Students will be able to calculate and interpret the main elasticity measures (price, income, cross‑price and promotional) and to explain how these measures influence key business decisions such as pricing, product strategy, promotional budgeting, market entry and supply planning. They will also recognise the assumptions and limitations of elasticity analysis.
These are the four determinants required by the Cambridge syllabus. They are often examined separately.
| Elasticity Type | Formula (percentage change) | Formula (mid‑point / arc method) | Interpretation |
|---|---|---|---|
| Price Elasticity of Demand (PED) | $$E_{p}= \frac{\%\Delta Q_{d}}{\%\Delta P}= \frac{\Delta Q_{d}/Q_{d}}{\Delta P/P}$$ | $$E_{p}= \frac{\displaystyle\frac{Q_{2}-Q_{1}}{(Q_{1}+Q_{2})/2}}{\displaystyle\frac{P_{2}-P_{1}}{(P_{1}+P_{2})/2}}$$ | Responsiveness of quantity demanded to a change in price. |
| Income Elasticity of Demand (YED) | $$E_{y}= \frac{\%\Delta Q_{d}}{\%\Delta Y}= \frac{\Delta Q_{d}/Q_{d}}{\Delta Y/Y}$$ | $$E_{y}= \frac{\displaystyle\frac{Q_{2}-Q_{1}}{(Q_{1}+Q_{2})/2}}{\displaystyle\frac{Y_{2}-Y_{1}}{(Y_{1}+Y_{2})/2}}$$ | How demand varies with consumer income. |
| Cross‑Price Elasticity (XED) | $$E_{c}= \frac{\%\Delta Q_{d}^{A}}{\%\Delta P^{B}}= \frac{\Delta Q_{d}^{A}/Q_{d}^{A}}{\Delta P^{B}/P^{B}}$$ | $$E_{c}= \frac{\displaystyle\frac{Q_{A2}-Q_{A1}}{(Q_{A1}+Q_{A2})/2}}{\displaystyle\frac{P_{B2}-P_{B1}}{(P_{B1}+P_{B2})/2}}$$ | Relationship between two goods (substitutes or complements). |
| Promotional (Advertising) Elasticity (PAED) | $$E_{a}= \frac{\%\Delta Q_{d}}{\%\Delta A}= \frac{\Delta Q_{d}/Q_{d}}{\Delta A/A}$$ | $$E_{a}= \frac{\displaystyle\frac{Q_{2}-Q_{1}}{(Q_{1}+Q_{2})/2}}{\displaystyle\frac{A_{2}-A_{1}}{(A_{1}+A_{2})/2}}$$ | Effect of a change in advertising expenditure on quantity demanded. |
| Elasticity of Supply (ES) – optional | $$E_{s}= \frac{\%\Delta Q_{s}}{\%\Delta P}= \frac{\Delta Q_{s}/Q_{s}}{\Delta P/P}$$ | $$E_{s}= \frac{\displaystyle\frac{Q_{s2}-Q_{s1}}{(Q_{s1}+Q_{s2})/2}}{\displaystyle\frac{P_{2}-P_{1}}{(P_{1}+P_{2})/2}}$$ | Responsiveness of quantity supplied to a change in price. |
A company sells 10 000 units at $20 each. After a 10 % price cut the price falls to $18 and sales rise to 12 000 units. Calculate PED using the arc formula and state the revenue implication.
Solution:
$$ \begin{aligned} \%\Delta P_{\text{mid}} &= \frac{P_{2}-P_{1}}{(P_{1}+P_{2})/2}\times100 = \frac{18-20}{(20+18)/2}\times100 = \frac{-2}{19}\times100 \approx -10.53\%\\[4pt] \%\Delta Q_{\text{mid}} &= \frac{Q_{2}-Q_{1}}{(Q_{1}+Q_{2})/2}\times100 = \frac{12\,000-10\,000}{(10\,000+12\,000)/2}\times100 = \frac{2\,000}{11\,000}\times100 \approx 18.18\%\\[4pt] E_{p} &= \frac{18.18\%}{-10.53\%}\approx -1.73 \end{aligned} $$Interpretation: |Ep| = 1.73 > 1 → demand is elastic. The price reduction therefore increases total revenue.
Advertising expenditure rises from $50 k to $55 k (a 10 % increase). Sales increase from 8 000 to 8 800 units (also a 10 % increase). Calculate PAED.
$$ E_{a}= \frac{10\%}{10\%}=1.0 $$The demand for the product is unit‑elastic to advertising; further spending will not generate a proportionally larger rise in sales.
Elasticity measures are a quantitative input to the 4 Ps of the marketing mix:
In strategic planning, elasticity feeds into decisions about market entry, competitive positioning and capacity investment.
| Elasticity Measure | Typical Value | Strategic Implication |
|---|---|---|
| Price Elasticity (PED) | Elastic (|E| > 1) | Consider price cuts, promotions or product differentiation to boost total revenue. |
| Price Elasticity (PED) | Inelastic (|E| < 1) | Price increases can raise revenue with limited loss of volume. |
| Income Elasticity (YED) | Positive > 1 (luxury) | Target high‑income markets; premium branding. |
| Income Elasticity (YED) | Positive < 1 (necessity) | Stable demand; focus on cost‑efficiency. |
| Income Elasticity (YED) | Negative (inferior) | Anticipate decline as incomes rise; consider redesign or exit. |
| Cross‑Price Elasticity (XED) | Positive > 0 (substitutes) | Monitor competitor pricing; possible price competition. |
| Cross‑Price Elasticity (XED) | Negative (complements) | Bundle or co‑market with the complementary product. |
| Promotional Elasticity (PAED) | High (|E| > 1) | Advertising is effective; allocate larger budgets. |
| Promotional Elasticity (PAED) | Low (|E| < 1) | Focus on price or product features rather than ads. |
| Elasticity of Supply (ES) – optional | High | Flexible production; can respond quickly to price changes. |
| Elasticity of Supply (ES) – optional | Low | Plan capacity upgrades before anticipated price‑driven demand spikes. |
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