# Price elasticity of demand

Author: Geoff Riley  Last updated: Sunday 23 September, 2012

Price elasticity of demand measures the responsiveness of demand after  a change in price

The formula for calculating the co-efficient of elasticity of demand is:

Percentage change in quantity demanded divided by the percentage change in price

Since changes in price and quantity usually move in opposite directions, usually we do not bother to put in the minus sign. We are more concerned with the co-efficient of elasticity of demand.

Example: Demand for rail services

At peak times, the demand for rail transport becomes inelastic – and higher prices are charged by rail companies who can then achieve higher revenues and profits

Values for price elasticity of demand

1. If Ped = 0 demand is perfectly inelastic - demand does not change at all when the price changes – the demand curve will be vertical.
2. If Ped is between 0 and 1 (i.e. the % change in demand from A to B is smaller than the percentage change in price), then demand is inelastic.
3. If Ped = 1 (i.e. the % change in demand is exactly the same as the % change in price), then demand is unit elastic. A 15% rise in price would lead to a 15% contraction in demand leaving total spending the same at each price level.
4. If Ped > 1, then demand responds more than proportionately to a change in price i.e. demand is elastic. For example if a 10% increase in the price of a good leads to a 30% drop in demand. The price elasticity of demand for this price change is –3

Factors affecting price elasticity of demand

• The number of close substitutes – the more close substitutes there are in the market, the more elastic is demand because consumers find it easy to switch
• The cost of switching between products – there may be costs involved in switching. In this case, demand tends to be inelastic. For example, mobile phone service providers may insist on a12 month contract.
• The degree of necessity or whether the good is a luxury – necessities tend to have an inelastic demand whereas luxuries tend to have a more elastic demand.
• The proportion of a consumer’s income allocated to spending on the good – products that take up a high % of income will have a more elastic demand
• The time period allowed following a price change – demand is more price elastic, the longer that consumers have to respond to a price change. They have more time to search for cheaper substitutes and switch their spending.
• Whether the good is subject to habitual consumption – consumers become less sensitive to the price of the good of they buy something out of habit (it has become the default choice).
• Peak and off-peak demand - demand is price inelastic at peak times and more elastic at off-peak times – this is particularly the case for transport services.
• The breadth of definition of a good or service – if a good is broadly defined, i.e. the demand for petrol or meat, demand is often inelastic. But specific brands of petrol or beef are likely to be more elastic following a price change.

Demand curves with different price elasticity of demand

Elasticity of demand and total revenue for a producer / supplier

The relationship between elasticity of demand and a firm’s total revenue is an important one.

• When demand is inelastic – a rise in price leads to a rise in total revenue –  a 20% rise in price might cause demand to contract by only 5% (Ped  = -0.25)
• When demand is elastic  – a fall in price leads to a rise in total revenue - for example a 10% fall in price might cause demand to expand by only 25% (Ped  = +2.5)

Peak and Off-Peak Demand and Prices

Why are prices for package holidays more expensive during school holiday weeks? Why are rail fares more expensive at peak times? During peak demand periods, market demand is higher and also more price inelastic. This allows producers to sell their products for higher prices and make increased profits.

The table below gives an example of the relationships between prices; quantity demanded and total revenue. As price falls, the total revenue initially increases, in our example the maximum revenue occurs at a price of £12 per unit when 520 units are sold giving total revenue of £6240.

 Price Quantity Total Revenue Marginal Revenue £ per unit Units £s £s 20 200 4000 18 280 5040 13 16 360 5760 9 14 440 6160 5 12 520 6240 1 10 600 6000 -3 8 680 5440 -7 6 760 4560 -11

Consider the elasticity of demand of a price change from £20 per unit to £18 per unit. The % change in demand is 40% following a 10% change in price – giving an elasticity of demand of -4 (i.e. highly elastic).

In this situation when demand is price elastic, a fall in price leads to higher total consumer spending / producer revenue

Consider a price change further down the estimated demand curve – from £10 per unit to £8 per unit. The % change in demand = 13.3% following a 20% fall in price – giving a co-efficient of elasticity of – 0.665 (i.e. inelastic). A fall in price when demand is price inelastic leads to a reduction in total revenue.

 Change in the market What happens to total revenue? Ped is inelastic and a firm raises its price. Total revenue increases Ped is elastic and a firm lowers its price. Total revenue increases Ped is elastic and a firm raises price. Total revenue decreases Ped is -1.5 and the firm raises price by 4% Total revenue decreases Ped is -0.4 and the firm raises price by 30% Total revenue increases Ped is -0.2 and the firm lowers price by 20% Total revenue decreases Ped is -4.0 and the firm lowers price by 15% Total revenue increases

Elasticity of demand and indirect taxation

Many products are subject to indirect taxes. Good examples include the duty on cigarettes (cigarette taxes in the UK are among the highest in Europe) alcohol and fuel. Here we consider the effects of indirect taxes on costs and the importance of elasticity of demand in determining the effects of a tax on price and quantity.

A tax increases the costs of a business causing an inward shift in supply. The vertical distance between the pre-tax and the post-tax supply curve shows the tax per unit. With an indirect tax, the supplier may be able to pass on some or all of this tax to the consumer by raising price. This is known as shifting the burden of the tax and this depends on the elasticity of demand and supply.

Consider the two charts above.

• In the left hand diagram, the demand curve is drawn as price elastic. The producer must absorb the majority of the tax itself (i.e. accept a lower profit margin on each unit sold). When demand is elastic, the effect of a tax is still to raise the price – but we see a bigger fall in equilibrium quantity. Output has fallen from Q to Q1 due to a contraction in demand.
• In the right hand diagram, demand is drawn as price inelastic (i.e. Ped <1 over most of the range of this demand curve) and therefore the producer is able to pass on most of the tax to the consumer through a higher price without losing too much in the way of sales. The price rises from P1 to P2 – but a large rise in price leads only to a small contraction in demand from Q1 to Q2.

Example: Will price cuts work for Sony?
Sony is cutting the price of its PlayStation 3 gaming console by nearly a fifth, hoping to jump-start sales of a five-year old device losing ground to Microsoft's Xbox. The price tag on the 160 GB version has fallen to £200 in the UK and from €299 to €249 in Europe

News reports, Aug 2011.

The usefulness of price elasticity for producers

Firms can use PED estimates to predict:

• The effect of a change in price on the total revenue & expenditure on a product.
• The price volatility in a market following changes in supply – this is important for commodity producers who suffer big price and revenue shifts from one time period to another.
• The effect of a change in an indirect tax on price and quantity demanded and also whether the business is able to pass on some or all of the tax onto the consumer.
• Information on the PED can be used by a business as part of a policy of price discrimination. This is where a supplier decides to charge different prices for the same product to different segments of the market e.g. peak and off peak rail travel or prices charged by many of our domestic and international airlines.
• Usually a business will charge a higher price to consumers whose demand for the product is price inelastic

Price elasticity of demand and changing market prices

The price elasticity of demand will influence the effects of shifts in supply on price and quantity in a market. This is illustrated in the next two diagrams.

In the left hand diagram below we have drawn a highly elastic demand curve. We see an outward shift of supply – which leads to a large rise in equilibrium price and quantity and only a relatively small change in the market price.

In the right hand diagram, a similar increase in supply is drawn together with an inelastic demand curve. Here the effect is more on the price. There is a sharp fall in the price and only a relatively small expansion in the equilibrium quantity.

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