Elasticity

Price Elasticity of Demand

Elasticity is a way of measuring how much buyers and sellers change their behaviour when prices change.

Suppose a gas station increases its price from $3.50 to $4.00 a gallon. Weekly sales fall from 10,000 to 9,500 gallons. This is a price increase of 14.3% (using the midpoint method) and a quantity decrease of only 5.1%. The relationship between these two percentages is what economists refer to as price elasticity of demand (Ed):

Ed = % change in quantity demanded / % change in price

So, in this case, Ed = -5.1% / 14.3% = -0.36. The absolute value of price elasticity of demand is 0.36, and this tells us demand is inelastic. People who drive will complain about gas prices, of course, but they'll still buy the gas they need to get to work.

The elasticity coefficient is always negative because demand curves go down as you move along them. Economists just ignore the negative sign and use the absolute value of the coefficient. A common mistake people make is thinking a straight-line demand curve has a constant elasticity — it's true the slope doesn't change, but elasticity relies on the price/quantity ratio (P/Q), and that ratio is different at every point on the line.

For AP exam calculations, you're expected to use the midpoint method, and the reason is that it avoids getting different answers depending on whether you start with the original or the new price and quantity. The formulas are: %ΔQ = (Q2 - Q1) / ((Q1 + Q2)/2), and %ΔP = (P2 - P1) / ((P1 + P2)/2).

Elastic, Inelastic, and Unit Elastic

Elasticity is categorized as elastic, inelastic, or unit elastic. Novo Nordisk increased the price of insulin by 15 percent, and sales didn't change much, because people with diabetes require the medication no matter if it costs $300 or $350. Louis Vuitton, however, raised their handbag prices by 15 percent, and a lot of customers decided not to buy. This difference in reaction is what distinguishes elastic and inelastic demand.

If |Ed| is greater than 1, demand is elastic: the quantity demanded changes by a larger percentage than the price. People have other options (substitutes), can delay the purchase, or can simply do without.

If |Ed| is less than 1, demand is inelastic; quantity doesn't really change. Think of gasoline, electricity, and prescription drugs: people have to pay the higher price because there's no easy alternative.

If |Ed| equals 1, demand is unit elastic and the percentage change in price exactly matches the percentage change in quantity. This happens only at the middle point of a straight-line demand curve.

And then there are the extremes. Perfectly elastic demand (|Ed| = infinity) is a horizontal line, and any price increase will cause demand to drop to zero. Perfectly inelastic demand (|Ed| = 0) is a vertical line: price can go up and down, but the quantity demanded never changes.

The Total Revenue Test

Let's consider total revenue. A bookstore sells 500 books at $12 each for a total of $6,000. Should the owner raise the price to $14? Total revenue (TR) = P × Q. When you increase the price, price and quantity have opposing effects on revenue. Elasticity decides which one is stronger.

When demand is elastic (|Ed| > 1), lowering the price will increase revenue. The big jump in quantity bought will more than make up for the lower price per item. In fact, Netflix reduced the cost of its basic plan from $9.99 to $6.99 in some areas in 2023 and got enough new subscribers to increase revenue in those regions. If you raise the price in an elastic situation, customers will leave more quickly than the extra money from the higher price will bring in.

In the inelastic range (|Ed| < 1), the situation is reversed. Lowering the price will decrease revenue because quantity doesn't go up much, and you're getting less money for each of roughly the same number of items. Pharmaceutical companies are a perfect example, and that's why they can increase prices every year and still see their revenue increase.

Revenue is at its highest point at unit elasticity (|Ed| = 1). Any price change in either direction will lower total revenue.

Determinants of Elasticity

Five things mainly explain why elasticity varies between different goods, and the AP exam likes to ask you to identify which of these apply in a specific case.

The biggest factor by far is how many substitutes are available. Dasani has to compete with Aquafina, Fiji, tap water and many store brands, so demand for Dasani is elastic. Your local electricity company has almost no competition, so demand for their electricity is inelastic. It's that straightforward.

Also important is whether the item is a necessity or a luxury. No one is looking for the best price on an ambulance. But a $300 price increase for a fancy watch? People will postpone the purchase, or abandon it. Things you absolutely have to have keep customers, but things that are a treat allow them to easily stop buying.

Budget share is important too. If table salt goes up 10% (about 40 cents a year) you won't care, but a 10% increase in rent dramatically changes your monthly budget. Items that are a larger part of your income cause a much bigger reaction.

Time horizon makes a difference. When gas got much more expensive in 2022, people kept driving (they needed to!). However, over the following two years, electric vehicle sales went up 35% and more people started using buses and trains. People found alternatives over time, which they hadn't had at first, and so demand became more responsive.

Fifth, how you define the market is key. People will always buy "food" so demand for it doesn't change much. But "organic blueberries from the farmer's market on Elm Street" is a different story, as there are many other places to get blueberries.

Cross-Price and Income Elasticity

The relationship between different items, along with your income, needs to be measured. If Pepsi increases their price by 10%, Coke sales go up by 7%. If a printer costs $50 less and ink cartridge sales increase, these connections between goods need their own type of elasticity.

To measure how the quantity of one good changes in relation to the price of another (cross-price elasticity of demand) you calculate the percentage change in the quantity demanded of good X divided by the percentage change in the price of good Y.

Exy = % change in Qd of good X / % change in price of good Y

The plus or minus sign tells you the category. If the result (Exy) is positive, the goods are substitutes (Coke and Pepsi, Uber and Lyft) — if one gets pricier, people switch to the other. A negative Exy means they are complements (printers and ink, hot dogs and buns) — cheaper printers mean more ink is bought. A result close to zero means the goods aren't really linked.

Looking at changes in income instead of price, income elasticity (Ei) is the percentage change in quantity demanded divided by the percentage change in income.

Ei = % change in Qd / % change in income

A positive Ei indicates a normal good. Within that, if Ei is greater than 1, it's a luxury (demand increases more quickly than income, like international travel or fancy clothes) and if Ei is between 0 and 1, it's a necessity (demand grows, but not as fast, such as food and utilities). A negative Ei means it's an inferior good: as people earn more, they buy less of it. People swap cheap pasta for Barilla when they get a raise.

On the AP exam, you're expected to be able to look at a number like -0.6 or +2.3 and instantly categorize the item.

Elasticity and the AP Exam

Around 15-20% of the AP Microeconomics exam covers elasticity, and the questions are pretty similar each year.

You'll need to work out the absolute value of price elasticity of demand (|Ed|) using the midpoint method with two price and quantity points. Then, using the number you get, say if demand is elastic, inelastic, or unit elastic. You also have to work out what happens to a company's total revenue after they change their price. Finally, you'll need to explain why one thing's demand is more flexible than another, by mentioning the reasons discussed.

Questions asking you to write a longer answer (free-response prompts) usually include elasticity as part of a larger problem. For example, a tax is added to something and you need to say how much of the cost the buyer and seller pay — this all depends on how flexible demand and supply are. Or, a company with inelastic demand raises its price and you have to explain why their revenue went up, not down.

Of all the things you have to do, the total revenue test and the midpoint formula are the most important. If you get the calculations right, the logical explanation is usually pretty easy.

Worked Example

A coffee shop sells large lattes for $5, selling 200 a week. The owner raises the price to $6, and they only sell 160 a week. Let's figure out how much demand changes when the price changes (that's the price elasticity of demand).

Percentage change in quantity (using the midpoint method): it's (160 - 200) divided by the average of 200 and 160, which is 180. This gives a %ΔQ of -40/180 or -22.2%.

Percentage change in price: (6 - 5) divided by the average of 5 and 6, which is 5.5, giving us 1/5.5 or 18.2%.

Elasticity coefficient: Ed = -22.2% divided by 18.2% and comes to -1.22. Ignoring the negative sign, we get 1.22. Because 1.22 is greater than 1, demand is elastic in this price range. That means people significantly reduce their purchases when the price goes up.

Let's check the total revenue. Before the price went up, it was $5 × 200 = $1,000. After the increase, it's $6 × 160 = $960. Revenue went down by $40, and as the rule for elastic demand says it would, a price rise actually reduced total revenue because the fall in the amount sold was greater than the price increase. The business owner would have done better to not change the price.