Elasticity (Edexcel A-Level Economics A): Revision Notes

Elasticity

Introduction to elasticity

Elasticity is a fundamental concept in economics that measures how sensitive one variable is to changes in another variable. When we analyse markets, we often want to know more than just the direction of a change - we want to understand the magnitude of the response. For example, if the price of a product falls, we know that quantity demanded will increase (the law of demand), but by how much? Elasticity provides the answer to this question.

The concept of elasticity is particularly useful for predicting how market equilibrium will change in response to shifts in market conditions. It helps firms make pricing decisions and assists governments in forecasting the effects of taxes, subsidies, and other policies.

Price elasticity of demand

Understanding price elasticity of demand

Price elasticity of demand (PED) measures how sensitive the quantity demanded of a good or service is to a change in its price. It tells us the proportionate change in quantity demanded that results from a proportionate change in price.

The formula for PED is:

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

More formally, we can write this as:

$\text{PED} = \frac{100 \times \Delta Q/Q}{100 \times \Delta P/P}$

where $\Delta$ means 'change in', $Q$ represents quantity, and $P$ represents price.

Calculating price elasticity of demand

To calculate PED, we need to work out the percentage changes in both quantity demanded and price, then divide one by the other.

Interpreting PED values

The numerical value of PED tells us how responsive demand is to price changes:

PED value	Classification	Meaning
PED = 0	Perfectly inelastic	Quantity demanded does not change at all when price changes
0 < PED < 1	Price inelastic	Percentage change in quantity demanded is smaller than percentage change in price
PED = 1	Unit price elastic	Percentage change in quantity demanded equals percentage change in price
1 < PED < ∞	Price elastic	Percentage change in quantity demanded is larger than percentage change in price
PED = ∞	Perfectly elastic	Consumers demand an unlimited quantity at the current price, but demand falls to zero if price rises

When demand is elastic, consumers are highly responsive to price changes. A small change in price leads to a large change in quantity demanded. For example, if a 2% price increase causes a 5% fall in quantity demanded, the elasticity is $-2.5$ (ignoring the sign, this is greater than 1), so demand is elastic.

When demand is inelastic, consumers are not very responsive to price changes. Even a significant price change produces only a small change in quantity demanded. For example, if a 2% price increase causes only a 1% fall in quantity demanded, the elasticity is $-0.5$ (the numerical value is less than 1), so demand is inelastic.

When demand is unitary elastic, the percentage changes in price and quantity are exactly equal in magnitude, giving an elasticity of exactly $-1$ (or 1 in absolute terms).

How PED varies along a demand curve

An important characteristic of a straight-line demand curve is that the price elasticity varies at different points along the curve. This happens even though the slope remains constant throughout.

At the top of the demand curve (where price is relatively high and quantity relatively low):

• Elasticity approaches infinity (perfectly elastic)
• The upper portion of the curve is relatively elastic

At the midpoint of the demand curve:

• Elasticity equals $-1$ (unit elastic)
• This is the point of unit elasticity

At the bottom of the demand curve (where price is relatively low and quantity relatively high):

• Elasticity approaches zero (perfectly inelastic)
• The lower portion of the curve is relatively inelastic

Perfectly elastic and perfectly inelastic demand

Two extreme cases deserve special mention:

Perfectly inelastic demand (PED = 0)

When demand is perfectly inelastic, quantity demanded does not change at all in response to a price change. The demand curve is vertical. Consumers demand exactly the same quantity regardless of price. This situation is very rare in practice, though demand for some life-saving medicines might come close.

Perfectly elastic demand (PED = infinity)

When demand is perfectly elastic, consumers demand an unlimited quantity at the prevailing price, but if price rises even slightly above this level, demand falls to zero. The demand curve is horizontal. This can occur when there are perfect substitutes available at a fixed price - consumers will buy entirely from the cheapest source.

Factors that influence price elasticity of demand

Several factors determine whether demand for a good or service will be elastic or inelastic:

1. Availability of substitutes

This is the most important factor. Goods that have close substitutes available tend to have more elastic demand. When the price of one product rises, consumers can easily switch to an alternative.

For example, cauliflower and broccoli are often seen as similar vegetables. If the price of cauliflower rises significantly one week, consumers might readily switch to broccoli instead. The demand for cauliflower is relatively price elastic because there are close substitutes available.

On the other hand, if the price of all vegetables rises together, demand will not change very much, as there are no close substitutes for vegetables in the diet. Goods with no close substitutes tend to have more inelastic demand.

2. Necessity versus luxury

If a good is regarded as a necessity, demand tends to be inelastic. Consumers feel they must continue purchasing it even when the price rises. However, if a good is regarded as a luxury item, consumers are more price sensitive and demand tends to be more elastic. They can choose to cut back or go without when prices rise.

This is closely related to the availability of substitutes. Labelling something as a necessity is essentially saying there are no substitutes for it.

3. Proportion of income spent on the good

Goods that represent a small proportion of overall expenditure tend to have inelastic demand. Consumers may not notice small changes in the price of inexpensive items such as salt or sugar, so their purchasing behaviour remains largely unchanged.

Conversely, items that figure large in the household budget (such as housing, cars, or holidays) tend to have more elastic demand. When a significant proportion of income is involved, consumers are much more sensitive to price changes.

4. Time period

The elasticity of demand tends to be more elastic in the long run than in the short run. When prices change, consumers may initially have limited ability to adjust their consumption. Habits and commitments may dictate consumption patterns in the short run.

However, over a longer time period, consumers can make adjustments. For example, an increase in the price of petrol may have limited effects in the short run if people are committed to driving to work. In the long run, however, consumers may buy smaller, more fuel-efficient cars, switch to electric vehicles, or even make greater use of public transport. These adjustments mean demand becomes more elastic over time.

Price elasticity of demand and total revenue

Understanding the relationship between PED and total revenue is crucial for firms making pricing decisions. Total revenue is calculated as price multiplied by quantity sold.

When a firm changes its price, two opposing effects occur:

• The price effect: revenue per unit changes
• The quantity effect: the number of units sold changes

Which effect dominates depends on the price elasticity of demand.

When demand is elastic:

If demand is elastic, the percentage change in quantity is larger than the percentage change in price. Therefore:

• A price decrease leads to a rise in total revenue (the increase in quantity more than compensates for the lower price)
• A price increase leads to a fall in total revenue (the decrease in quantity more than offsets the higher price)

When demand is inelastic:

If demand is inelastic, the percentage change in quantity is smaller than the percentage change in price. Therefore:

• A price increase leads to a rise in total revenue (the higher price more than compensates for the fall in quantity)
• A price decrease leads to a fall in total revenue (the lower price is not offset by the increase in quantity)

When demand is unit elastic:

When elasticity equals $-1$, the percentage changes in price and quantity are exactly equal. Therefore:

• Total revenue does not change when price changes

The relationship is summarised in this table:

Price elasticity of demand	For a price increase, total revenue...	For a price decrease, total revenue...
Elastic	falls	rises
Unit elastic	does not change	does not change
Inelastic	rises	falls

Income elasticity of demand

Understanding income elasticity of demand

While PED measures sensitivity to price changes, income elasticity of demand (YED) measures how sensitive quantity demanded is to changes in consumer incomes. This helps economists distinguish between different types of goods.

The formula for YED is:

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

Unlike PED, the income elasticity of demand can be either positive or negative, depending on the nature of the good.

Normal goods and inferior goods

For normal goods, quantity demanded increases as consumer income rises. Therefore, YED is positive. Most goods and services fall into this category - as people become wealthier, they buy more of these products.

For inferior goods, quantity demanded falls as consumer income rises. Therefore, YED is negative. These are goods that consumers choose to buy less of when they can afford better alternatives. Examples might include cheap own-brand products, fast food, or budget accommodation that people replace with superior options as their income increases.

Necessities and luxury goods

Among normal goods (those with positive YED), we can make a further distinction:

Necessities are goods with a YED that is positive but less than 1. As income rises, consumers do spend more on these goods, but proportionally less of their income. The quantity demanded rises less than proportionately with income. These are goods that consumers need but don't greatly increase consumption of when they become wealthier.

Luxury goods are goods with a YED greater than 1. As income rises, consumers spend proportionally more on these goods. They are income elastic - people devote an increasing share of their income to these products as they become wealthier.

Interpreting YED values

The following table summarises the interpretation of YED values:

YED value	Description	Meaning
YED < -1	Income-elastic inferior good	Quantity demanded falls sharply as income rises
-1 < YED < 0	Income-inelastic inferior good	Quantity demanded falls slightly as income rises
YED = 0	No relationship	Quantity demanded does not change with income
0 < YED < 1	Income-inelastic normal good (necessity)	Quantity demanded rises less than proportionately with income
YED > 1	Income-elastic normal good (luxury)	Quantity demanded rises more than proportionately with income

Cross elasticity of demand

Understanding cross elasticity of demand

Cross elasticity of demand (XED) measures the sensitivity of quantity demanded of one good to a change in the price of another good or service. This elasticity reveals the relationship between goods.

The formula for XED is:

$\text{XED} = \frac{\% \text{ change in quantity demanded of good X}}{\% \text{ change in price of good Y}}$

Like YED, the cross elasticity can be either positive or negative, and the sign provides important information about the relationship between the goods.

Substitutes and complements

When the XED is positive, the two goods are substitutes. An increase in the price of good Y leads to an increase in the quantity demanded of good X. Consumers switch from the now-more-expensive good Y to the alternative good X.

For example, if the price of apples rises, the demand for pears may increase. Apples and pears are substitutes - if one becomes relatively more expensive, consumers switch to the other.

A high positive value for XED indicates that two goods are very close substitutes. This information can help firms identify their close competitors.

When the XED is negative, the two goods are complements. An increase in the price of good Y leads to a decrease in the quantity demanded of good X. These goods tend to be consumed together, so if one becomes more expensive and its demand falls, demand for the complementary good also falls.

For example, coffee and sugar tend to be consumed together. If the XED between these goods is negative, it confirms they are complements. When the price of coffee rises and people buy less coffee, they also buy less sugar.

Interpreting XED values

The following table summarises the interpretation of XED values:

XED value	Description	Meaning
XED < -1	Strong complement	Goods are strongly complementary
-1 < XED < 0	Weak complement	Goods are weak complements
XED = 0	Unrelated	No relationship between the goods
0 < XED < 1	Weak substitute	Goods are weak substitutes
XED > 1	Strong substitute	Goods are strong substitutes

An XED of zero indicates that the goods are unrelated - they are neither substitutes nor complements. A change in the price of one good has no effect on demand for the other.

Using elasticities

The various elasticity measures are valuable tools for both firms and governments in their decision making.

For firms:

Suppose you are responsible for setting prices for a product. Understanding PED is crucial:

• If demand is elastic, you would hesitate to raise prices because this would reduce total revenue
• If demand is inelastic, raising prices could increase revenue
• Knowing the YED helps forecast changing demand if real incomes are rising or if the economy is heading into recession
• Understanding the XED helps anticipate changes in demand when competitors change their prices or when the prices of complementary goods change

For governments:

Elasticity measures help governments assess the likely impact of policies:

• When imposing an indirect tax, the government can use PED to forecast the resulting tax revenues
• If the government introduces a subsidy to reduce the selling price of a good, knowing the PED allows them to assess the impact of this policy
• Understanding YED helps predict how demand patterns will change as the economy grows and incomes rise
• This information is valuable for planning public services and infrastructure