Price Elasticity of Supply (PES) – Cambridge IGCSE Economics (0455)
1. Definition
The price elasticity of supply measures how responsive the quantity supplied of a good is to a change in its price, ceteris paribus (all other factors remaining unchanged).
2. Formulae
Percentage‑change form
\[
\text{PES}= \frac{\%\;\text{change in quantity supplied}}{\%\;\text{change in price}}
\]
Algebraic (initial – new) form
\[
\text{PES}= \frac{\dfrac{Q_{2}-Q_{1}}{Q_{1}}}{\dfrac{P_{2}-P_{1}}{P_{1}}}
= \frac{(Q_{2}-Q_{1})\times P_{1}}{(P_{2}-P_{1})\times Q_{1}}
\]
Where:
- \(Q_{1}\) = initial quantity supplied
- \(Q_{2}\) = new quantity supplied
- \(P_{1}\) = initial price
- \(P_{2}\) = new price
3. Steps for Calculating PES
- Identify the initial and new price and quantity supplied.
- Find the changes: \(\Delta Q = Q_{2}-Q_{1}\) and \(\Delta P = P_{2}-P_{1}\).
- Calculate the percentage changes (multiply by 100):
- \(\%\Delta Q = \dfrac{\Delta Q}{Q_{1}}\times 100\)
- \(\%\Delta P = \dfrac{\Delta P}{P_{1}}\times 100\)
- Divide \(\%\Delta Q\) by \(\%\Delta P\) to obtain PES.
- Interpret the numeric result (see Section 4).
4. Interpretation of PES Values
| PES value |
Term used in the syllabus |
Supply response |
| 0 |
Perfectly inelastic |
Quantity supplied does not change, no matter how price changes (zero response). |
| 0 < PES < 1 |
Inelastic |
Quantity supplied changes proportionally less than price. |
| 1 |
Unit‑elastic |
Quantity supplied changes exactly proportionally with price. |
| PES > 1 |
Elastic |
Quantity supplied changes proportionally more than price. |
| \(\infty\) |
Perfectly elastic |
Any infinitesimally small rise in price causes an infinitely large increase in quantity supplied. |
5. Why PES Matters – Decision‑Making Contexts
For producers
- Elastic supply: output can be increased quickly when prices rise, making price‑increase strategies attractive.
- Inelastic supply: output cannot be expanded easily; firms are more likely to focus on cost‑reduction or product differentiation.
For governments
- If supply is inelastic, a tax will mainly burden producers because they cannot cut output much.
- If supply is elastic, a tax will cause a large fall in output, potentially harming employment in that sector.
6. Determinants of PES (as listed in the syllabus)
- Time period – short‑run vs. long‑run; longer periods allow firms to adjust plant size, technology and input stocks, raising PES.
- Availability of inputs – readily available raw materials or labour enable quicker output changes.
- Spare production capacity – firms operating below capacity can increase output with little extra cost.
- Mobility of factors of production – easy movement of labour and capital between industries raises PES.
- Nature of the good – perishable or highly specialised goods usually have lower PES.
7. Worked Example
Price of wheat rises from $200 / tonne to $250 / tonne. Quantity supplied rises from 1 000 tonnes to 1 300 tonnes.
| Variable |
Initial (1) |
New (2) |
| Price (\(P\)) |
$200 |
$250 |
| Quantity supplied (\(Q\)) |
1 000 tonnes |
1 300 tonnes |
Step‑by‑step calculation
\[
\Delta Q = 1\,300-1\,000 = 300 \quad\Rightarrow\quad
\%\Delta Q = \frac{300}{1\,000}\times 100 = 30\%
\]
\[
\Delta P = 250-200 = 50 \quad\Rightarrow\quad
\%\Delta P = \frac{50}{200}\times 100 = 25\%
\]
\[
\text{PES}= \frac{30\%}{25\%}=1.2
\]
Interpretation: PES = 1.2 > 1 → the supply of wheat is **elastic** in this price range.
8. Diagram – How to Draw & Label a PES Diagram
- Draw a standard upward‑sloping supply curve on axes (price \(P\) on the vertical axis, quantity \(Q\) on the horizontal axis).
- Mark two points on the curve:
- Point A \((P_{1},Q_{1})\) – the original price‑quantity pair.
- Point B \((P_{2},Q_{2})\) – the new price‑quantity pair after the price change.
- From each point draw a horizontal line to the \(Q\)-axis and a vertical line to the \(P\)-axis, forming two rectangles.
- Label the horizontal distances as \(\Delta Q = Q_{2}-Q_{1}\) and the vertical distances as \(\Delta P = P_{2}-P_{1}\).
- Write the PES formula beside the diagram and, if desired, substitute the numerical values to show the calculation.
- Caption example: “Illustration of PES = \(\frac{\%\Delta Q}{\%\Delta P}\) using points A and B on the supply curve.”
9. Evaluation (AO3) – Limitations of Using PES
Prompt: Discuss one limitation of using price elasticity of supply to predict producer behaviour.
Possible points to consider:
- Data reliability – accurate measurement of quantity supplied and price changes can be difficult, especially in informal markets.
- Assumption of ceteris paribus – in reality, other factors (technology, input prices, government policy) often change simultaneously, distorting the observed elasticity.
- Short‑run vs. long‑run – PES calculated for a short period may underestimate the true responsiveness once firms have time to adjust.
- Discrete vs. continuous changes – the formula assumes a small, continuous change; large jumps in price may give a misleading elasticity.
10. Quick Revision Questions
- Define price elasticity of supply.
- Explain why PES is usually higher in the long run than in the short run.
- Calculate PES for \(P_{1}=£50\), \(P_{2}=£55\), \(Q_{1}=200\) units, \(Q_{2}=230\) units. Show all steps.
- Interpret a PES of 0.4 for a particular product.
- Why would a government consider the PES of a good before imposing a tax? Provide one reason.
- Sketch a supply curve and label the elements needed to calculate PES (see Section 8).
- Discuss one limitation of using PES to predict how producers will respond to a price change.