Calculating PES
Definition
Price elasticity of supply (PES): the percentage change in quantity supplied divided by the percentage change in the good's own price.
PES=% ΔQs% ΔP \text{PES} = \dfrac{\%\,\Delta Q_s}{\%\,\Delta P} PES=%ΔP%ΔQsThe PES Formula
% Δ=change in valueoriginal value×100% \%\,\Delta = \dfrac{\text{change in value}}{\text{original value}} \times 100\% %Δ=original valuechange in value×100%- Each percentage change is found as the change divided by the original value, multiplied by 100, so both figures share the same base and cancel to a pure number.
- The result is a coefficient that is normally positive, because quantity supplied and price move in the same direction along an upward-sloping supply curve.
Key Idea
- The % change in quantity supplied always goes on top of the fraction, and the % change in price underneath.
- Because it is a ratio of two percentages, PES carries no units.
Working Through It
- Work out the % change in quantity supplied.
- Work out the % change in price.
- Divide the first by the second to obtain the PES coefficient.
Example
- Case A: the price of a good rises from £20 to £22, a +10% rise, and quantity supplied rises from 500 to 600 units, a +20% rise.
- The coefficient is +2, so supply is elastic and output responds more than proportionately.
- Case B: the same +10% price rise lifts quantity supplied by only +5%.
- The coefficient is +0.5, so supply is inelastic and output responds less than proportionately.
Interpreting The Result
- A coefficient greater than 1 means supply is elastic, so quantity supplied changes by a larger percentage than price.
- A coefficient between 0 and 1 means supply is inelastic, so quantity supplied changes by a smaller percentage than price.
- The number carries little meaning until it is turned into this verdict of elastic or inelastic.
Limits Of The Figure
- The figure is only as reliable as the two data points it is calculated from.
- Its value depends on the time period over which it is measured, so the same market can yield different coefficients.
- It assumes other supply conditions stay constant, which may not hold in practice.
Exam technique
- Set out both percentage changes clearly before dividing.
- Keep the positive sign for a normal upward-sloping supply curve.
- Finish by stating whether the value is elastic or inelastic.
Common Mistake
- Do not invert the formula; it is the change in quantity supplied over the change in price, not the other way round.
- Do not stop at the number without interpreting what it means for supply.
Self review
- State the formula for PES.
- Calculate PES if a +10% price rise raises quantity supplied by +20%.
- Is a PES of 0.5 elastic or inelastic?
- Why does PES have no units?
