Quantity of tickets

Figure 2. The Demand for Football Tickets

For given prices of related goods and consumer incomes, higher ticket prices reduce the quantity of tickets demanded.

How should we measure the responsiveness of the quantity of tickets demanded to the price of tickets? One obvious measure is the slope of the demand curve. The downward slope of the demand curve shows that quantity demanded increases as the price of a good falls. Each price cut of £ 1 leads to 8000 extra ticket sales per game.

Suppose, however, that we wish to compare the price responsive ness of football ticket sales with the price responsiveness of the quantity of care demanded: clearly, £ 1 is a trivial cut in the price of a car and will have a negligible effect on the quantity of cars demanded.

When commodities arc measured in different units it is often best to examine the percentage change, which is unit-free. This suggests that we think about the effect of a 1 per cent price cut on the quantity of care and football tickets demanded. Similarly, it is not the absolute number of cars or tickets we should examine but the percentage change in quantity demanded. Not only does this solve the problem of comparing things measured in different quantity units, it also takes account of the size of the market. Presumably an extra sale of 8000 tickets is more important when ticket sales arc 4000 than when they number 40000.

Thus we reach the definition of the price elasticity of demand, which economists use to measure responsiveness to price changes.

The price elasticity of demand is the percentage change in the quantity of a good demanded divided by the corresponding percentage change in its price.

Although we shall shortly introduce other demand elasticities – the cross price elasticity and the income elasticity — the (own) price elasticity is perhaps the most frequently used of the three. Whenever economists speak of the demand elasticity they mean the price elasticity of demand as it has been defined above.

If a 1 per cent price increase reduces the quantity demanded by 2 per cent, the demand elasticity is – 2. Because the quantity falls 2 per cent, we express this as a change of — 2 per cent, then divide by the price change of 1 per cent (a price rise) to obtain —2. If a price fall of 4 per cent increases the quantity demanded by 2 per cent, then the demand elasticity is — 1/2, since the quantity change of 2 per cent is divided by the price change of – 4 per cent. Since demand curve slopes down, we arc either dividing a positive percentage change in quantity (a quantity rise) by a negative percentage change in price (a price fall) or dividing a negative percentage change in quantity (a quantity fall) by a positive percentage change in price (a price rise). The price elasticity of demand tells us about movements along a demand curve and the demand elasticity must be a negative number.

For further brevity, economists sometimes omit the minus sign. It is easier to say the demand elasticity is 2 than to say it is -2. Whenever the price elasticity of demand is expressed as a positive number, it should be understood (unless there is an explicit warning to the contrary) that a minus sign should be added. Otherwise, we should be implying that demand curves slope upwards, a rare but not unknown phenomenon.