## Price Elasticity of Demand

The quantity demanded of a good is affected by changes in the price of the good, changes in prices of other goods, changes in income and changes in other relevant factors. Elasticity is a measure of just how much the quantity demanded will be affected by a change in price, income, price of other goods etc..

If the price of steak increases by 1% and the quantity demanded then falls by 20% we can see there has been a very large drop in the amount demanded in comparison to the change in price. The price elasticity of demand for steak is said to be high.

If the quantity of steak demanded was to only fall by 0.01%, we can see this is a fairly insignificant fall in quantity in response to the 1% increase in price. In this case the price elasticity of demand for steak is low.

It can be calculated using the following formula:

percentage change in quantity demanded
percentage change in price

(To help you remember quantity is on top of price think of the football team QPR).  The table below shows a number of calculations of price elasticity of demand.

 % change in price % change in quantity elasticity 10 20 2 50 25 0.5 7 28 4 9 3 0.33

Elasticity figure are actually negative, but economists forget this point in the name of simplicity.

Elastic and Inelastic Demand

Different values of price elasticity are given special names:

·        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% or 2 and the demand for CDs is therefore elastic.

·        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% rise in price by rail company resulted in a 1% fall in train journeys made then price elasticity would be 1% / 10% or 0.1 and the demand for rail journeys is therefore inelastic.

Special Cases of Elasticity

·        Demand is infinitely inelastic if the value of elasticity is zero (zero divided by any number). Any change in price would have no effect on the quantity demanded.

·        Demand has unitary elasticity if the value of elasticity is exactly 1. This means that a percentage change in the price of a good will lead to an exact and opposite change in the quantity demanded. For example a good would have unitary elasticity if a 10% increase led to a 10% fall in the quantity demanded.

·        Demand is infinitely elastic if the value of elasticity is infinity (any number divided by zero). A fall in price would lead to an infinite increase in quantity demanded (i.e. increasing from zero), whilst an increase in price would lead to the quantity demanded falling to zero.

The case of unitary elasticity is the curve (known as a rectangular hyperbola). The perfectly inelastic curve looks like an I and the perfectly elastic curve looks like an E (without the top!).

Knowing these special cases it makes it easier to spot whether a demand curve is relatively elastic or inelastic. The demand curve on the left is relatively elastic (as it looks more like the E) and the demand in the centre is relatively inelastic (as it looks more like an I).

Changes in Elasticity Along the Demand Curve

We mentioned earlier that a good is infinitely elastic if a fall in price leads to an infinite rise in quantity. This must occur if quantity was previously zero and rises to in response to a fall in price - this can be seen at the top of the demand curve.

The opposite occurs at the bottom of the demand curve leading to an elasticity of zero.

Also shown on the diagram is the point where elasticity is unitary (equal to one), this by definition occurs exactly halfway along the demand curve.

If elasticity is infinite where the demand curve crosses the price axis, but is equal to zero when it crosses the quantity axis, then elasticity must change as you move along the demand curve. Demand is price inelastic if it has a value less than 1 and elastic if greater than 1, these regions are shown above.

Importance of elasticity for a business

·        If the business is producing on the price elastic section of the demand curve, a small percentage change in price leads to a large percentage change in quantity demanded. Lowering the price will have the effect of increasing total revenue and raising the price will decrease total revenue, e.g., if the price of Mars Bars increased by 25% ceteris paribus, we would expect their sales to fall dramatically as consumers shift to other chocolate bars. This would have the effect of reducing their total revenue.

·        If the business is producing on the unitary price elasticity section of the demand curve, small changes in price do not change total revenue as a percentage change in price will be exactly offset by an inverse change in quantity.

·        If the business is producing on the price inelastic section of the demand curve, a small percentage change in price leads to a small percentage change in quantity demanded. This will have the effect of decreasing total revenue when the price is increased and increasing total revenue when the price falls. For example if a firm invented a miracle cure for the common cold and decided upon a price of 50p a pack. The firm sold 10 million packs in the first year of sales. Next year they decide to raise prices by 25% and sales fall to 9 million (10% fall), the level of sales have dropped, but the total revenue has increased.

It is important to note that the revenue maximising level of production occurs when elasticity is unitary, but this isn't necessarily the level where profit is maximised. We don't know the firm's costs at different levels of output. Furthermore elasticities are notoriously difficult to calculate and errors in the elasticity figures could lead to incorrect pricing decisions.

Factors Affecting the Price Elasticity of Demand

Two factors are usually highlighted by economists:

·        The availability of substitutes. If a product has many substitutes then its price elasticity is likely to be high. An increase in price will lead to consumers shifting demand to one of its many substitutes (e.g., chocolate bars). However if the good has few substitutes, consumers will find it harder to replace that good, so its price elasticity is likely to be low (e.g. salt).The more widely a product is defined the fewer substitutes it is likely to have. Spaghetti has many substitutes, but food has none.

·        Time. The longer the period of time, the more price elastic is the demand for the product. For example if the price of leaded petrol was to increase by 50% my demand for it would not change in the shirt run. However as time goes on I would change my car to one that used unleaded petrol, therefore in the longrun elasticity becomes greater.