The concept and calculation of price elasticity of demand

Price elasticity of demand (PED) measures how the quantity demanded of a product responds to a change in its price.

Formula for price elasticity of demand

$\text{Price elasticity of demand}=\frac{\text{\% change in quantity demanded}}{\text{\% change in price}}$

PED values are typically negative because an increase in price usually leads to a decrease in quantity demanded, and vice versa. When interpreting results, the negative sign is often ignored to focus on the magnitude.

Categories of price elasticity of demand

• Price elastic demand - Occurs when the absolute value of PED is greater than 1. A small percentage change in price leads to a larger percentage change in quantity demanded.
• Price inelastic demand - Occurs when the absolute value of PED is less than 1. A percentage change in price results in a smaller percentage change in quantity demanded.

Worked example - Calculating price elasticity of demand

A company raises the price of its product from $20 to $24, causing quantity demanded to fall from 800 units to 560 units per week. Calculate the PED.

Step 1: Identify the values

• Original price = $20
• New price = $24
• Original quantity demanded = 800 units
• New quantity demanded = 560 units

Step 2: Calculate percentage changes

% change in price = (($24 - $20) / $20) × 100 = 20%
% change in quantity demanded = ((560 - 800) / 800) × 100 = -30%

Step 3: Apply the formula

$\text{Price elasticity of demand}=\frac{-30\%}{20\%}=-1.5$

Step 4: Interpretation

The absolute value is 1.5, indicating elastic demand where the percentage change in quantity demanded is greater than the percentage change in price.

Factors influencing price elasticity of demand

Several factors determine whether demand for a product is price elastic or inelastic.

Key influences on price elasticity

• Necessity of the product - Essential items, such as basic food like milk, tend to have inelastic demand.
• Availability of substitutes - If close alternatives or competitor products exist, demand is more elastic.
• Brand loyalty and differentiation - Businesses often use strategies like unique branding to build loyalty, reducing elasticity.
• Time period - Elasticity increases over time as consumers have more opportunity to discover and switch to alternatives.
• Impact of technology - Online access, such as through the internet, makes it simpler to compare prices and find substitutes, increasing elasticity.
• Product category vs brand - Broad categories (e.g., petrol) are often inelastic, while specific brands within them are more elastic due to competition.
• Proportion of income - Products that take up a large share of consumers' budgets, like expensive electronics, tend to have more elastic demand.

The impact of price elasticity on sales revenue

Sales revenue is calculated as the price per unit multiplied by the quantity sold. The elasticity of demand affects how revenue changes when prices are adjusted.

Formula for sales revenue

$\text{Sales revenue}=\text{price per unit}\times \text{quantity sold}$

Effects on revenue for elastic demand

For products with elastic demand, a price increase reduces total revenue because the percentage fall in quantity demanded exceeds the percentage rise in price. Conversely, a price decrease boosts revenue as the gain from higher sales volume outweighs the loss from lower price per unit.

Effects on revenue for inelastic demand

For products with inelastic demand, a price increase raises total revenue since the percentage drop in quantity demanded is smaller than the percentage rise in price. A price decrease lowers revenue because the increase in sales volume is not enough to offset the reduced price per unit.

Worked example - Assessing revenue impact from price changes

A firm sells a product with a PED of -1.8 (elastic). The current price is $25, and quantity sold is 300 units. If the price rises to $28, calculate the new revenue and compare it to the original.

Step 1: Calculate original revenue

Original revenue = $25 × 300 = $7,500

Step 2: Determine percentage change in price

% change in price = (($28 - $25) / $25) × 100 = 12%

Step 3: Calculate percentage change in quantity and new quantity

% change in quantity = PED × % change in price = -1.8 × 12% = -21.6%
New quantity = 300 × (1 - 0.216) = 235.2 units

Step 4: Calculate new revenue

New revenue = $28 × 235.2 = $6,585.6
Revenue decreases by $914.4, confirming that for elastic demand, a price rise reduces total revenue.

The concept and calculation of income elasticity of demand

Income elasticity of demand (YED) measures how the quantity demanded of a product changes in response to a shift in consumers' real income, which accounts for inflation or deflation over the period.

Formula for income elasticity of demand

$\text{Income elasticity of demand}=\frac{\text{\% change in quantity demanded}}{\text{\% change in real income}}$

Categories of income elasticity

• Normal goods - Have positive YED less than 1. Demand increases with rising income, but at a slower rate than the income growth.
• Luxury goods - Have positive YED greater than 1. Demand rises faster than income.
• Inferior goods - Have negative YED. Demand decreases as income rises and increases when income falls.

Worked example - Calculating income elasticity of demand

Real income rises from $50,000 to $52,500 annually, causing demand for a luxury good to increase from 200 units to 220 units. Calculate the YED.

Step 1: Identify the values

• Original real income = $50,000
• New real income = $52,500
• Original quantity demanded = 200 units
• New quantity demanded = 220 units

Step 2: Calculate percentage changes

% change in real income = (($52,500 - $50,000) / $50,000) × 100 = 5%
% change in quantity demanded = ((220 - 200) / 200) × 100 = 10%

Step 3: Apply the formula

$\text{Income elasticity of demand}=\frac{10\%}{5\%}=2$

Step 4: Interpretation

A YED of 2 indicates a luxury good, where demand grows twice as fast as income.

Business applications of elasticity concepts

Elasticity measures provide valuable insights for decision-making in manufacturing and sales strategies.

Uses of price elasticity in business

• Businesses use PED to decide on price adjustments, predicting impacts on sales volume and revenue.
• For elastic products, lowering prices can maximise revenue; for inelastic ones, raising prices may be more profitable.

Uses of income elasticity in business

• YED helps forecast demand during economic changes, such as growth or recession.
• Manufacturers can adjust production and marketing based on expected income trends.