The formula for price elasticity of demand (PED) is

% change in quantity demanded

% change in price of the good

So if the price of osteopathy rose by 10% and the quantity bought fell by 5% then the PED would be –5%/+10% = -0.5. This tells us that demand for osteopathy is not particularly sensitive to changes in price. It is what economists call price inelastic. Take another example, if the price of eye tests fell by 20% and the quantity of eye tests bought rose by 30% then the value of PED would be +30%/-20% = -1.5. In this case the demand for eye tests is price elastic, i.e. sensitive to changes in price.

Notice several things about PED. First, the value of PED is always negative reflecting the inverse relationship between price and quantity demanded. Second, PED is just a number, it is not expressed in terms of any particular units.

How do we know whether demand is elastic or inelastic? The rule is:

Demand is price inelastic whenever the % change in price leads to a smaller % change in quantity demanded. This gives PED values between 0 and –1.

Demand is price elastic whenever the % change in price leads to a larger % change in quantity demanded. This gives PED values between –1 and –infinity.

Price elasticity of demand allows us to predict what will happen to spending when price changes. Take the example of the increase in the price of osteopathy used above. As the price of osteopathy rises, people will buy fewer treatments but will they spend less? Suppose the price of a treatment rose from £20 an hour to £22 (a price increase of 10%). At £20 an hour, consumers were buying 1,000 treatments per week and spending £20,000. After the price rise, they bought 950 a week (a fall of 5%) but their spending had risen to £20,900 (= 950 x £22). So the answer in this case is no. People spend more on osteopathy after the price rise because the percentage increase in price is greater than the percentage fall in sales volume. So although osteopaths sell fewer treatments, the higher price of each treatment more than offsets the lost quantity of treatments sold. This gives us a general rule:

If PED is inelastic, a rise in price will lead to people spending more while a fall in price will lead to people spending less;

If PED is elastic, a rise in price will lead to people spending less while a fall in price will lead to people spending more.

Price elasticity of demand allows economists to analyse and predict the effect of changes in prices on different markets. We can see an example of this by looking at the debate over cost sharing in health care.

Cost sharing is the term used to describe different forms of direct charging for health care services. Increasingly, direct charging is seen as a way of reducing demand but also as a way of raising revenue. How effective is this policy? For instance, in the UK, many people have to pay prescription charges, that is they have to pay a certain amount every time they want to have a prescription dispensed. What has been the effect of this charging? Estimates made by Hughes and McGuire have indicated that demand for prescriptions is rather price inelastic with a mean value of -0.32. This would suggest that prescription charges would be an effective way of raising revenue but not have a great effect on the level of demand. Hughes and McGuire calculated, for instance, that the rise in prescription charges from £3.75 in 1992 to £4.25 in 1993 would have resulted in the generation of an estimated £17.3 million in extra revenue but led to a fall of 2.3 million in the number of prescriptions dispensed. However, their research also suggests that demand for prescriptions is becoming more price elastic as time passes. They found that PED was –0.125 in 1969, -0.22 in 1980, -0.68 in 1985 and –0.94 in 1991. This suggests that raising prescription charges is now likely to raise less revenue but lead to greater reductions in use of prescribed medicines than it did in the past.

The concept of elasticity can be applied to the impact of both income and changes in the prices of other goods on quantity demanded. Income elasticity of demand (YED) measures how demand reacts to changes in income.

The formula for income elasticity of demand is:

% change in quantity demanded

% change in income

If the result is positive then the goods are normal, if it is negative then they are inferior. All the evidence suggest that health care is not only a normal good but that it is income elastic, i.e. rising income leads to a greater % rise in demand for health care.

Cross price elasticity of demand (XED) measures how demand reacts to changes in the price of other goods.

The formula for cross price elasticity of demand is:

% change in quantity demanded of main good

% change in price of other good

If cross price elasticity of demand is positive then this indicates that the goods are substitutes. If it is negative then the goods are complements.

Finally, the concept of elasticity can be applied to supply. Price elasticity of supply (PES) measures how sensitive quantity supplied is to a change in the price of the good.

The formula for price elasticity of supply is:

% change in quantity supplied

% change in price of the good

Price elasticity of supply is always positive, reflecting the positive relationship between price and quantity supplied. PES becomes more elastic over time. This reflects the time it takes to switch resources into a market. For instance, in health care the PES is likely to be fairly inelastic in the short run but much more elastic in the long run. Even if price rises significantly it will take time for firms to react and to produce more health care. For instance, to deliver more health care new hospitals will need to be built or existing hospitals extended and extra doctors and nurses will need to be trained. All of this takes time.

The concept of elasticity has helped to make our market theory more sophisticated. However, the model still suffers from being rather static.