the concept of elasticity of demand: price, income and promotional

8.1 Marketing Analysis – Elasticity

Learning objective

Understand the concept of elasticity of demand and be able to calculate and interpret:

• Price elasticity of demand (PED)
• Income elasticity of demand (YED)
• Advertising (promotional) elasticity of demand (AED)

1. What is elasticity?

Elasticity measures the responsiveness of the quantity demanded of a product to a change in another variable (price, consumer income, or advertising expenditure). It is expressed as a ratio of percentage changes, giving a unit‑free figure that can be compared across products and markets.

2. Price elasticity of demand (PED)

2.1 Definition & formula

PED shows how much the quantity demanded changes when the price changes.

$$\text{PED}= \frac{\%\Delta Q_d}{\%\Delta P}$$

Because price and quantity move in opposite directions (law of demand), PED is normally negative. For classification we use the absolute value (|PED|).

2.2 Mid‑point (arc) method – calculation steps

1. Identify the initial price \(P_1\) and quantity \(Q_1\) and the new price \(P_2\) and quantity \(Q_2\).
2. Calculate the percentage change in quantity (mid‑point formula):
   $$\%\Delta Q_d = \frac{Q_2-Q_1}{\dfrac{Q_1+Q_2}{2}}\times 100$$
3. Calculate the percentage change in price (mid‑point formula):
   $$\%\Delta P = \frac{P_2-P_1}{\dfrac{P_1+P_2}{2}}\times 100$$
4. Insert the two percentages into the PED formula.

2.3 Worked example (price change)

Suppose the price of a sports drink falls from £2.00 to £1.60 and the quantity sold rises from 5 000 units to 6 500 units.

• \(\%\Delta Q_d = \dfrac{6 500-5 000}{(5 000+6 500)/2}\times100 = \dfrac{1 500}{5 750}\times100 \approx 26.1\%.\)
• \(\%\Delta P = \dfrac{1.60-2.00}{(2.00+1.60)/2}\times100 = \dfrac{-0.40}{1.80}\times100 \approx -22.2\%.\)
• \(\text{PED}= \dfrac{26.1\%}{-22.2\%}= -1.18.\) Absolute value = 1.18 → elastic.

Interpretation: a 1 % fall in price leads to a 1.18 % increase in quantity demanded. Because |PED| > 1, total revenue will rise when price falls.

2.4 Interpretation checklist (PED)

Absolute PED value	Demand type	Revenue implication when price falls
0 < |PED| < 1	Inelastic	Revenue falls
|PED| = 1	Unit‑elastic	Revenue unchanged
|PED| > 1	Elastic	Revenue rises

2.5 Factors that affect PED

• Availability of close substitutes – more substitutes → higher elasticity.
• Proportion of consumer’s income spent on the good – higher proportion → higher elasticity.
• Nature of the good (necessity vs. luxury) – luxuries are more elastic.
• Time horizon – demand is usually more elastic in the long run.

2.6 Business decisions (pricing)

• Choose a price‑cut or price‑rise based on whether demand is elastic or inelastic.
• Use PED to estimate the likely impact on total revenue.
• Apply elastic demand for market‑share expansion (penetration pricing); apply inelastic demand for premium‑pricing strategies.
• Anticipate competitor reactions by understanding rivals’ price‑elasticities.

3. Income elasticity of demand (YED)

3.1 Definition & formula

$$\text{YED}= \frac{\%\Delta Q_d}{\%\Delta Y}$$

\(\%\Delta Y\) = percentage change in consumer income.

3.2 Mid‑point (arc) method – calculation steps (parallel to PED)

1. Identify the initial income \(Y_1\) and quantity \(Q_1\) and the new income \(Y_2\) and quantity \(Q_2\).
2. Percentage change in quantity:
   $$\%\Delta Q_d = \frac{Q_2-Q_1}{\dfrac{Q_1+Q_2}{2}}\times 100$$
3. Percentage change in income:
   $$\%\Delta Y = \frac{Y_2-Y_1}{\dfrac{Y_1+Y_2}{2}}\times 100$$
4. Insert the two percentages into the YED formula.

3.3 Worked example (income change)

Sales of a premium coffee increase from 8 000 cups to 9 600 cups when average consumer income rises from £30 000 to £33 000.

• \(\%\Delta Q_d = \dfrac{9 600-8 000}{(8 000+9 600)/2}\times100 = \dfrac{1 600}{8 800}\times100 \approx 18.2\%.\)
• \(\%\Delta Y = \dfrac{33 000-30 000}{(30 000+33 000)/2}\times100 = \dfrac{3 000}{31 500}\times100 \approx 9.5\%.\)
• \(\text{YED}= \dfrac{18.2\%}{9.5\%}=1.91.\)

Interpretation: the coffee is a luxury good; a 1 % rise in income generates a 1.91 % rise in quantity demanded.

3.4 Interpretation checklist (YED)

YED value	Good type	Implication for demand
YED > 1	Luxury	Demand rises more than proportionally with income.
0 < YED < 1	Normal (necessity)	Demand rises, but less than proportionally.
YED = 0	Neutral	Demand unaffected by income changes.
YED < 0	Inferior	Demand falls as income rises.

3.5 Business decisions (product positioning & segmentation)

• Use YED to decide whether a product should be marketed as a luxury (high‑income) or a mass‑market (necessity) offering.
• Target segments whose income trends match the product’s YED (e.g., luxury goods to affluent consumers).
• Incorporate expected income growth into sales forecasts.
• Allocate resources toward goods with favourable YED in the prevailing economic climate.

4. Advertising (promotional) elasticity of demand (AED)

4.1 Definition & formula

$$\text{AED}= \frac{\%\Delta Q_d}{\%\Delta A}$$

\(\%\Delta A\) = percentage change in advertising expenditure.

4.2 Mid‑point (arc) method – calculation steps (parallel to PED)

1. Identify the initial advertising spend \(A_1\) and quantity \(Q_1\) and the new spend \(A_2\) and quantity \(Q_2\).
2. Percentage change in quantity:
   $$\%\Delta Q_d = \frac{Q_2-Q_1}{\dfrac{Q_1+Q_2}{2}}\times 100$$
3. Percentage change in advertising spend:
   $$\%\Delta A = \frac{A_2-A_1}{\dfrac{A_1+A_2}{2}}\times 100$$
4. Insert the two percentages into the AED formula.

4.3 Worked example (advertising change)

A cosmetics company raises its advertising budget from £120 000 to £150 000. In the following month sales rise from 4 000 units to 4 800 units.

• \(\%\Delta Q_d = \dfrac{4 800-4 000}{(4 000+4 800)/2}\times100 = \dfrac{800}{4 400}\times100 \approx 18.2\%.\)
• \(\%\Delta A = \dfrac{150 000-120 000}{(120 000+150 000)/2}\times100 = \dfrac{30 000}{135 000}\times100 \approx 22.2\%.\)
• \(\text{AED}= \dfrac{18.2\%}{22.2\%}=0.82.\)

Interpretation: a 1 % increase in advertising spend generates a 0.82 % increase in quantity demanded. The firm can now compare the additional contribution margin from the extra £30 000 spend to decide if the campaign is profitable.

4.4 Interpretation checklist (AED)

AED value	Advertising effectiveness	Typical action
AED > 1	Highly effective – large sales lift per £1 spent	Consider increasing spend (if margin allows).
0 < AED < 1	Effective but modest	Maintain or fine‑tune spend.
AED ≈ 0	Little or no impact	Re‑evaluate creative/message or shift budget.
AED < 0	Negative impact (rare)	Cease or radically redesign campaign.

4.5 Business decisions (advertising budget)

• Calculate the expected sales lift per £1 of advertising to assess return on investment.
• Allocate budget to the media or campaigns with the highest AED.
• Use AED to decide between short‑term sales promotions and long‑term brand‑building activities.
• Monitor AED over time; a falling AED may signal advertising saturation.

5. Factors that influence the three elasticities

• Substitutes and complements – more close substitutes raise PED; complementary goods affect cross‑price elasticity (useful for later study).
• Share of income spent on the good – a larger share generally raises both PED and YED.
• Nature of the good – necessities have lower PED & YED; luxuries have higher values.
• Time horizon – elasticities are usually higher in the long run.
• Advertising saturation – the marginal effect of additional spend falls as consumers become accustomed to the message, reducing AED over time.

6. Short‑run vs. long‑run elasticity

In the short run consumers have limited ability to change habits, find substitutes, or re‑allocate income, so elasticities tend to be lower. Over the long run they can:

• Switch to alternatives → higher PED.
• Adjust spending patterns as incomes change → higher YED.
• Experience diminishing returns to advertising → AED may initially rise then fall.

Understanding this time dimension helps managers decide whether a pricing or promotional change is a temporary tactic or a strategic shift.

7. Limitations of elasticity analysis

• Ceteris paribus assumption – elasticity isolates one variable, but in reality many factors change simultaneously.
• Data quality – reliable calculation requires accurate sales, price, income and advertising data; poor data give misleading results.
• Short‑run vs. long‑run relevance – values derived from a short‑term period may not apply later.
• Non‑linear demand curves – elasticity varies along the curve; a single figure can oversimplify.
• Behavioural influences – brand loyalty, perceived quality and social trends can dampen or amplify elastic responses.

8. Business decisions using elasticities (summary)

1. Pricing decisions – use PED to predict revenue impact of price changes and to choose between penetration (elastic) and premium (inelastic) strategies.
2. Product positioning & market segmentation – YED indicates whether a product should target high‑income (luxury) or mass‑market (necessity) consumers.
3. Advertising budgeting – AED shows the expected sales lift per £1 spent and helps allocate spend to the most efficient campaigns.
4. Forecasting & planning – combine the three elasticities with expected changes in price, income and advertising to produce sales forecasts for budgeting.
5. Strategic review – monitor shifts in elasticities over time; a move from inelastic to elastic demand may signal new competition or changing consumer preferences.

9. Summary table of elasticities

Elasticity type	Formula	Typical range	Main business implication
Price elasticity (PED)	\(\displaystyle \frac{\%\Delta Q_d}{\%\Delta P}\)	0 < |PED| < ∞ (usually –∞ to 0)	Pricing strategy, revenue forecasting, market‑share tactics
Income elasticity (YED)	\(\displaystyle \frac{\%\Delta Q_d}{\%\Delta Y}\)	–∞ to +∞	Product positioning, segment targeting, sales forecasting
Advertising elasticity (AED)	\(\displaystyle \frac{\%\Delta Q_d}{\%\Delta A}\)	0 to +∞ (rarely negative)	Advertising budget allocation, promotional effectiveness analysis

10. Key points to remember

• Elasticities are unit‑free ratios, allowing comparison across markets and products.
• For PED the sign is negative; use the absolute value when classifying demand as elastic, unit‑elastic or inelastic.
• Elasticities can change over time because of shifts in consumer preferences, income levels, competitive activity and the time horizon.
• Accurate, up‑to‑date data are essential for reliable calculations.
• Always consider the limitations of elasticity analysis before making strategic decisions.