Price Elasticity of Supply (PES)
1. Definition (AO1)
The price elasticity of supply measures how responsive the quantity supplied of a good is to a change in its market price, ceteris paribus (all other factors held constant).
2. Formula (AO1)
\[
\text{PES}= \frac{\displaystyle\left|\%\Delta Q_{s}\right|}{\displaystyle\left|\%\Delta P\right|}
= \frac{\displaystyle\left|\frac{\Delta Q_{s}}{Q_{s0}}\right|}{\displaystyle\left|\frac{\Delta P}{P_{0}}\right|}
\]
- \(\Delta Q_{s}=Q_{s1}-Q_{s0}\) – change in quantity supplied
- \(Q_{s0}\) – initial quantity supplied
- \(\Delta P=P_{1}-P_{0}\) – change in price
- \(P_{0}\) – initial price
Because supply and price move in the same direction, the elasticity coefficient is always **positive** (the absolute‑value signs make this explicit).
Why the size of the coefficient matters (AO2)
- Large PES ( > 1 ): a given percentage rise in price generates a larger percentage increase in output. Firms can quickly expand production, earn higher revenue, and may choose to invest in extra capacity.
- Small PES ( < 1 ): output changes only a little when price changes. Firms face rigid capacities, so price movements have limited impact on revenue and on short‑run production decisions.
3. Interpretation of the Result (AO2)
| PES value | Interpretation |
|---|
| > 1 | Elastic supply – output responds more than proportionally to price. |
| = 1 | Unit‑elastic supply – percentage change in output equals percentage change in price. |
| < 1 | Inelastic supply – output responds less than proportionally to price. |
| = 0 | Perfectly inelastic – quantity supplied does not change when price changes. |
| = ∞ | Perfectly elastic – any tiny price change causes an infinite change in quantity supplied. |
4. Methods for Calculating PES (AO2)
4.1 Simple (base‑year) method
\[
\%\Delta Q_{s}= \frac{\Delta Q_{s}}{Q_{s0}}\times100,\qquad
\%\Delta P= \frac{\Delta P}{P_{0}}\times100
\]
4.2 Mid‑point (arc) method – preferred for large changes (AO2)
\[
\%\Delta Q_{s}= \frac{\Delta Q_{s}}{\frac{Q_{s0}+Q_{s1}}{2}}\times100,\qquad
\%\Delta P= \frac{\Delta P}{\frac{P_{0}+P_{1}}{2}}\times100
\]
4.3 Step‑by‑step procedure
- Record the initial price (\(P_{0}\)) and quantity supplied (\(Q_{s0}\)).
- Record the new price (\(P_{1}\)) and new quantity supplied (\(Q_{s1}\)).
- Calculate the changes: \(\Delta P=P_{1}-P_{0}\) and \(\Delta Q_{s}=Q_{s1}-Q_{s0}\).
- Choose a method (simple or midpoint) and compute the percentage changes.
- Insert the percentages into the PES formula.
- Interpret the numerical value using the table above and comment on the speed/ease of firm reaction.
5. Worked Example (Mid‑point Method)
Market: Wheat
| Period | Price (\$ per ton) | Quantity Supplied (thousand tons) |
|---|
| Initial | 200 | 500 |
| New | 240 | 560 |
- \(P_{0}=200,\;P_{1}=240\) \(Q_{s0}=500,\;Q_{s1}=560\)
- \(\Delta P=40,\;\Delta Q_{s}=60\)
- Mid‑point price \(= (200+240)/2 = 220\) Mid‑point quantity \(= (500+560)/2 = 530\)
- \(\%\Delta P = \dfrac{40}{220}\times100 = 18.2\%\)
- \(\%\Delta Q_{s}= \dfrac{60}{530}\times100 = 11.3\%\)
- \(\displaystyle \text{PES}= \frac{11.3\%}{18.2\%}=0.62\)
- Interpretation: PES = 0.62 < 1 → supply is **inelastic** over this price range. The firm can only adjust output slowly, so price changes have limited effect on revenue.
Diagram suggestion (AO3)
- Draw a relatively steep supply curve.
- Mark the initial point \((P_{0},Q_{0})\) and the new point \((P_{1},Q_{1})\).
- Show the horizontal and vertical percentage changes as arrows on the axes.
- Label the calculated PES on the diagram.
6. Factors Influencing the Elasticity of Supply (and the direction of impact) (AO2)
| Factor |
Effect on PES |
Implication for Speed of Firm Reaction |
| Time period |
Long‑run → higher PES (more flexibility to change plant size, adopt new tech). |
Faster adjustment in the long run. |
| Availability of inputs |
Readily available inputs → higher PES. |
Quickly increase output when price rises. |
| Mobility of factors of production |
Highly mobile labour & capital → higher PES. |
Rapid reallocation of resources. |
| Storage capability |
Goods that can be stored (e.g., wheat, oil) → higher PES. |
Firms can hold inventories and release them swiftly. |
| Complexity & length of production process |
Simple, short processes → higher PES; complex, long processes → lower PES. |
Simple products can be scaled up quickly; complex products adjust slowly. |
| Availability of raw materials (syllabus requirement) |
Seasonal or scarce raw materials → lower PES. |
Supply adjustments are slow or impossible until the next harvest/season. |
| Government regulations / taxes (syllabus requirement) |
Stringent regulations, licences, or high taxes → lower PES. |
Firms face legal or cost barriers that delay output changes. |
7. Implications for Firm Behaviour (AO2‑AO3)
- High PES (elastic supply)
- Firms can react quickly to price incentives.
- Likely to expand capacity, invest in flexible technology, or use inventory buffers.
- Revenue is highly sensitive to price changes, so price‑setting strategies matter.
- Low PES (inelastic supply)
- Production capacity is rigid; output cannot be altered much in the short run.
- Firms focus on cost‑minimisation rather than output expansion.
- Price changes mainly affect profit margins, not volume.
- Strategic decisions linked to the factors above:
- Invest in storage facilities when raw materials are seasonal.
- Lobby for deregulation or seek tax‑efficient structures to raise PES.
- Adopt modular production techniques to increase factor mobility.
8. Quick Revision Checklist (AO1‑AO3)
- Know the definition, the absolute‑value formula, and why the coefficient is always positive.
- Remember the interpretation thresholds (>1, =1, <1, =0, =∞).
- Be able to calculate PES using both the simple base‑year method and the midpoint (arc) method.
- Identify all six core factors plus the two syllabus‑required factors (raw‑material availability, government regulation) and state whether each raises or lowers PES and how it affects the speed of reaction.
- Explain the practical implications of a high or low PES for a firm’s short‑run and long‑run decisions (capacity, inventory, pricing, lobbying).
- Practice drawing a supply‑curve diagram, marking the two price‑quantity points, and annotating the percentage changes and the resulting PES.