the limitations of the concept of elasticity in its various forms

8.1 Marketing Analysis – Elasticity (Limitations)

Learning Objectives

• Define the four core elasticities (PED, XED, YED, PES) and the promotional elasticity of demand (PE‑promo).
• Calculate each elasticity using the standard percentage‑change formula.
• Interpret the sign and magnitude (elastic, inelastic, unit‑elastic; substitutes/complements; normal/inferior; luxury/necessity).
• Explain how each elasticity influences the four Ps of marketing (Product, Price, Promotion, Place).
• Identify the key limitations of elasticity analysis and suggest ways to mitigate them.

1. Core Elasticities – Definitions, Formulae & Interpretation

Elasticity	Definition (ceteris paribus)	Standard Formula	Sign & Typical Interpretation
Price Elasticity of Demand (PED)	Percentage change in quantity demanded resulting from a 1 % change in the product’s own price.	\[ \text{PED}= \frac{\%\Delta Q_{d}}{\%\Delta P} =\frac{\frac{Q_{2}-Q_{1}}{Q_{1}}}{\frac{P_{2}-P_{1}}{P_{1}}} \]	Negative for normal goods. |E| > 1 → elastic; |E| < 1 → inelastic; |E| = 1 → unit‑elastic.
Cross‑Price Elasticity of Demand (XED)	Percentage change in quantity demanded of good A when the price of related good B changes by 1 %.	\[ \text{XED}= \frac{\%\Delta Q_{dA}}{\%\Delta P_{B}} =\frac{\frac{Q_{A2}-Q_{A1}}{Q_{A1}}}{\frac{P_{B2}-P_{B1}}{P_{B1}}} \]	Positive → substitutes; Negative → complements; magnitude shows strength of the relationship.
Income Elasticity of Demand (YED)	Percentage change in quantity demanded resulting from a 1 % change in consumer income.	\[ \text{YED}= \frac{\%\Delta Q_{d}}{\%\Delta Y} =\frac{\frac{Q_{2}-Q_{1}}{Q_{1}}}{\frac{Y_{2}-Y_{1}}{Y_{1}}} \]	Positive > 0 → normal goods (luxury if >1, necessity if <1); Negative → inferior goods.
Price Elasticity of Supply (PES)	Percentage change in quantity supplied resulting from a 1 % change in the product’s own price.	\[ \text{PES}= \frac{\%\Delta Q_{s}}{\%\Delta P} =\frac{\frac{Q_{s2}-Q_{s1}}{Q_{s1}}}{\frac{P_{2}-P_{1}}{P_{1}}} \]	Positive. |E| > 1 → elastic supply (quick response); |E| < 1 → inelastic supply (capacity constraints).
Promotional Elasticity of Demand (PE‑promo)	Percentage change in quantity demanded resulting from a 1 % change in promotional expenditure (advertising, sales‑promotion, etc.).	\[ \text{PE‑promo}= \frac{\%\Delta Q_{d}}{\%\Delta A} =\frac{\frac{Q_{2}-Q_{1}}{Q_{1}}}{\frac{A_{2}-A_{1}}{A_{1}}} \]	Positive. Large values indicate that demand is highly responsive to advertising spend; small values suggest diminishing returns.

2. Worked Calculations

2.1 Price Elasticity of Demand (PED)

Price rises from £10 to £12; quantity demanded falls from 1 000 to 800 units.

\[ \text{PED}= \frac{\frac{800-1000}{1000}}{\frac{12-10}{10}} = \frac{-0.20}{0.20}= -1.0 \]

Interpretation: |PED| = 1 → unit‑elastic for this interval. A further price rise could move the curve into a more elastic region (flatter) or an inelastic region (steeper) depending on consumer preferences.

2.2 Cross‑Price Elasticity (XED)

Tea price rises 20 % (from £2.00 to £2.40) and coffee demand rises 12 % (500 → 560 cups).

\[ \text{XED}= \frac{+12\%}{+20\%}=+0.60 \]

Interpretation: Positive → coffee and tea are substitutes, but the magnitude (0.60) shows a relatively weak substitution effect.

2.3 Income Elasticity (YED)

Disposable income rises 10 % (£5 000 → £5 500); smartphone demand rises 30 % (20 000 → 26 000 units).

\[ \text{YED}= \frac{+30\%}{+10\%}=+3.0 \]

Interpretation: YED > 1 → smartphones are a luxury good in this market; demand is highly responsive to income changes.

2.4 Price Elasticity of Supply (PES)

Wheat price rises 10 % (£150 → £165); output rises from 1 000 t to 1 050 t (5 %).

\[ \text{PES}= \frac{+5\%}{+10\%}=0.5 \]

Interpretation: PES < 1 → supply is relatively inelastic in the short run because planting cycles limit rapid output changes.

2.5 Promotional Elasticity (PE‑promo)

Advertising spend increases from £20 000 to £25 000 (25 %). Quantity sold rises from 8 000 to 9 600 units (20 %).

\[ \text{PE‑promo}= \frac{+20\%}{+25\%}=0.80 \]

Interpretation: A PE‑promo of 0.8 indicates a moderate response to advertising; a further increase in spend would generate proportionally smaller sales gains.

3. Implications for the Four Ps of Marketing

Elasticity	Product	Price	Promotion	Place (Distribution)
PED	Product differentiation can shift the demand curve, making it more inelastic.	Elastic demand → price cuts raise total revenue; Inelastic demand → price rises raise revenue.	When demand is elastic, promotional discounts are effective; when inelastic, price‑based promotions have limited impact.	Highly elastic products often require wider distribution to capture price‑sensitive shoppers.
XED	Designing product lines to avoid cannibalisation (low positive XED) or to exploit complementarity (negative XED).	Substitutes (positive XED) limit price‑raising power; complements (negative XED) allow joint price strategies.	Cross‑promotions are useful when XED is negative (e.g., bundle a printer with ink).	Placement near the related good (e.g., coffee near tea) can boost sales of substitutes.
YED	Luxury vs. necessity positioning guides product features and packaging.	Luxury goods (YED > 1) can sustain higher prices in growing‑income markets; inferior goods (YED < 0) may be priced lower during downturns.	Advertising intensity can be adjusted to match income‑elasticity (high YED → premium advertising).	Distribution in high‑income areas for luxury goods; mass‑market channels for inferior goods.
PES	Product design that allows rapid scaling (modular, off‑the‑shelf components) raises PES.	When supply is inelastic, firms may keep prices high to protect margins.	Promotion of “limited‑edition” or “scarcity” can be profitable when PES is low.	Strategic stock‑holding or multiple sourcing mitigates low PES in the short run.
PE‑promo	Product improvements that enhance advertising effectiveness increase PE‑promo.	High PE‑promo suggests price can be kept stable while using advertising to grow volume.	Directly informs the advertising budget: marginal ROI = PE‑promo × (Price / Advertising cost).	Channel‑specific promotions (e.g., in‑store displays) can raise PE‑promo for certain retail outlets.

4. General Limitations of Elasticity Analysis

1. Ceteris Paribus Assumption – In reality, other variables (tastes, expectations, number of buyers, etc.) change simultaneously.
2. Time‑Period Dependence – Elasticities differ in the short, medium and long run; a single figure cannot capture this dynamic.
3. Data Quality & Availability – Reliable, up‑to‑date data on quantities, prices, incomes and advertising spend are often scarce or costly.
4. Linear Approximation – Textbook examples use straight‑line curves, whereas real demand and supply curves are non‑linear; elasticity varies along the curve.
5. Aggregation vs. Segmentation – Market‑wide elasticities mask heterogeneity among consumer groups (age, region, income, lifestyle).

5. Specific Limitations by Elasticity Type

Elasticity	Key Limitation	Implication for Managers
PED	Calculated over a single price interval; elasticity can vary at other price points. Ignores broader substitution possibilities beyond the immediate market.	Pricing decisions based on one PED may mis‑estimate revenue effects when large price changes are contemplated.
XED	Identifying the “related” good is subjective; relationships evolve with technology and consumer habits. Aggregate data can blend substitute and complementary effects, obscuring the true magnitude.	Product‑line, bundling or line‑extension strategies can be flawed if XED is mis‑estimated.
YED	Assumes a stable income distribution; ignores shifts in preferences as incomes rise. Thresholds between “necessity” and “luxury” are fuzzy, leading to over‑ or under‑estimation of demand growth.	Market‑entry forecasts in emerging economies may be unreliable if YED is applied without considering distributional changes.
PES	Heavily dependent on production capacity, technology and time lags; short‑run PES is often near‑zero. External constraints (regulation, raw‑material scarcity, weather) are not captured.	Capacity‑expansion or inventory‑holding decisions can be misguided if PES is assumed constant.
PE‑promo	Advertising effectiveness can decay over time (diminishing returns) – a single PE‑promo may over‑state long‑run impact. Hard to isolate the effect of advertising from other simultaneous marketing activities.	Budget allocations based on an inflated PE‑promo may lead to overspending on promotion with limited sales lift.

6. Mitigating the Limitations

• Calculate separate elasticities for short‑run, medium‑run and long‑run periods.
• Combine quantitative elasticity estimates with qualitative research (focus groups, consumer surveys, expert interviews).
• Update calculations regularly to reflect price changes, income trends, new competitors and advertising innovations.
• Segment the market and compute segment‑specific elasticities where data allow (e.g., by age, region, income bracket).
• Use scenario‑planning or sensitivity analysis: test how different elasticity assumptions affect profit, market share or capacity utilisation.
• When possible, employ econometric techniques (regression analysis) to control for multiple variables simultaneously.

7. Diagram – How PED Varies Along a Demand Curve

8. Examiner Checklist – What to Include in a Full Answer

1. State the correct definition and formula for the elasticity being examined.
2. Show a clear, step‑by‑step calculation using percentage changes (or midpoint method if specified).
3. Interpret the sign and magnitude (elastic, inelastic, unit‑elastic; substitute/complement; normal/inferior; luxury/necessity).
4. Identify the relevant time horizon (short‑run vs. long‑run) and note any assumptions made.
5. Link the elasticity result to at least one of the 4 Ps (pricing, product, promotion, place) and explain the business implication.
6. Highlight one key limitation of the elasticity estimate and suggest a realistic way to mitigate it (e.g., segment‑specific analysis, scenario testing, updated data).