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.
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.
Price rises from \$10 to \$12 and quantity supplied rises from 100 to 130 units.
Average price \( \bar P = (10+12)/2 = 11\)
Average quantity \( \bar Q = (100+130)/2 = 115\)
% Δ P = \(\frac{12-10}{11}\times100 = 18.2\%\)
% Δ Qs = \(\frac{130-100}{115}\times100 = 26.1\%\)
PES = 26.1 % ÷ 18.2 % = 1.44 (rounded)
Since PES > 1, supply is elastic.
Price rises from \$20 to \$22 (a 10 % rise) and quantity supplied rises from 500 to 520 units.
Average quantity \(\bar Q = (500+520)/2 = 510\)
% Δ Qs = \(\frac{520-500}{510}\times100 = 3.9\%\)
Since PES < 1, supply is inelastic.
| 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. |
| 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. |
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