Chapter 6 — Elasticity

How Responsive Are Buyers and Sellers?

Chapter 5 told you that when prices rise, the quantity demanded falls — the law of demand. It did not tell you by how much. The size of the response matters enormously, both for understanding markets and for designing policy. If gasoline prices rise by 20%, do people drive 20% less? 5% less? 1% less? Each of these is consistent with the law of demand. They imply very different things about how the gasoline market works, who bears the burden of a gas tax, how long supply disruptions hurt the economy, and whether higher prices will actually reduce consumption enough to matter for climate policy.

The concept that captures the size of the response is elasticity. Elasticity is the most useful number in microeconomics. It is also the bridge from the qualitative supply-and-demand framework of Chapter 5 to the quantitative predictions you need to make real decisions. By the end of this chapter, you should be able to compute elasticities, classify goods as elastic or inelastic, predict who pays a tax based on the elasticities of supply and demand, and understand why some goods (insulin, cigarettes, drinking water) are very different from others (restaurant meals, vacation flights, brand-name clothing) in how their markets respond to price changes.

The chapter is more numerical than Chapter 5 — you will be doing arithmetic — but the arithmetic is genuinely simple. Take your time with the formula in §6.1, and the rest of the chapter follows.

6.1 Price elasticity of demand

Price elasticity of demand is a measure of how much the quantity demanded responds to a change in price. Formally:

Price elasticity of demand = % change in quantity demanded ÷ % change in price

If the price of a good rises by 10% and the quantity demanded falls by 20%, the elasticity is −20 ÷ 10 = −2. The minus sign reflects the law of demand (price up, quantity down) and is conventional in economic discussions. We usually drop the minus sign and just refer to the elasticity as 2.

If the price rises by 10% and the quantity demanded falls by only 5%, the elasticity is 5 ÷ 10 = 0.5.

The interpretation:

• Elasticity > 1: elastic. A given percentage change in price produces a larger percentage change in quantity. Buyers are very responsive. Examples: restaurant meals, vacation flights, brand-name clothing, second cars, name-brand food versus generics.
• Elasticity = 1: unit elastic. A given percentage change in price produces an equal percentage change in quantity.
• Elasticity < 1: inelastic. A given percentage change in price produces a smaller percentage change in quantity. Buyers are not very responsive. Examples: insulin, water, salt, gasoline (in the short run), cigarettes for an addicted smoker.

The two extreme cases:

• Perfectly elastic (elasticity = ∞): any price increase causes quantity demanded to drop to zero. The demand curve is horizontal. (Rare in real markets, but a useful theoretical limit.)
• Perfectly inelastic (elasticity = 0): quantity demanded does not respond to price at all. The demand curve is vertical. (Also rare, but think of a one-time payment for an immediate-life-saving treatment when no substitute exists.)

The midpoint formula

When you calculate percent changes between two points, the answer depends on which point you treat as the "starting" price. To avoid this asymmetry, economists use the midpoint formula:

% change in quantity = (Q₂ − Q₁) / [(Q₁ + Q₂)/2]

% change in price = (P₂ − P₁) / [(P₁ + P₂)/2]

Elasticity = % change in quantity ÷ % change in price (in absolute value)

The midpoint formula uses the average of the two prices and the average of the two quantities as the denominator, so the answer is the same whether you go from P₁ to P₂ or from P₂ to P₁.

Worked example. Price rises from $10 to $12. Quantity demanded falls from 100 units to 80 units.

% change in quantity = (80 − 100) / [(100 + 80)/2] = −20 / 90 = −0.222 = −22.2%

% change in price = (12 − 10) / [(10 + 12)/2] = 2 / 11 = 0.182 = 18.2%

Elasticity = 22.2% / 18.2% = 1.22

This good is elastic (elasticity > 1). A 1% price increase causes a 1.22% drop in quantity demanded.

6.2 Why does elasticity vary across goods?

Different goods have very different elasticities. Insulin is highly inelastic; airline travel is highly elastic; gasoline is somewhere in between. What determines where a good falls?

There are four main determinants.

Determinant 1 — Availability of substitutes. The more (and better) substitutes a good has, the more elastic its demand. If the price of Coca-Cola rises, consumers can easily switch to Pepsi, store-brand cola, water, juice, or coffee. Demand for Coca-Cola is elastic. If the price of insulin rises, type-1 diabetics have no substitute — insulin is required for life. Demand for insulin is highly inelastic.

This is the most important determinant. The narrower the definition of the good, the more substitutes exist (Coca-Cola has Pepsi as a near-substitute), and the more elastic demand becomes. The broader the definition (cola in general, all sweetened drinks, all beverages), the fewer substitutes, and the more inelastic demand becomes.

Determinant 2 — Necessity vs. luxury. Necessities tend to have inelastic demand (water, basic food, shelter, healthcare). Luxuries tend to have elastic demand (vacations, designer clothes, expensive cars). The reasoning: when something is essential, you keep buying it even at higher prices because you can't easily live without it. When something is optional, a higher price gives you a clear out — just don't buy it.

This determinant interacts with the first one. "Necessity" is partly a function of "lack of substitutes." Water is a necessity in part because nothing substitutes for hydration; insulin is a necessity in part because no other drug does what it does for type-1 diabetics.

Determinant 3 — Time horizon. Demand is more elastic in the long run than in the short run. When gas prices rise, you can't immediately buy a more fuel-efficient car or move closer to work. In the short run, your demand for gas is fairly inelastic — you keep driving more or less the same amount. Over a few years, though, you can replace your car, change jobs, move, switch to public transit, or reorganize your life around lower gas consumption. Long-run demand for gas is much more elastic than short-run demand.

This is one of the most important features of elasticity for understanding economic policy. A short-run analysis of the effect of a gas tax will see small consumption responses; a long-run analysis will see much larger ones. The two are not contradictory; they're talking about different time horizons.

Determinant 4 — Share of the budget. Goods that take up a large share of your budget tend to have more elastic demand than goods that take up a small share. If the price of toothpicks rises by 50%, you probably don't even notice; toothpicks are a tiny fraction of your spending. If the price of housing rises by 50%, you respond significantly because housing is a large fraction of your budget.

The reasoning: a small-share good's price change is inconsequential to your overall financial situation, so you have no strong reason to adjust. A large-share good's price change reshapes your budget meaningfully, forcing real adjustments.

6.3 Income elasticity

Price elasticity is not the only kind. Income elasticity of demand measures how much the quantity demanded responds to a change in income.

Income elasticity = % change in quantity demanded ÷ % change in income

Income elasticity can be positive or negative.

• Positive income elasticity (normal goods): as income rises, quantity demanded rises. Most goods are normal. Income elasticity above 1 means a luxury — quantity demanded rises faster than income (vacations, restaurant meals, fancy electronics). Income elasticity between 0 and 1 means a necessity — quantity demanded rises but slower than income (food, basic clothing, utilities).
• Negative income elasticity (inferior goods): as income rises, quantity demanded falls. Examples: ramen noodles, used cars, generic-brand groceries, second-hand clothing. As people get richer, they buy less of these things and substitute toward higher-quality alternatives.

Knowing the income elasticity of a good tells you what will happen to its market when the economy grows or shrinks. In a recession (incomes fall), demand for normal goods falls but demand for inferior goods rises. This is why secondhand stores sometimes do better in recessions.

6.4 Cross-price elasticity

Cross-price elasticity measures how much the quantity demanded of one good responds to a change in the price of another good.

Cross-price elasticity of A with respect to B = % change in quantity demanded of A ÷ % change in price of B

Cross-price elasticity tells you whether two goods are substitutes or complements:

• Positive cross-price elasticity: the goods are substitutes. When the price of B rises, consumers switch to A, so quantity of A demanded rises. Coffee and tea. Beef and chicken. Coke and Pepsi.
• Negative cross-price elasticity: the goods are complements. When the price of B rises, consumers buy less of B and less of A (because they're consumed together). Hamburgers and hamburger buns. Cars and gasoline. Tennis rackets and tennis balls.

Cross-price elasticity is also useful for thinking about market definition. Antitrust regulators sometimes use cross-price elasticity to decide whether two firms are competitors or not. If a small price increase by Firm A causes consumers to switch to Firm B, then A and B are substitutes (and competitors); if not, they're not in the same market.

6.5 Price elasticity of supply

The mirror concept: how much does the quantity supplied respond to a change in price?

Price elasticity of supply = % change in quantity supplied ÷ % change in price

The interpretation parallels demand. Elasticity > 1 is elastic supply (sellers respond strongly to price changes); < 1 is inelastic supply; = 1 is unit elastic.

The determinants of supply elasticity are different from the determinants of demand elasticity. The main one is time horizon: supply is much more elastic in the long run than in the short run. In the short run, sellers can only adjust by working their existing capacity harder or holding inventory. In the long run, they can build new factories, hire and train workers, expand land use, develop new technologies. Short-run supply elasticity is small; long-run supply elasticity is large.

Other determinants of supply elasticity: - Availability of inputs. If the inputs needed to produce more are abundant and cheap, supply is more elastic. If they're scarce and expensive (or fixed in supply, like beachfront land), supply is less elastic. - Mobility of factors. Workers and capital that can easily move into the industry create more elastic supply. Specialized factors that are hard to redirect create less elastic supply. - Spare capacity. Industries with spare capacity can ramp up quickly (elastic short-run supply). Industries running at full capacity cannot (inelastic short-run supply).

6.6 Tax incidence (a preview of Chapter 7)

One of the most useful applications of elasticity is figuring out who actually bears the burden of a tax. The intuitive answer — "whoever the law says has to pay it" — is usually wrong. The economic answer is: the side of the market with the more inelastic curve bears more of the burden.

The reasoning is intuitive once you see it. If demand is highly inelastic, buyers will keep buying even at much higher prices, so sellers can pass most of the tax onto buyers as a higher price. If demand is highly elastic, buyers will leave the market at any price increase, so sellers have to absorb most of the tax themselves to keep buyers around. The same logic works in reverse for supply.

Two extreme cases.

Case 1 — Inelastic demand, elastic supply. Imagine a tax on cigarettes. Demand for cigarettes is highly inelastic (addiction). Supply is fairly elastic (cigarette factories can produce more or less without much adjustment cost). Result: most of the tax falls on consumers as a higher price. This is what happens in real life — cigarette taxes are mostly paid by smokers, not by tobacco companies.

Case 2 — Elastic demand, inelastic supply. Imagine a tax on luxury yachts. Demand for luxury yachts is fairly elastic (lots of substitutes, very much a discretionary purchase). Supply is fairly inelastic (specialized boatbuilders, hard to redirect quickly). Result: most of the tax falls on producers (yacht builders), not on consumers. This is roughly what happened with the U.S. luxury tax of 1991 — the tax was supposed to hit rich consumers but ended up hitting luxury yacht builders, many of whom went out of business.

The general principle: the more inelastic side bears more of the tax burden, regardless of who legally writes the check. We will spend Chapter 7 on this in much more detail. For now, the takeaway is that elasticity isn't just an abstract number — it's the key to predicting who actually pays for any government policy that affects market prices.

6.7 Elasticity and total revenue

Elasticity also tells you what happens to total revenue (price × quantity) when the price changes. The relationship is critical for businesses thinking about pricing, for governments thinking about taxes, and for economists thinking about who gains and loses from price changes.

• If demand is elastic (elasticity > 1): a price increase reduces total revenue, because the quantity falls by more than the price rises. A price decrease increases total revenue.
• If demand is inelastic (elasticity < 1): a price increase raises total revenue, because the quantity falls by less than the price rises. A price decrease reduces total revenue.
• If demand is unit elastic (elasticity = 1): total revenue is unchanged when the price changes.

This is why a luxury restaurant raising prices may earn more revenue (their demand is inelastic — people want the experience) while a discount store raising prices may earn less (their demand is elastic — customers go elsewhere). It is also why oil-producing countries sometimes restrict supply: oil demand is fairly inelastic in the short run, so reducing supply raises prices and revenue. (We will see this in Chapter 20 when we look at OPEC.)

For policy, the same logic explains why governments tax inelastic goods more heavily than elastic goods. Cigarette taxes are higher than restaurant taxes because cigarette demand is more inelastic — the government raises more revenue per unit of tax with less reduction in quantity.

6.8 Worked example: the labor demand elasticity and the minimum wage

Let's apply elasticity to one of the most important debates in economics: the minimum wage.

The simple supply-and-demand model says that imposing a minimum wage above the equilibrium wage reduces employment of low-wage workers. The size of the reduction depends on the elasticity of labor demand — how much firms reduce their hiring in response to higher wages.

If labor demand is very elastic, even a small minimum wage increase causes a large reduction in employment. If labor demand is inelastic, a minimum wage increase causes only a small reduction in employment.

Empirically, what is the elasticity of low-wage labor demand?

The honest answer is that it varies, and economists have been arguing about it for decades. Card and Krueger's 1994 study of fast-food employment in New Jersey and Pennsylvania (after a New Jersey minimum wage increase) found no significant employment effect — implying near-zero elasticity. Neumark and Wascher's later work, using different data, found larger negative effects — implying more elastic labor demand. Dube and others, with more recent data, have found small effects, generally consistent with the Card-Krueger framework. The CBO's analyses estimate elasticities in the range of −0.1 to −0.4 for low-wage workers, meaning that a 10% increase in the minimum wage would cause employment to fall by 1–4%.

The empirical disagreement is genuine, but the direction is generally agreed: minimum wage increases probably reduce employment somewhat, but the effect is smaller than the simplest version of the supply-and-demand model would predict. Why is the labor demand elasticity smaller than expected?

Several explanations have been proposed:

1. Monopsony power. When employers have wage-setting power (which is more common in low-wage labor markets than the perfectly competitive model assumes), the standard prediction reverses for moderate minimum wage increases. We will see this in Chapter 21.

2. Productivity adjustments. Firms facing higher wages can sometimes get more productivity out of workers (less turnover, more training, better selection), which offsets some of the cost increase.

3. Price pass-through. Firms can pass some of the wage increase onto consumers as higher prices, depending on the elasticity of consumer demand for their products. This means the wage increase doesn't fully reduce employment.

4. Search frictions. Workers don't immediately quit when wages rise, and firms don't immediately fire workers; the labor market adjusts slowly.

The point of this preview is not to settle the minimum wage debate (we'll come back to it in much more depth in Chapters 7 and 21). The point is that elasticity is the analytical concept that lets us ask the question precisely: given an X% minimum wage increase, what is the predicted Y% change in employment? The answer depends on the labor demand elasticity, which depends on the structure of the labor market, which is contested empirically. Without elasticity, we couldn't even formulate the question clearly.

6.9 Where this is going

Chapter 7 takes elasticity to the most contested microeconomic policy debates: rent control, minimum wage (in much more depth), taxes, subsidies. You will see why elasticity is the key to predicting who pays for any government intervention.

Chapter 8 introduces consumer and producer surplus — and elasticity will determine how much surplus is lost when government policies distort the market.

For now, take away three things. First, elasticity is the size of the response. The law of demand says quantity falls when prices rise; elasticity tells you by how much. Second, elasticity varies systematically with substitutes, necessity, time horizon, and budget share. Third, the more inelastic side of a market bears more of the burden of a tax — a result that explains a lot of who actually pays for government policies.

Key terms recap: price elasticity of demand — % change in quantity demanded ÷ % change in price elastic / inelastic / unit elastic — elasticity > 1, < 1, = 1 midpoint formula — uses average of starting and ending values to make percent changes symmetric income elasticity — measures responsiveness to income changes cross-price elasticity — measures responsiveness to other goods' prices price elasticity of supply — same concept as demand but on the seller side tax incidence — the more inelastic side bears more of the burden total revenue — price × quantity; changes depending on elasticity

Themes touched: Tradeoffs, Incentives, Data tells stories (elasticity estimates are empirical), Disagreement (about minimum wage labor elasticity).