- The estimate is unit-free and applies to the specified interval. It does not mean sales fell by 1.22 units, and it need not describe every point on the demand curve.
Watch out for this
A PED of -2 is inelastic because -2 is less than 1.
Use the absolute magnitude for classification. A magnitude of 2 indicates a more than proportionate quantity response.
Check your understanding
A question gives an own-price rise of 8% and a quantity-demanded fall of 20%, ceteris paribus. What is PED?
- -0.4; inelastic.
- -2.5; elastic.
- +2.5; elastic.