Mathematically, the slopes of demand and supply curves relate changes in price to changes in quantity demanded or quantity supplied. Steeper curves mean that price changes are correlated with relatively small quantity changes. When demand curves are steep, this implies that consumers are not very price-sensitive and won’t change their quantity demanded much in response to price changes. Similarly, steep supply curves mean that producers’ quantities supplied are not particularly sensitive to price changes. Flatter demand or supply curves, on the other hand, imply that price changes are associated with large quantity changes. Markets with flat demand curves have consumers whose quantities demanded change a lot as price varies. Markets with flat supply curves will see big movements in quantity supplied as prices change.

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The concept of elasticity expresses the responsiveness of one value to changes in another (and here specifically, the responsiveness of quantities to prices). An elasticity relates the percentage change in one value to the percentage change in another. So, for example, when we talk about the sensitivity of consumers’ quantity demanded to price, we refer to the price elasticity of demand: the percentage change in quantity demanded resulting from a given percentage change in price.

You might be thinking that the price elasticity of demand sounds a lot like the slope of the demand curve: how much quantity demanded changes when price does. While elasticity and slope are certainly related, they’re not the same.

The slope relates a change in one level (prices) to another level (quantity). The demand curve we introduced in the tomato example was Q = 1,000 – 200P. The slope of this demand curve is –200; that is, quantity demanded falls by 200 pounds for every dollar per pound increase in price.

There are two big problems with using just the slopes of demand and supply curves to measure price responsiveness. First, slopes depend on the units of measurement. If we measured tomato prices P in cents per pound rather than dollars, the demand curve would be Q = 1,000 – 2P, because the quantity of tomatoes demanded would fall by 2 pounds for every 1 cent increase in price. But the fact that the coefficient on P is now 2 instead of 200 doesn’t mean that consumers are 1/100th as price-sensitive as before. Nothing has changed about consumers’ price responsiveness in this market: The quantity demanded still falls by 200 pounds for each $1 increase in price. The change in the slope simply reflects a change in the units of P. The second problem with slopes is that you can’t compare them across different products. Suppose we were studying consumers’ grocery shopping patterns, and wanted to compare consumers’ price sensitivity for tomatoes in the market at Pike Place Market to their price sensitivity for bunches of celery. Does the fact that consumers demand 100 fewer celery bunches for every 10-cent-per-bunch increase in price mean that consumers are more or less price sensitive in the celery market than in the tomato market? The slope of the celery demand curve implied by these numbers is –10 (if we measure quantity demanded in bunches and price in cents per celery bunch). How could we ever compare this slope to the –200 slope for tomatoes?

Using elasticities to express responsiveness avoids these tricky issues, because everything is expressed in relative percentage changes. That eliminates the units problem (a 10% change is a 10% change regardless of what units the thing changing is measured in) and makes magnitudes comparable across markets.

The price elasticity of demand is the ratio of the percentage change in quantity demanded to an associated percentage change in price. Mathematically, its formula is

Price elasticity of demand = (% change in quantity demanded)/(% change in price)

The price elasticity of supply is exactly analogous:

Price elasticity of supply = (% change in quantity supplied)/(% change in price)

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To keep the equations simpler from now on, we’ll use some shorthand notation. E^D will denote the price elasticity of demand, E^S the price elasticity of supply, %ΔQ^D and %ΔQ^S the percentage change in quantities demanded and supplied, respectively, and %ΔP the percentage change in price. In this shorthand, the two equations above become

So, for example, if the quantity demanded of a good falls by 10% in response to a 4% price increase, the good’s price elasticity of demand is E^D = –10%/4% = –2.5. There are a couple of things to note about this example. First, because demand curves slope downward, the price elasticity of demand is always negative (or more precisely, always nonpositive; in special cases that we discuss later, it can be zero). Second, because it is a ratio, a price elasticity can also be thought of as the percentage change in quantity demanded for a 1% increase in price. That is, for this good, a 1% increase in price leads to a –2.5% change in quantity demanded.

The price elasticity of supply works exactly the same way. If producers’ quantity supplied increases by 25% in response to a 50% increase in price, for example, the price elasticity of supply is E^S = 25%/50% = 0.5. The price elasticity of supply is always positive (or again more precisely, always nonnegative) because quantity supplied increases when a good’s price rises. And just as with demand elasticities, supply elasticities can be thought of as the percentage change in quantity in response to a 1% increase in price.

Now that we’ve defined elasticities, let’s use them to think about how responsive quantities demanded and supplied are to price changes.

When demand (supply) is very price-sensitive, a small change in price will lead to large changes in quantities demanded (supplied). That means the numerator of the elasticity expression, the percentage change in quantity, will be very large in magnitude compared to the percentage change in price in the denominator. For price elasticity of demand, the change in quantity will have the opposite sign as the price change, and the elasticity will be negative. But its magnitude (its absolute value) will be large if consumers are very responsive to price changes.

Examples of markets with large-magnitude price elasticities of demand would be those where consumers have a lot of ability to substitute away from or toward the good in question. The demand for apples at the grocery store is probably fairly price-responsive because consumers have an array of other fruits they could buy instead if apple prices are high; if apple prices are low, they will buy apples instead of other fruits. The price elasticity of demand for apples might be something like –4: For every 1% increase in price, consumers’ quantity demanded would fall by 4%.

Markets with less price-responsive demand have elasticities that are small in magnitude. The demand for candy at the circus (certainly for the parents of small children) probably has a fairly small price elasticity of demand. In this case, the price elasticity of demand might be something like –0.3: for every 1% increase in price, quantity demanded would fall by 0.3%. (If you prefer, you could also express this as saying for every 10% price increase, quantity demanded would drop by 3%.)

Markets with large price elasticities of supply—where the quantity supplied is sensitive to price differences—would be those where it was easy for suppliers to vary their amount of production as price changes. Perhaps they have a cost structure that allows them to make as many units as they’d like without driving up their per-unit costs too much. In the market for software, for example, if a program is wildly popular and drawing a high price, it’s fairly easy for the game’s producer to make additional copies available for download. So, the elasticity of supply might be quite large in this market, something like 12 (a 1% increase in price leads to a 12% increase in quantity supplied).

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Markets with low price elasticities of supply have quantities supplied that are fairly unresponsive to price changes. This would occur in markets where it is costly for producers to vary their production levels, or it is difficult for producers to enter or exit the market. The supply curve for tickets to the Super Bowl might have a very low price elasticity of supply because there are only so many seats in the stadium. If the ticket price rises today, the stadium owners can’t really put in additional seats. The supply elasticity in this market might be close to zero. It’s probably slightly positive, however, because the owners could open some obstructed-view seats or make other temporary seating arrangements.

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Elasticities and Time Horizons Often, a key factor determining the flexibility consumers and producers have to respond to price differences, and therefore the price elasticity of their quantities demanded and supplied, is the time horizon.

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In the short run, consumers are often limited in their ability to change their consumption patterns, but given more time, they can make adjustments that give them greater flexibility. The classic example of this is in the market for gasoline. If there is a sudden price spike, many consumers are essentially stuck having to consume roughly the same quantity of gas as they did before the price spike. After all, they have the same car, the same commute, and the same schedule as before. Maybe they can double up on a few trips, or carpool more often, but their ability to respond to prices is limited. For this reason, the short-run price elasticity of gasoline demand is relatively low; empirical estimates by economists that specialize in the market suggest it is around –0.2. That is, for a 1% change in the price of gas, the quantity demanded changes by only –0.2% in the direction opposite the price changes. Over longer horizons, however, individuals have greater scope to adjust their consumption. If the gas spike lasts, they can set up a permanent ride-sharing arrangement, buy a more efficient car, or even move closer to work. The long-run price elasticity of demand for gasoline is therefore much larger in magnitude; empirical studies typically find it is something like –0.8. This means that in the long run, consumers can make four times the quantity adjustment to price changes they can make in the short run.

The same logic holds for producers and supply elasticities. The longer the horizon, the more options they have to adjust output to price changes. Manufacturers already producing at capacity might not be able to increase their output much in the short run if prices increase, even though they would like to. If prices stay high, however, they can hire more workers, build larger factories, and new firms can set up their own production operations and enter the market.

For these reasons, the price elasticities of demand and supply for most products are larger in magnitude (i.e., more negative for demand and more positive for supply) in the long run than in the short run. As we see in the next section, larger-magnitude elasticities imply flatter demand and supply curves. As a result, long-run demand and supply curves tend to be flatter than their short-run versions.

Classifying Elasticities by Magnitude Economists have special terms for elasticities of particular magnitudes. Elasticities with magnitudes (in absolute value) greater than 1 are referred to as elastic. In the above examples, apples have elastic demand and software has elastic supply. Elasticities with magnitudes less than 1 are referred to as inelastic. The demand for circus candy and the supply of Super Bowl tickets are inelastic. If the price elasticity of demand is exactly –1, or the price elasticity of supply is exactly 1, this is referred to as unit elastic. If price elasticities are zero—that is, there is no response in quantity to price changes—the associated goods are called perfectly inelastic. Finally, if price elasticities are infinite in magnitude (–∞ for demand, +∞ for supply)—the quantity demanded or supplied changes infinitely in response to any price change—this is referred to as perfectly elastic.

As we discussed above, economists often use linear (straight-line) demand and supply curves, mostly for the sake of convenience. Because they are so common, it’s worth discussing how elasticities are related to linear curves. Even more important, drawing this connection shows exactly how curves’ slopes and elasticities, the two measures of price responsiveness we’ve been using, are related but still different.

We can rewrite the elasticity formula in a way that makes it easier to see the relationship between elasticity and the slope of a demand or supply curve. A percentage change in quantity (%ΔQ) is the change in quantity (ΔQ) divided by the original quantity level Q. That is, %ΔQ = ΔQ/Q. Similarly, the percentage change in price is %ΔP = ΔP/P. Substituting these into the elasticity expression from above, we have

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where E is a demand or supply elasticity, depending on whether Q denotes quantity demanded or supplied.

Rearranging terms yields

or

where “slope” refers to ΔP/ΔQ, the slope of the demand or supply curve in the standard price-versus-quantity space.

Elasticity of a Linear Demand Curve Suppose we’re dealing with the demand curve in Figure 2.15. Its slope is –2, but its elasticity varies as we move along it because P/Q does. Think first about the point A, where it intercepts the vertical axis. At Q = 0, P/Q is infinite because P is positive ($20) and Q is zero. This, combined with the fact that the curve’s (constant) slope is negative, means the price elasticity of demand is –∞ at this point. The logic behind this is that consumers don’t demand any units of the good at A when its price is $20, but if price falls at all, their quantity demanded will become positive, if still small. Even though this change in quantity demanded is small in numbers of units of the good, the percentage change in consumption is infinite, because it’s rising from zero.

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As we move down along the demand curve, the P/Q ratio falls, reducing the magnitude of the price elasticity of demand. (Remember, the slope isn’t changing, so that part of the elasticity stays the same.) It will remain elastic—that is, have a magnitude larger than 1—for some distance. Eventually, the absolute value of the elasticity will fall to 1, and at that point the demand curve is unit elastic. For the curve in Figure 2.15, this happens to be when P = 10 and Q = 5, because E^D = –(1/2) × (10/5) = –1. This is labeled point B in the figure.9 As we continue down and to the right along the demand curve, the magnitude of the elasticity will fall further and demand will become inelastic. At the point where the demand curve hits the horizontal axis (point C in the figure), price is zero, so P/Q = 0, and the price elasticity of demand is zero.

To recap, the price elasticity of demand changes from –∞ to zero as we move down and to the right along a linear demand curve.

Elasticity of a Linear Supply Curve A similar effect happens as we move along a linear supply curve, like the one in Figure 2.16. Again, because the slope of the curve is constant, the changes in elasticity along the curve are driven by the price-to-quantity ratio. At point A, where the supply curve intercepts the vertical axis, Q = 0 and P/Q is infinite. The price elasticity of supply is +∞ at this point. The same logic holds as with the demand curve: For the smallest increase in price, the quantity supplied rises from zero to a positive number, an infinite percentage change in quantity supplied.

As we move up along the supply curve, the P/Q ratio falls. It’s probably obvious that it must fall from infinity, but you might wonder whether it keeps falling, because both P and Q are rising. It turns out that, yes, it must keep falling. The way to see this is to recognize that the P/Q ratio at any point on the supply curve equals the slope of a ray from the origin to that point. (The rise of the ray is the price P, and its run is the quantity Q. Because slope is rise over run, the ray’s slope is P/Q.) We’ve drawn some examples of such rays for different locations on the supply curve in Figure 2.16. It’s clear from the figure that as we move up and to the right along the supply curve, the slopes of these rays from the origin continue to fall.

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Unlike with the demand curve, however, the P/Q ratio never falls to zero because the supply curve will never intercept the horizontal axis. Therefore, the price elasticity of supply won’t drop to zero. In fact, while the P/Q ratio is always falling as we move up along the supply curve, you can see from the figure that it will never drop below the slope of the supply curve itself. Some linear supply curves like the one in Figure 2.16 intercept the vertical axis at a positive price, indicating that the price has to be at least as high as the intercept for producers to be willing to supply any positive quantity. Because the price elasticity of supply equals (1/slope) × (P/Q), such supply curves approach becoming unit elastic at high prices and quantities supplied, but never quite get there. Also, because P/Q never falls to zero, the only way a supply curve can have an elasticity of zero is if its inverse slope is zero—that is, if it is vertical. We discuss cases like this below.

The formula relating elasticities to slopes also sheds some light on what demand and supply curves look like in two special but often discussed cases: perfectly inelastic and perfectly elastic demand and supply.

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Perfectly Inelastic We discussed above that when the price elasticity is zero, demand and supply are said to be perfectly inelastic. We just saw that this will be true for any linear demand at the point where it intercepts the horizontal (quantity) axis. But what would a demand curve look like that is perfectly inelastic everywhere? A linear demand curve with a slope of –∞ would drive the price elasticity of demand to zero due to the inverse relationship between elasticity and slope. Because a curve with an infinite slope is vertical, a perfectly inelastic demand curve is vertical. An example of such a curve is shown in Figure 2.17a. This makes intuitive sense: A vertical demand curve indicates that the quantity demanded by consumers is completely unchanged regardless of the price. Any percentage change in price will induce a 0% change in quantity demanded. In other words, the price elasticity of demand is zero.

While perfectly inelastic demand curves don’t really exist (after all, there are almost always possibilities for consumers and producers to substitute toward or away from a good as prices hit either extreme of zero or infinity), we might see some situations approaching them. For example, diabetics might have very inelastic demand for insulin. Their demand curve will be almost vertical if they will buy it at any price.

The same logic holds for supply: A vertical supply curve indicates perfectly inelastic supply and no response of quantity supplied to price differences. The supply of tickets for a particular concert or sporting event might also be close to perfectly inelastic, with a near-vertical supply curve, due to capacity constraints of the arena.

One implication of perfect inelasticity is that any shift in the market’s demand or supply curve will result in a change only in the market equilibrium price, not the quantity. That’s because there is absolutely no scope for quantity to change in the movement along a perfectly inelastic demand curve from the old to the new equilibrium. Likewise, for perfectly inelastic supply, if there is a demand curve shift, all equilibrium movement is in price, not quantity.

Perfectly Elastic When demand or supply is perfectly elastic, on the other hand, the price elasticity is infinite. This will be the case for linear demand or supply curves that have slopes of zero—those that are horizontal. An example of such a curve is shown in Figure 2.17b. This shape makes intuitive sense, too. As flat demand or supply curves imply large quantity responses to price differences, perfectly flat curves imply infinitely large quantity changes to price differences. If price is just above a horizontal demand curve, the quantity demanded will be zero. But if price fell just a bit, to below the demand curve, the quantity demanded would be infinite. Similarly, a small price change from above to below a horizontal supply curve would shift producers’ quantity supplied from infinite to zero.

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Small producers of commodity goods probably face demand curves for their products that are approximately horizontal. (We’ll discuss this more in Chapter 8.) For instance, a small corn farmer can probably sell as many bushels of corn as she wants at the market price. If the farmer decided that the price was too low and insisted that she be paid more than the going rate, no one would buy her corn. They could buy from someone else for less. Effectively, then, it is as if the farmer faces an infinite quantity demanded for her corn at the going price (or below it, if for some reason she’s willing to sell for less) but zero quantity demanded of her corn above that price. In other words, she faces a flat demand curve at the going market price.

Supply curves are close to perfectly elastic in competitive industries in which producers all have roughly the same costs, and entry and exit are very easy. (We’ll also discuss this point at greater length in Chapter 8.) These conditions mean that competition will drive prices toward the (common) level of costs, and differences in quantities supplied will be soaked up by the entry and exit of firms from the industry. Because of the strictures of competition in the market, no firm will be able to sell at a price above costs, and obviously no firm will be willing to supply at a price below costs. Therefore, the industry’s supply curve is essentially flat at the producers’ cost level.

As opposed to the perfectly inelastic case, shifts in supply in a market with perfectly elastic demand will only move equilibrium quantity, not price. There’s no way for the equilibrium price to change when the demand curve is flat. Similarly, for markets with perfectly elastic supply, demand curve shifts move only equilibrium quantities and not prices.

We’ve been focusing on price elasticities to this point, and with good reason: They are a key determinant of demand and supply behavior and play an important role in helping us understand how markets work. However, they are not the only elasticities that matter in demand and supply analysis. Remember how we divided up all the factors that affected demand or supply into two categories: price and everything else? Well, each of those other factors that went into “everything else” has an influence on demand or supply that can be measured with an elasticity.

The most commonly used of these elasticities measure the impact of two other factors on quantity demanded. These are the income elasticity of demand and the cross-price elasticity of demand.

The income elasticity of demand is the ratio of the percentage change in quantity demanded to the corresponding percentage change in consumer income (I):

(Equivalently, it is the percentage change in quantity demanded associated with a 1% change in consumer income.)

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Income elasticities describe how responsive demand is to income changes. Goods are sometimes categorized by the sign and size of their income elasticity. Goods that have an income elasticity that is negative, meaning consumers demand a lower quantity of the good when their income rises, are called inferior goods. This name isn’t a comment on their inherent quality; it just describes how their consumption changes with people’s incomes. (Note, however, that low-quality versions of many product categories are inferior goods by this economic definition.) Examples of likely inferior goods are bus tickets, youth hostels, and hot dogs.

Goods with positive income elasticities (consumers’ quantity demanded rises with their income) are called normal goods. As the name indicates, most goods fit into this category.

Normal goods with income elasticities above 1 are sometimes called luxury goods. Having an income elasticity that is greater than 1 means the quantity demanded of these products rises at a faster rate than income. As a consequence, the share of a consumer’s budget that is spent on a luxury good becomes larger as the consumer’s income rises. (To keep a good’s share of the budget constant, quantity consumed would have to rise at the same rate as income. Because luxury goods’ quantities rise faster, their share increases with income.) Yachts, butlers, and fine art are all luxury goods.

We will dig deeper into the relationship between incomes and consumer demand in Chapter 4 and Chapter 5.

The cross-price elasticity of demand is the ratio of the percentage change in one good’s quantity demanded (say, good X) to the percentage change in the price of another good Y:

(To avoid confusion, sometimes the price elasticities we discussed above, which are concerned with the percentage change in quantity demanded to the percentage change in the price of the same good, are referred to as own-price elasticities of demand.)

When a good has a positive cross-price elasticity with another good, that means consumers demand a higher quantity of it when the other good’s price rises. In other words, the good is a substitute for the other good: Consumers switch to the good when the other one becomes more expensive. Many pairs of goods are substitutes for one another—different brands of cereal, meals at restaurants versus dinners at home, colleges, and so on. Economist Aviv Nevo, who measured the elasticities for cereals mentioned above, also measured the cross-price elasticities of the cereals. He found that Froot Loops, for example, is a substitute for other kids’ cereals, like Frosted Flakes and Cap’n Crunch ( and 0.149, respectively). However, it is much less of a substitute for the more adult Shredded Wheat, which had a cross-price elasticity of only 0.020.10

When a good has a negative cross-price elasticity with another good, consumers demand less of it when the other good’s price increases. This indicates that the goods are complements. Complements tend to be goods that are consumed together. If either of the goods within each pair were to become more expensive, consumers would buy not just less of that good itself, but of the other good in the pair as well. Milk and cereal are complements, as are tennis rackets and tennis balls, or computers and software.

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