The concept of elasticity in economics

Elasticity is a measure used in economics to show how much one variable changes in response to a change in another variable. It helps economists understand the sensitivity of demand or supply to various factors. In the context of demand, elasticity focuses on how quantity demanded responds to changes in price, income, or prices of related goods.

This concept is important because individuals and firms respond to incentives and face constraints, and elasticity quantifies the magnitude of those responses.

Defining price elasticity of demand

Price elasticity of demand (PED) measures the responsiveness of the quantity demanded of a good or service to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

PED helps predict how consumers will react to price changes, which is crucial for businesses setting prices and governments implementing taxes.

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 is usually negative because quantity demanded typically falls as price rises, but economists often discuss its absolute value (magnitude) for simplicity.

Note that elasticity varies along a linear demand curve, meaning the slope of the curve does not equal elasticity. A steeper slope does not necessarily mean lower elasticity.

Worked example - Calculating price elasticity of demand

The price of a product increases from $10 to $12, and the quantity demanded decreases from 200 units to 150 units. Calculate the PED.

Step 1: Identify the values

• Old price = $10
• New price = $12
• Old quantity = 200 units
• New quantity = 150 units

Step 2: Calculate percentage changes

$\text{Percentage change in quantity demanded}=\frac{150-200}{200}\times 100=-25\%$

$\text{Percentage change in price}=\frac{12-10}{10}\times 100=20\%$

Step 3: Apply the PED formula

$\text{PED}=\frac{-25\%}{20\%}=-1.25$

Step 4: Interpretation

The magnitude of PED is 1.25, indicating elastic demand in this price range.

Types of price elasticity of demand

The value of PED determines whether demand is elastic, inelastic, or unit elastic. These categories describe how proportional the change in quantity demanded is to the change in price, with a benchmark magnitude of 1 separating them.

Categories based on PED magnitude

• Elastic demand - When the magnitude of PED is greater than 1, meaning the percentage change in quantity demanded is larger than the percentage change in price. Demand is highly responsive to price changes.
• Inelastic demand - When the magnitude of PED is less than 1, meaning the percentage change in quantity demanded is smaller than the percentage change in price. Demand is not very responsive to price changes.
• Unit elastic demand - When the magnitude of PED is exactly 1, meaning the percentage change in quantity demanded equals the percentage change in price. The changes are proportional.

These types apply to specific ranges along the demand curve, as elasticity can change with different price levels.

Factors influencing price elasticity of demand

Several factors determine how elastic or inelastic the demand for a good is. Understanding these helps explain why some products have more responsive demand than others.

Key factors affecting PED

• Availability of substitutes - Goods with many close substitutes (e.g., different brands of soda) tend to have elastic demand, as consumers can easily switch if the price rises.
• Necessity versus luxury - Necessities (e.g., insulin) often have inelastic demand because consumers need them regardless of price, while luxuries (e.g., designer clothing) have more elastic demand.
• Proportion of income spent - Goods that take up a small portion of income (e.g., salt) usually have inelastic demand, as price changes have little impact on budgets.
• Time period - Demand is often more elastic over longer periods, as consumers have time to adjust habits or find alternatives.
• Brand loyalty - Strong loyalty can make demand inelastic, as consumers stick with a preferred brand despite price increases.

The impact of price changes on total revenue

Total revenue (TR) is the total money received from selling a good, calculated as price times quantity sold. The effect of a price change on TR depends on whether demand is elastic, inelastic, or unit elastic.

How PED affects total revenue

• Elastic demand - If price increases, quantity demanded falls by a larger percentage, so TR decreases. If price decreases, quantity demanded rises by a larger percentage, so TR increases.
• Inelastic demand - If price increases, quantity demanded falls by a smaller percentage, so TR increases. If price decreases, quantity demanded rises by a smaller percentage, so TR decreases.
• Unit elastic demand - A price change leads to a proportional change in quantity demanded, so TR remains the same.

This relationship is key for firms deciding on pricing strategies, as it shows whether raising or lowering prices will boost revenue.

Summary of price changes and total revenue

Worked example - Determining the impact on total revenue

A firm sells 100 units of a product at $20 each, generating $2,000 in total revenue. After a price increase to $25, quantity demanded falls to 70 units. Calculate the new total revenue and explain the impact using PED.

Step 1: Identify the values and calculate PED

• Old price = $20, new price = $25
• Old quantity = 100 units, new quantity = 70 units

$\text{Percentage change in quantity}=\frac{70-100}{100}\times 100=-30\%$

$\text{Percentage change in price}=\frac{25-20}{20}\times 100=25\%$

$\text{PED}=\frac{-30\%}{25\%}=-1.2$

Step 2: Calculate new total revenue

New TR = $25 × 70 = $1,750

Step 3: Compare total revenues

Original TR = $2,000, new TR = $1,750 (decrease of $250)

Step 4: Interpretation

Since PED magnitude is 1.2 (elastic), the price increase leads to a decrease in TR, as expected for elastic demand.