# Price elasticity of demand

## Price Elasticity of Demand (PED)

The quantity demanded of a good or service is affected by changes in its price.  Elasticity measures how responsive demand is to the change in price.

Some goods are not very responsive to changes in price, in other words, the price can go up by a certain percentage and demand will fall by a smaller percentage, for example, petrol, cigarettes and alcohol.

Other goods will be far more responsive to a change in price; a percentage increase in price leads to a bigger percentage decrease in the quantity demanded.

Price elasticity of demand is measured using the following formula:

Price elasticity of demand = % change in quantity / % change in price

An easy way of remembering which way around the formula goes is to think of the football team Queens Park Rangers – QPR. Q (quantity) on the top of the formula and Pr (price) on the bottom; not the best aide memoir, but it will help you to remember!

### Positive or Negative value?

The value of PED is very important.  PED will always be a negative figure, the following table provides some examples of PED values.

You can see that you answer for PED is always negative, this is because:

• If the price goes down, the quantity demanded will go up.
• If the price goes up, the quantity demanded will go down.

Any positive number divided by a negative number, or any negative number divided by a positive number will give you a negative number for an answer.  Because all PED values are negative, you may often seeing figures with the minus sign missing.  This is done for simplicities sake.

### PED values – Elastic and Inelastic Demand

Demand is price inelastic, if the value of elasticity is less than one. If the demand for a good is inelastic then a percentage change in the price will bring about a smaller percentage change in the quantity demanded. For example, if a 10% increase in price by a rail company results in a 1% fall in train journeys made, then price elasticity would be -1% / 10% = -0.1 and the demand for rail journeys is therefore inelastic.

There has been a 100% increase in the price which has led to a 25% decrease in the quantity demanded.  The value of PED is therefore -25/100=-0.25.  If the value of PED is between 0 and 1 then the price elasticity of demand is inelastic.  This means that a percentage change in the price will lead to a smaller percentage change in the quantity demanded.

Demand is price elastic, if the value of elasticity is greater than one.  If demand for a good is price elastic then a percentage change in price will lead to an even larger percentage change in the quantity demanded. For example if a 10% rise in the price of CDs leads to a 20% fall in the demand, then price elasticity is -20% / 10% = -2 and the demand for CDs is therefore elastic.

There has been a 25% increase in the price which has led to a 50% decrease in the quantity demanded.  The value of PED is therefore -50/25=-2.  If the value is above 1 then the price elasticity of demand is elastic.

Try this to help you remember which demand curve is relatively inelastic and elastic – the inelastic curve looks more like an “I” and the elastic curve looks more like an “E” (this one takes more imagination!).

### Special Cases of Elasticity

Demand is infinitely inelastic if the value of elasticity is zero (zero divided by any number equal zero). This means that any change in price will have no effect on the quantity demanded.

If the value is 0 then the price elasticity of demand is perfectly inelastic.

Perfectly elastic demand is at the other extreme; any increase in price will lead to demand for that product falling to zero.  Perfectly elastic demand has a value of infinity, ∞.

If the value of elasticity is equal to 1, then it is described as having unitary elasticity.  This mean that a percentage change in price will lead to an exact and opposite change in the quantity demanded.  If the price increased by 20% and the quantity fell by 20% then the product would have unitary elasticity.  The demand curve for a good with unitary elasticity is called a rectangular hyperbola.

### Changes in Elasticity Along the Demand Curve

The value of elasticity changes over a straight-lined demand curve.

This shows that the top half of the demand curve is elastic and the bottom half is inelastic.  It is also to identify the following points:

• Perfectly elastic, ∞, at the top of the demand curve.
• Unitary elastic, 1, at the mid-point of the demand curve.
• Perfectly inelastic, 0, at the bottom of the demand curve.

Value of elasticity on the bottom of the demand curve moves from 0 to 1 (inelastic) and from 1 to infinity (elastic) on the top half of the e curve, this is shown on the diagram below.

### The Importance of elasticity for businesses

It is possible to calculate the revenue a business will receive from the demand curve, using the formula:

Total revenue = price x quantity

The total revenue for the firm in the diagram is 24, when the price is 6 and the quantity is 4.

The total revenue for a business increases from 16 to 24 when it raises its price on the inelastic section of the demand curve in the example below.

If the business wishes to increases its revenue and it faces an inelastic demand cure it should increase its price.

The total revenue for a business increases from 16 to 24 when it lowers its price on the elastic section of the demand curve in the example below.

If the business wishes to increases its revenue and it faces an elastic demand cure it should decrease its price.

The revenue maximising level of sales occurs when elasticity is unitary.  This is shown in the diagram below at an output of 5.  The demand curve diagram allows you to calculate revenue to equal 25.  This can also be shown on the top diagram: at the maximum point on the total revenue curve, revenue is equal to 25.

It is important to state that this level isn’t necessarily where profit is maximised.  This is because you don’t know what firm’s costs are.  You will learn how to calculate the profit maximising level of output next year.  This is just the revenue maximising point of output.

### Problems with measuring price elasticity of demand

Unfortunately, calculating elasticities is notoriously difficult.  Estimations of price elasticity of demand for the same the same good vary significantly when calculated by different economists.

When calculating elasticity we assume that all other factors affecting demand remain constant.  In reality, there are many factors, in addition to price, that might be changing which may affect the quantity demanded.  If many factors are changing at the same time then it will be also impossible to estimate elasticity.  Was it the change in price that caused the change in sales or some other variable?  It is impossible to separate out the impact of the different variables.  Ceteris paribus does not apply in the real world.

### Factors Affecting the value of Price Elasticity of Demand

There are four main factors that will affect the price elasticity of demand:

• The availability of close substitutes.  If the good has many substitutes it will be easy for customers to switch to another one if the price rises therefore it will be more elastic.
• The time period involved.  The value of elasticity will change over time.  The good will become more elastic over time.  Imagine there has been an increase in the price of petrol, in the short run people will continue to buy petrol as there will very few alternatives.  As time progresses and if the price of petrol remains high, there will become more other options available to drivers over time, such as LPG fuel, smaller car or public transport.  This will lead to demand becoming more elastic over time.
• Is the product a luxury or necessity?  A necessity will be more inelastic as people will continue to buy it even if the price increases.