Price elasticity of demand and its impact on revenue

Price elasticity of demand (PED) measures how the quantity demanded of a product responds to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Formula for price elasticity of demand

$\text{PED}=\frac{\text{percentage change in quantity demanded}}{\text{percentage change in price}}$

Where:

• Percentage change in quantity demanded = $\frac{\text{new quantity}-\text{old quantity}}{\text{old quantity}}\times 100$
• Percentage change in price = $\frac{\text{new price}-\text{old price}}{\text{old price}}\times 100$

PED values indicate whether demand is elastic (PED > 1, responsive to price changes), inelastic (PED < 1, less responsive), or unit elastic (PED = 1, proportional response).

How PED affects total revenue

Total revenue for a firm is calculated as price multiplied by quantity sold (P × Q). The effect of a price change on revenue depends on PED.

Revenue effects by elasticity type:

• Elastic demand (PED > 1) - A price reduction leads to a larger percentage increase in quantity demanded, causing total revenue to rise.
• Inelastic demand (PED < 1) - A price increase results in a smaller percentage decrease in quantity demanded, so total revenue rises.
• Unit elastic demand (PED = 1) - Revenue remains unchanged as price changes are matched by proportional quantity adjustments.

Worked example - Calculating PED and its impact on revenue

A company sells 800 units of a product at £12 each. After reducing the price to £10, sales increase to 1,100 units. Calculate the PED and determine the effect on total revenue.

Step 1: Identify the values

• Old price = £12
• New price = £10
• Old quantity = 800 units
• New quantity = 1,100 units

Step 2: Calculate percentage changes

Percentage change in quantity = $\frac{\mathrm{1,100}-800}{800}\times 100=37.5\%$

Percentage change in price = $\frac{10-12}{12}\times 100=-16.67\%$

Step 3: Apply the PED formula

$\text{PED}=\frac{37.5\%}{-16.67\%}\approx -2.25$

Step 4: Assess revenue impact

Old revenue = £12 × 800 = £9,600

New revenue = £10 × 1,100 = £11,000

Revenue increases by £1,400 because demand is elastic (PED > 1), and the price reduction boosts sales significantly.

Applications of price elasticity in pricing and taxation

PED helps explain why prices vary across different markets and influences government revenue from indirect taxes, such as value-added tax (VAT).

How PED influences pricing strategies in markets

Examples of pricing strategies based on elasticity:

• High-demand events - Concert tickets for popular artists often have inelastic demand, allowing higher prices without much loss in sales.
• Seasonal variations - Theme parks charge more during busy periods when demand is inelastic due to holidays, but lower fees off-peak to attract price-sensitive visitors.
• Timing of purchases - Transport firms set higher fares for last-minute travel (inelastic demand from urgent needs) compared to advance bookings (more elastic demand).
• Holiday periods - Restaurants increase prices during festive seasons when demand becomes less responsive to cost changes.

Effects of indirect taxes on government income

Indirect taxes raise product prices, and their revenue impact depends on PED.

Tax revenue effects:

• If demand is inelastic, quantity demanded falls little, leading to higher tax revenue for the government.
• If demand is elastic, quantity demanded drops significantly, reducing overall tax income despite the price rise.

Strategies businesses use to make demand more price inelastic

Firms aim to reduce PED to maintain revenue during price increases.

Key strategies include:

• Effective advertising - Promoting unique benefits to differentiate from alternatives.
• Building brand loyalty - Establishing a strong image that positions the product as essential or superior.
• Market expansion through mergers - Combining with competitors to gain greater control and reduce substitutes.
• Securing monopolies - Using patents or regulations to limit competition and make demand less sensitive to price.

Income elasticity of demand and its business implications

Income elasticity of demand (YED) shows how quantity demanded varies with income changes. It is calculated as the percentage change in quantity demanded divided by the percentage change in income.

Formula for income elasticity of demand

$\text{YED}=\frac{\text{percentage change in quantity demanded}}{\text{percentage change in income}}$

Where:

• Percentage change in quantity demanded = $\frac{\text{new quantity}-\text{old quantity}}{\text{old quantity}}\times 100$
• Percentage change in income = $\frac{\text{new income}-\text{old income}}{\text{old income}}\times 100$

Types of goods based on YED

Classification by income response:

• Normal goods (YED > 0) - Demand rises with income. Luxury items often have YED > 1, meaning demand grows faster than income during booms but falls sharply in recessions.
• Inferior goods (YED < 0) - Demand decreases as income rises, with sales dropping in economic growth periods but increasing during downturns.

Business applications of YED

YED aids in predicting demand shifts, especially in growing economies where rising incomes boost sales of items like cars or electronics.

Worked example - Calculating YED for a normal good

In a growing economy, average income rises from £40,000 to £44,000, and demand for a luxury watch increases from 200 to 280 units. Calculate the YED.

Step 1: Identify the values

• Old income = £40,000
• New income = £44,000
• Old quantity = 200 units
• New quantity = 280 units

Step 2: Calculate percentage changes

Percentage change in quantity = $\frac{280-200}{200}\times 100=40\%$

Percentage change in income = $\frac{\mathrm{44,000}-\mathrm{40,000}}{\mathrm{40,000}}\times 100=10\%$

Step 3: Apply the YED formula

$\text{YED}=\frac{40\%}{10\%}=4$

Step 4: Interpretation

With YED = 4 (> 1), this is a luxury normal good; demand grows four times faster than income.

Cross elasticity of demand and competitive strategies

Cross elasticity of demand (XED) assesses how the quantity demanded of one product changes when the price of another product varies. It is calculated as the percentage change in quantity demanded of product A divided by the percentage change in price of product B.

Formula for cross elasticity of demand

$\text{XED}=\frac{\text{percentage change in quantity demanded of product A}}{\text{percentage change in price of product B}}$

Types of relationships based on XED

Product relationships:

• Substitutes (XED > 0) - A price fall in one product reduces demand for the other, e.g., if a rival's price drops 10% and demand for a firm's item falls 20%, XED = 2.
• Complements (XED < 0) - Products used together; a price rise in one decreases demand for the other.

Business strategies using XED

Strategic applications:

• Firms monitor competitors' prices to anticipate demand shifts for substitutes.
• Many businesses bundle complements, like consoles with games, to boost overall sales.
• Restaurants offer meal deals at low prices (despite inelastic food demand) to drive sales of high-margin drinks, leveraging negative XED.

Challenges in calculating elasticity values

Estimating elasticity is useful but faces several practical difficulties that can affect accuracy.

Key issues in elasticity calculations

Main challenges include:

• Data requirements - Accurate values need information from at least two time periods to measure changes.
• Isolating variables - It's hard to separate price effects from other influences like income or tastes.
• Time sensitivity - Data over extended periods may become unreliable due to market shifts.
• Technological changes - Rapid innovations can alter demand patterns, making calculations outdated.
• Historical limitations - Past data may not predict future behaviour in dynamic markets.