# Price Elasticity of Demand

As discussed above, the price elasticity of demand is a measure of how the quantity demanded will change for a unit change in price. This is an important aspect of the demand curve of a product, and hence the demand behaviour of the product.

The price elasticity of demand is found by dividing a certain change in quantity by the change in price which caused it. The changes are always proportionate, or percentage based, meaning that the elasticity of demand has no units and hence does not depend on the units of quantity or demand. For example, if a 1% increase in price caused a 2% decrease in quantity, the price elasticity of demand would be approximately -2. It would not be exactly -2, as the elasticity uses the average of the price and quantity values according to the following equation:

(Q2 – Q1) / ((Q1 + Q2) / 2)
(P2 – P1) / ((P1 + P2) / 2)

So, if price rose by 1%: from 100 to 101, and quantity fell by 2%: from 100 to 98, the price elasticity of demand would be:

(98 – 100) / ((100 + 98) / 2)
(101 – 100) / (100 + 101) / 2)

= -2 / 99
1 / 100.5

= -2.03

This value is defined as the arc elasticity of demand, because it is calculated over a certain section, or arc, of the demand curve. The average values are used for quantity and price because this way the elasticity will be the same regardless of what the starting and finishing prices are.

Whilst the arc elasticity is relatively easy to calculate, for non linear demand curves the arc elasticity is not completely accurate. As such, the price elasticity of demand may need to be calculated for a certain point on the demand curve. This will need to be done using differentials, and will provide a figure for the point elasticity. However, whilst this figure is accurate, it will only be valid for a single point on the curve.

Relative measures of elasticity

There are specific definitions given to each range of values of the price elasticity of demand:

Elasticity = - ∞

This is referred to as perfectly elastic demand: the quantity demanded will vary widely, and there will only be one possible price at which there is any demand. Whilst this may not be realistic in a market economy, it can be seen for things such as TV licenses. Here, there is a fixed price, and hence no one will pay more or less than the price: anyone who attempts to sell a TV license for more would not have any customers.

-1 > Elasticity > - ∞

This is referred to as relatively elastic demand, because any change in price causes a proportionately larger change in quantity. For example, the demand for newspapers is relatively elastic, because there are a large number of alternative sources from which people can obtain news. Therefore, if the price doubles, quantity is likely to fall by more than half as people switch to using the internet or TV for new. This helps to explain the rise in popularity of free newspapers. In addition, when demand is relatively elastic, and increase in price will cause a fall in revenue, as the quantity demanded will fall by a greater amount.

Elasticity = 1

This is referred to as being unitary elasticity, as a certain percentage change in price creates the same percentage change in quantity demanded. This implies that any change in price will not alter the revenue generated.

0 > Elasticity > -1

This is referred to a relatively inelastic demand, because the percentage change in quantity will be smaller than the percentage change in price. As a result, any increase in price will result in an overall increase in revenue as the quantity demanded will fall by less than the price rises.

Elasticity = 0

This is referred to as perfectly inelastic demand, which would result in a vertical demand curve. In practice this is unlikely; however some critical medical treatments come close to achieving it. For example, the latest treatments for cancer are often sold at very high prices because people often need them to survive, hence they are willing to pay large amounts of money for them and the quantity simply depends on how many people have the disease.

The main use of the price elasticity of demand is in determining how quantities and revenues are likely to change for a given product, thus enabling companies to maximise their revenue and profits through pricing. For example, if a company manufacturing TVs works out that the price elasticity of demand for their products is -1.2, then they know that raising the price will cause a fall in revenue. As such, the company is unlikely to pursue this as a strategy. However, by reducing the quantity of TVs demanded, the company can also reduce their manufacturing costs. Hence, even though the revenue may fall, the cost savings may mean that profits increase

When considering the price elasticity of demand, and particularly when considering using it in pricing, it is important to understand the various factors which can influence the demand curve. These include:

• The availability of substitutes: a wider array of substitutes increases the price elasticity of demand, as in the example of the newspaper market.
• Whether the product is a necessity or a luxury: necessary products, such as medicines, tend to be more inelastic that luxury products
• The proportion of income that the item will take up: a product which takes up more of consumer’s income will tend to be more elastic, such as salmon being more elastic that tuna
• The time period of any changes: price elasticity will increase in the long term as customers will have longer to adjust their consumption patterns. For example, a rise in petrol prices will not have a great impact in the short term, as many people depend on cars. However, if it persists for a long time the demand will fall as people switch to using public transport
• Whether the price change is permanent or temporary: one off sales will increase the quantity sold on that day by more than a permanent price reduction
• The existence of psychological price points: changing the price from £5 to £4.99 will have a greater impact that from £4.99 to £4.98. Similarly, a greater impact will occur if a price moves from being above that of a substitute good to being below it, thus making the good cheaper than its substitute

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