Measuring elasticity

DMU (the law of Diminishing Marginal Utility) tells us that demand curves will always slope downwards. But even though all demand curves slope downwards, they will do so to different degrees. The elasticity of an economic variable refers to its responsiveness to changes. Therefore, the price elasticity refers to the responsiveness of quantity demanded to changes in price, and reflects the slope of the demand curve. There are several ways to calculate the price elasticity of demand, but generally speaking we can divide the percentage change in quantity demanded by the percentage change in price. This will always give us a negative number (due to the first law of demand) and is is therefore conventional to just report the absolute value. If the elasticity is greater than 1 (i.e. changes in price lead to an even bigger change in quantity demanded) we can label it an elastic good. If the elasticity is between 0 and 1 (i.e. the change in price is proportionally bigger than the resulting change in quantity demanded) then it is inelastic.

The formula for price elasticity, where V = volume and P = price

For example, if Honda raised the price of a CR-V by 10%, there would probably be a large fall in quantity demanded as people switched to similar cars from other companies. Let’s imagine they sell 20% fewer cars as a result. In this case we can say that the price elasticity of demand is 2. If all SUV manufacturers raised their prices, we’d expect a less pronounced impact on demand. Maybe it would only fall by 5%. In which case we could say that the SUV market as a whole has a price elasticity of 0.5. The slope of the demand curve is only an indicator of the elasticity, and different sections of the demand curve will have different slopes. But generally speaking:

  • An elastic demand curve is very flat – small changes in price lead to large changes in quantity demanded.
  • An inelastic demand curve will be very steep – even a large change in price has a small change on quantity demanded.

Many factors will influence the price elasticity, but we can list some of the main ones:

The reason we’d expect the demand for Honda CR-Vs to be rea- sonably price elastic is because it’s a competitive market with plenty of close substitutes. This means it’s relatively easy for the substitution effect to kick in. But we can make two important points about substitutes. Firstly, substitutes are subjectively determined. In the same way that value is subjective, what constitutes a substitute is too. If I have fond memories of a previous Honda that I owned, I will be less sensitive to price changes than someone who has never driven one before. In the example above I then talked about the entire SUV market. But maybe you would be happy with a large saloon instead. While substitutes are subjectively determined, there are also degrees of substitutability. We can put these into four categories. Think of them as having the product at the core of expanding concentric circles, with broader and broader degrees of substitutability

If your spending on a certain good constitutes a small part of your budget, you’re unlikely to care much about price changes. Things like matches, toothpicks or salt are items we spend very little on over the course of a year and even if the price doubled you might not even notice.

The greater the hassle of finding alternatives, the less responsive your demand will be to price changes. The internet has made searching far cheaper than previously and makes it easier to compare prices from different sellers. This makes demand more responsive to price changes.

The second law of demand is that elasticity increases over time. We can demonstrate this by considering what happens when fuel prices rise. In the short term there may not be a massive effect, because it will be quite inelastic. But remember that we demand petrol to satisfy our pressing needs and some of these needs will be more pressing than others. If petrol becomes more expensive, we reduce unnecessary journeys and improve our energy efficiency by taking the golf clubs out of the boot, driving at 55 mph or only going to the supermarket once a week. The more time that passes, the easier it is to find substitutes. You start getting the train to work or get taxis when you need to go to the airport. Over the medium term, if fuel prices remain high you will consider buying a more fuel-efficient car. You wouldn’t go out and buy a new car as soon as fuel prices went up, but higher fuel prices could mean that fuel efficiency is something you consider when you do come round to replacing it. If more time elapses we might expect more permanent solutions. You may start working from home more or move house to reduce your commute. The bottom line is that substitutes are everywhere, but can be costly to find (after all, there’s a reason you’ve chosen to use a car in the first place). If the price of a good rises, then consumers will reduce their consumption by a larger amount in the long run than in the short run. This is because the more time you have to deal with a price change, the easier it is to adapt (and therefore the less costly it is). Elasticity increases over time and indeed rising fuel prices are market signals to encourage people to make this steady transition away from fossil fuels.

So far we’ve considered one type of elasticity, but there are two more to pay attention to:

Income elasticity is the responsiveness of demand to changes in income and is calculated by the percentage change in quantity demanded divided by the percentage change in income. Intuitively, you may think that the more income you have, the greater your demand will be. And for many goods this is the case. There would be a positive income elasticity, and we call them “normal” goods. (If the income elasticity is greater than 1, we tend to call them superior.) But think about low quality products that have obvious, higher standard alternatives. For example, you may buy reasonably cheap cuts of meat, or low quality wine. But if your income rises you may decide to switch to rump steak and champagne. For some goods you’ll therefore consume less if your income rises. In this case the income elasticity would be negative, and we label these goods as inferior.

The formula for income elasticity, where Q = quantity and I = income

Things like new cars, private education, donations to environmental causes and swimming pools are all highly income elastic. As income rises the demand for these goods expands even more rapidly and therefore spending on them rises as a proportion of income.

A really important implication of this is that recessions are not necessarily bad for business. This is because falling incomes will only lead to falling demand if the good is a normal one. If the good is inferior (i.e. the cheap cuts of meat or the cheap wine), demand will rise. Another implication is that economic growth is good for environmental protection. Indeed we can also think of workplace diversity, lower infant mortality and gender rights as normal goods and therefore pursuing economic growth (and rising incomes) will help deliver them by default.

Cross-price elasticity is the responsiveness of demand to changes in price of an alternative good and is calculated by dividing the percentage change in the quantity demanded of one good with the percentage change of price of another good.

If the cross-price elasticity is positive, it means that when the price of good X goes up, the demand for good Y will. This implies that the two goods are substitutes. We’ve discussed previously how consumers can respond to price changes by switching to an alternative and here’s how we determine the substitution effect. Substitutes are two goods that provide a similar function and typical examples include hamburgers and tacos, Coke and Pepsi, butter and margarine, ball point and felt tip pens. If the price of the former goes up, we’d expect people to switch to the latter.

The formula for cross price elasticity, where Qx = quantity of good X and Py = price of good Y

However, not all goods act as alternatives to each other. Some goods need to be used with another product. If the cross-price elas- ticity is negative, it means that if the price of Y goes up the demand for X will fall. This is because fewer people will demand Y and therefore fewer people will demand X. We call such goods comple- ments, and define them as goods that are consumed jointly. Typical examples include burgers and fries, hats and gloves, window frames and glass panels, cars and petrol. If the price of the former goes up, we’d expect people to buy less of both. Companies don’t have to make money across all product lines – they can give away things for free if they encourage the purchase of complementary goods.

Why do people in Maine eat cheap lobsters?

The Alchian–Allen effect, also known as the third law of demand, claims that if you add a per unit levy to the prices of two substitute goods, the relative consumption of the higher priced good will rise. This can be directly applied to travel expenses. Imagine that the price of a standard train ticket from London to Liverpool is £40, while a first-class ticket is £60. One way of viewing this is that the first class ticket is 1.5 times as expensive as travelling on standard. Now, imagine that the travel agent that makes the booking charges a flat rate of £10 per booking. The standard ticket is now £50, and first class is £70. The relative price of the first-class ticket has now fallen to 1.4 times standard. First-class travel has become relatively cheaper. Ceteris paribus, we would expect a shift from standard to first class.

This tweet demonstrates an ignorance of the Alchian-Allen effect: