Cambridge Syllabus Notes

The Allocation of Resources – Price Elasticity of Supply (PES)

Learning Objective

Define the price elasticity of supply, calculate it (including the Cambridge‑required midpoint method), interpret the resulting values and explain why PES is crucial for the efficient allocation of scarce resources.

1. Definition & Formula (AO1)

Definition: The price elasticity of supply measures how responsive the quantity of a good or service that producers are willing and able to supply is to a change in its market price.

Formula (plain‑text – the version used in paper exams):

PES = (% Δ Qs) ÷ (% Δ P)

Mid‑point (arc) formula – Cambridge exam technique:

PES = $\displaystyle \frac{\frac{Q_{2}-Q_{1}}{(Q_{1}+Q_{2})/2}}{\frac{P_{2}-P_{1}}{(P_{1}+P_{2})/2}}$

Note: The LaTeX version is shown for completeness but the plain‑text version above is the one you should write in the exam.

2. How to Calculate PES – Worked Examples (AO2)

Example 1 – Elastic Supply

Price rises from $10 to $12 and quantity supplied rises from 100 to 130 units.

Mid‑point values –
Average price $ \bar P = (10+12)/2 = 11$
Average quantity $ \bar Q = (100+130)/2 = 115$
Percentage changes (mid‑point method) –
% Δ P = $\frac{12-10}{11}\times100 = 18.2\%$
% Δ Qs = $\frac{130-100}{115}\times100 = 26.1\%$
Apply the formula –
PES = 26.1 % ÷ 18.2 % = **1.44** (rounded)

Since PES > 1, supply is elastic.

Example 2 – Inelastic Supply

Price rises from $20 to $22 (a 10 % rise) and quantity supplied rises from 500 to 520 units.

Average price $\bar P = (20+22)/2 = 21$
Average quantity $\bar Q = (500+520)/2 = 510$
% Δ P = $\frac{22-20}{21}\times100 = 9.5\%$
% Δ Qs = $\frac{520-500}{510}\times100 = 3.9\%$
PES = 3.9 % ÷ 9.5 % = **0.41** (rounded)

Since PES < 1, supply is inelastic.

3. Interpreting PES Values (AO1/AO2)

Value (or range)	Elasticity description	Typical supply‑curve shape
PES > 1	Elastic supply – quantity supplied changes proportionally more than price.	Flatter than 45° (relatively horizontal).
PES = 1	Unitary elastic supply – quantity changes by the same proportion as price.	45° line through the origin.
0 < PES < 1	Inelastic supply – quantity changes proportionally less than price.	Steeper than 45° but still upward sloping.
PES = 0	Perfectly inelastic supply – quantity supplied does not respond to price.	Vertical line.
PES = ∞	Perfectly elastic supply – producers will supply any quantity at a given price but none at any other price.	Horizontal line.

4. Determinants of PES (Cambridge phrasing)

Determinant	Effect on elasticity	Why it matters
Time horizon	Long‑run → higher elasticity	Firms can adjust plant size, hire labour, or adopt new technology.
Availability of inputs	Abundant inputs → higher elasticity	Raw materials, labour or capital are easy to obtain, so output can be expanded quickly.
Spare (unused) capacity	More spare capacity → higher elasticity	Firms operating below full capacity can increase output with little extra cost.
Mobility of factors of production	Greater mobility → higher elasticity	Labour and capital can move between industries, allowing rapid adjustments.
Nature of the good	Perishable or seasonal goods → lower elasticity	Cannot be stored; output cannot be expanded quickly.
Storage possibilities	Easy storage → higher elasticity	Producers can stock‑pile and smooth output over time.
Technology & production methods	Flexible, modern technology → higher elasticity	Scale‑up or scale‑down is quicker and cheaper.
Number of firms in the market	Many firms → higher elasticity	Industry as a whole can adjust output more readily.

5. Why PES Matters for Resource Allocation

Predicts how quantity supplied will respond to price changes caused by taxes, subsidies, price floors or ceilings.
Helps evaluate the likely size of surpluses or shortages after government intervention.
Guides firms in investment decisions – high elasticity signals flexibility, low elasticity signals the need for long‑term contracts or inventory buffers.
Informs policymakers where to allocate scarce inputs (labour, capital) to achieve the greatest output response.

Suggested diagram: three supply curves on the same axes (price on the vertical axis, quantity on the horizontal). Show a vertical line (perfectly inelastic), a 45° line (unitary elastic) and a horizontal line (perfectly elastic). Label each curve.

Definition of PES