definition of price elasticity of supply (PES)

Price Elasticity of Supply (PES) – Definition, Calculation & Economic Significance

1. Definition

The price elasticity of supply measures how responsive the quantity supplied of a good is to a change in its market price. It reflects the speed and ease with which producers can adjust output when prices move.

2. Formula & Calculation (Mid‑point / Arc Method)

Cambridge AS & A‑Level examinations require the mid‑point (arc) formula:

\[ \text{PES}= \frac{\displaystyle\frac{\Delta Q_s}{\frac{Q_{1}+Q_{2}}{2}}}{\displaystyle\frac{\Delta P}{\frac{P_{1}+P_{2}}{2}}} = \frac{\frac{Q_{2}-Q_{1}}{(Q_{1}+Q_{2})/2}}{\frac{P_{2}-P_{1}}{(P_{1}+P_{2})/2}} \]

• \(Q_{1}, P_{1}\) – initial quantity supplied and price
• \(Q_{2}, P_{2}\) – new quantity supplied and price

Worked Example

Suppose the price of wheat rises from £2.00 /kg to £2.50 /kg and the quantity supplied increases from 1 000 tonnes to 1 300 tonnes.

1. Calculate the changes:
   \(\Delta P = £2.50 - £2.00 = £0.50\)
   \(\Delta Q_s = 1 300 - 1 000 = 300\) tonnes
2. Find the mid‑points:
   \(\displaystyle \frac{P_{1}+P_{2}}{2}= \frac{£2.00+£2.50}{2}= £2.25\)
   \(\displaystyle \frac{Q_{1}+Q_{2}}{2}= \frac{1 000+1 300}{2}= 1 150\) tonnes
3. Insert into the formula:
   \[ \text{PES}= \frac{\frac{300}{1 150}}{\frac{0.50}{2.25}} = \frac{0.2609}{0.2222} \approx 1.17 \]
4. Interpretation: A 25 % rise in price (\(\frac{0.50}{2.25}\times100\)) leads to a 26 % rise in quantity supplied, giving an elastic supply (\(PES>1\)).

3. Sign Convention

The PES coefficient is always reported as a **positive** number. Whether the price moves up or down is indicated separately in the question or answer.

4. Interpretation of the Coefficient

• Elastic supply (PES > 1) – Quantity supplied changes by a larger percentage than price. Indicates that producers can adjust output quickly and with relative ease.
• Unit‑elastic supply (PES = 1) – Quantity supplied changes by exactly the same percentage as price.
• Inelastic supply (0 < PES < 1) – Quantity supplied changes by a smaller percentage than price. Shows that output adjustment is slower or more difficult.
• Perfectly inelastic supply (PES = 0) – No response of quantity supplied to price changes (vertical supply curve).
• Perfectly elastic supply (PES = ∞) – Producers are willing to supply any quantity at a given price; the supply curve is horizontal.

5. Determinants of PES (Exam‑style Examples)

1. Time period – In the long run firms can acquire new plant, hire labour, or change technology.
   Example: Car manufacturers can add a new production line over several years, making supply more elastic in the long run.
2. Availability of inputs – When key inputs are abundant and cheap, output can be increased rapidly.
   Example: A textile firm with ready access to cotton can boost output quickly when prices rise.
3. Production flexibility – Industries that use versatile technology can vary output with little cost.
   Example: Electronic assembly plants that can re‑program robots to produce different models.
4. Storage capacity – Goods that can be stored allow producers to respond to price changes by releasing inventories.
   Example: Wheat can be stockpiled, so farmers can increase market supply when prices surge.
5. Nature of the good – Perishable or long‑growing‑period goods limit how fast supply can adjust.
   Example: Fresh strawberries have a short harvesting window, giving a low PES in the short run.

6. Implications for Market Outcomes

Understanding PES helps predict how a shift in price affects equilibrium and welfare:

• A more elastic supply curve means that a given price change produces a larger change in quantity and a smaller change in equilibrium price. Conversely, an inelastic supply leads to a bigger price movement and a smaller quantity response.
• Because consumer surplus is the area above price and below the demand curve, a smaller price rise (elastic supply) preserves more consumer surplus, while a larger price rise (inelastic supply) erodes it.
• Producer surplus (area below price and above the supply curve) expands more when supply is elastic, since producers can increase output without a steep rise in marginal cost.

7. Classification Table

Elasticity Range	Supply Response	Typical Example (exam‑style)
PES > 1	Highly responsive – quantity changes by a larger % than price	Electronics produced on flexible assembly lines
PES = 1	Proportionate response – equal % change	Standard agricultural crops in the medium term
0 < PES < 1	Weakly responsive – quantity changes by a smaller % than price	Perishable fruit in the short run
PES = 0	No response to price	Land in a fixed location
PES = ∞	Perfectly elastic – horizontal supply curve	Electricity in a deregulated market with excess capacity

8. Suggested Diagram

Include a single graph with the following five supply curves labelled:

• Perfectly inelastic (vertical)
• Inelastic (steep upward)
• Unit‑elastic (45° line)
• Elastic (flatter upward)
• Perfectly elastic (horizontal)

Axes: Price (P) on the vertical axis, Quantity Supplied (Q_s) on the horizontal axis. Indicate the approximate PES value for each curve next to the line.