**PART 2**

**CHAPTER 4**

*If the demand for illegal drugs is inelastic, increased arrests of illegal-drug sellers will increase total expenditures on illegal drugs.*©bikeriderlondon/Shutterstock

**LEARNING OBJECTIVES**

*After reading this chapter, you should be able to:*

1. **LO1**Define the price elasticity of demand and explain what determines whether demand is elastic or inelastic.

2. **LO2**Calculate the price elasticity of demand using information from a demand curve.

3. **LO3**Understand how changes in the price of a good affect total revenue and total expenditure depending on the price elasticity of demand for the good.

4. **LO4**Explain the cross-price elasticity of demand and the income elasticity of demand.

5. **LO5**Discuss the price elasticity of supply, explain what determines whether supply is elastic or inelastic, and calculate the price elasticity of supply using information from a supply curve.

**M**any illicit-drug users commit crimes to finance their addiction. The connection between drugs and crime has led to calls for more vigorous efforts to stop the smuggling of illicit drugs. But can such efforts reduce the likelihood that your iPhone or laptop computer will be stolen? If attempts to reduce the supply of illicit drugs are successful, our basic supply and demand analysis tells us that the supply curve for drugs will shift to the left and the market price of drugs will increase. Given that demand curves are downward-sloping, drug users will respond by consuming a smaller quantity of drugs. But the amount of crime drug users commit depends not on the *quantity* of drugs they consume, but rather on their *total expenditure* on drugs. Depending on the specific characteristics of the demand curve for illicit drugs, a price increase might reduce total expenditure on drugs, but it also could raise total expenditure.

Suppose, for example, that extra border patrols shift the supply curve in the market for illicit drugs to the left, as shown in __Figure 4.1__. As a result, the equilibrium quantity of drugs would fall from 50,000 to 40,000 ounces per day and the price of drugs would rise from $50 to $80 per ounce. The total amount spent on drugs, which was $2,500,000 per day (50,000 ounces/day × $50/ounce), would rise to $3,200,000 per day (40,000 ounces/day × $80/ounce). In this case, then, efforts to stem the supply of drugs would actually increase the likelihood of your laptop being stolen.

**FIGURE 4.1 The Effect of Extra Border Patrols on the Market for Illicit Drugs.**Extra patrols shift supply leftward and reduce the quantity demanded, but they may actually increase the total amount spent on drugs.

Other benefits from stemming the flow of illicit drugs might still outweigh the resulting increase in crime. But knowing that the policy might increase drug-related crime would clearly be useful to law-enforcement authorities.

Could reducing the supply of illegal drugs cause an increase in drug-related burglaries?

Our task in this chapter will be to introduce the concept of elasticity, a measure of the extent to which quantity demanded and quantity supplied respond to variations in price, income, and other factors. In __Chapter 3__, *Supply and Demand,* we saw how shifts in supply and demand curves enabled us to predict the direction of change in the equilibrium values of price and quantity. An understanding of price elasticity will enable us to make even more precise statements about the effects of such changes. In the illicit-drug example just considered, the decrease in supply led to an increase in total spending. In many other cases, a decrease in supply will lead to a reduction in total spending. Why this difference? The underlying phenomenon that explains this pattern, as we’ll see, is price elasticity of demand. We’ll explore why some goods have higher price elasticity of demand than others and the implications of that fact for how total spending responds to changes in prices. We’ll also discuss price elasticity of supply and examine the factors that explain why it takes different values for different goods.

**PRICE ELASTICITY OF DEMAND**

When the price of a good or service rises, the quantity demanded falls. But to predict the effect of the price increase on total expenditure, we also must know by how much quantity falls. The quantity demanded of some goods such as salt is not very sensitive to changes in price. Indeed, even if the price of salt were to double, or to fall by half, most people would hardly alter their consumption of it. For other goods, however, the quantity demanded is extremely responsive to changes in price. For example, when a luxury tax was imposed on yachts in the early 1990s, purchases of yachts plummeted sharply. (Refer to __The Economic Naturalist 4.2__ example presented later in this chapter.)

**PRICE ELASTICITY DEFINED**

The ** price elasticity of demand** for a good is a measure of the responsiveness of the quantity demanded of that good to changes in its price. Formally, the price elasticity of demand for a good is defined as the percentage change in the quantity demanded that results from a 1 percent change in its price. For example, if the price of beef falls by 1 percent and the quantity demanded rises by 2 percent, then the price elasticity of demand for beef has a value of −2.

Although the definition just given refers to the response of quantity demanded to a 1 percent change in price, it also can be adapted to other variations in price, provided they’re relatively small. In such cases, we calculate the price elasticity of demand as the percentage change in quantity demanded divided by the corresponding percentage change in price. Thus, if a 2 percent reduction in the price of pork led to a 6 percent increase in the quantity of pork demanded, the price elasticity of demand for pork would be

(4.1)

Strictly speaking, the price elasticity of demand will always be negative (or zero) because price changes are always in the opposite direction from changes in quantity demanded. So for convenience, we drop the negative sign and speak of price elasticities in terms of absolute value. The demand for a good is said to be ** elastic** with respect to price if the absolute value of its price elasticity is greater than 1. It is said to be

**FIGURE 4.2 Elastic and Inelastic Demand.**Demand for a good is called elastic, unit elastic, or inelastic with respect to price if the price elasticity is greater than 1, equal to 1, or less than 1, respectively.

**EXAMPLE 4.1Elasticity of Demand**

**What is the elasticity of demand for pizza?**

When the price of pizza is $1 per slice, buyers wish to purchase 400 slices per day, but when price falls to $0.97 per slice, the quantity demanded rises to 404 slices per day. At the original price, what is the price elasticity of demand for pizza? Is the demand for pizza elastic with respect to price?

The fall in price from $1 to $0.97 is a decrease of 3 percent. The rise in quantity demanded from 400 slices to 404 slices is an increase of 1 percent. The price elasticity of demand for pizza is thus (1 percent)/(3 percent) = 1/3. So when the initial price of pizza is $1, the demand for pizza is not elastic with respect to price; it is inelastic.

**CONCEPT CHECK 4.1**

What is the elasticity of demand for season ski passes?

When the price of a season ski pass is $400, buyers, whose demand curve for passes is linear, wish to purchase 10,000 passes per year, but when price falls to $380, the quantity demanded rises to 12,000 passes per year. At the original price, what is the price elasticity of demand for ski passes? Is the demand for ski passes elastic with respect to price?

**DETERMINANTS OF PRICE ELASTICITY OF DEMAND**

**Cost-Benefit**

What factors determine the price elasticity of demand for a good or service? To answer this question, recall that before a rational consumer buys any product, the purchase decision must first satisfy the Cost-Benefit Principle. For instance, consider a good (such as a dorm refrigerator) that you buy only one unit of (if you buy it at all). Suppose that, at the current price, you have decided to buy it. Now imagine that the price goes up by 10 percent. Will a price increase of this magnitude be likely to make you change your mind? The answer will depend on factors like the following.

**Substitution Possibilities**

When the price of a product you want to buy goes up significantly, you’re likely to ask yourself, “Is there some other good that can do roughly the same job, but for less money?” If the answer is yes, then you can escape the effect of the price increase by simply switching to the substitute product. But if the answer is no, you are more likely to stick with your current purchase.

If the price of salt were to double, would you use less of it?

These observations suggest that demand will tend to be more elastic with respect to price for products for which close substitutes are readily available. Salt, for example, has no close substitutes, which is one reason that the demand for it is highly inelastic. Note, however, that while the quantity of salt people demand is highly insensitive to price, the same cannot be said of the demand for any *specific brand* of salt. After all, despite what salt manufacturers say about the special advantages of their own labels, consumers tend to regard one brand of salt as a virtually perfect substitute for another. Thus, if Morton were to raise the price of its salt significantly, many people would simply switch to some other brand.

The vaccine against rabies is another product for which there are essentially no attractive substitutes. A person who is bitten by a rabid animal and does not take the vaccine faces a certain and painful death. Most people in that position would pay any price they could afford rather than do without the vaccine.

**Budget Share**

Suppose the price of key rings suddenly were to double. How would that affect the number of key rings you buy? If you’re like most people, it would have no effect at all. Think about it—a doubling of the price of a $1 item that you buy only every few years is simply nothing to worry about. By contrast, if the price of the new car you were about to buy suddenly doubled, you would definitely want to check out possible substitutes such as a used car or a smaller new model. You also might consider holding on to your current car a little longer. The larger the share of your budget an item accounts for, the greater is your incentive to look for substitutes when the price of the item rises. Big-ticket items, therefore, tend to have higher price elasticities of demand.

**Time**

Home appliances come in a variety of models, some more energy-efficient than others. As a general rule, the more efficient an appliance is, the higher its price. Suppose that you were about to buy a new air conditioner and electric rates suddenly rose sharply. It would probably be in your interest to buy a more efficient machine than you’d originally planned. However, what if you’d already bought a new air conditioner before you learned of the rate increase? You wouldn’t think it worthwhile to discard the machine right away and replace it with a more efficient model. Rather, you’d wait until the machine wore out, or until you moved, before making the switch.

As this example illustrates, substitution of one product or service for another takes time. Some substitutions occur in the immediate aftermath of a price increase, but many others take place years or even decades later. For this reason, the price elasticity of demand for any good or service will be higher in the long run than in the short run.

*RECAP*

**FACTORS THAT INFLUENCE PRICE ELASTICITY**

The price elasticity of demand for a good or service tends to be larger when substitutes for the good are more readily available, when the good’s share in the consumer’s budget is larger, and when consumers have more time to adjust to a change in price.

**SOME REPRESENTATIVE ELASTICITY ESTIMATES**

The entries in __Table 4.1__ show that the price elasticities of demand for different products often differ substantially—in this sample, ranging from a high of 3.5 for public transportation to a low of 0.1 for food. This variability is explained in part by the determinants of elasticity just discussed. Note, for example, that the price elasticity of demand for green peas is more than nine times that for coffee, reflecting the fact that there are many more close substitutes for green peas than for coffee.

Note also the contrast between the low price elasticity of demand for food and the high price elasticity of demand for green peas. Unlike green peas, food occupies a substantial share of most family budgets and there are few substitutes for broad spending categories like food.

**USING PRICE ELASTICITY OF DEMAND**

An understanding of the factors that govern price elasticity of demand is necessary not only to make sense of consumer behavior, but also to design effective public policy. Consider, for example, the debate about how taxes affect smoking among teenagers.

**The Economic Naturalist 4.1**

**Will a higher tax on cigarettes curb teenage smoking?**

Consultants hired by the tobacco industry have testified in Congress against higher cigarette taxes aimed at curbing teenage smoking. The main reason teenagers smoke is that their friends smoke, these consultants testified, and they concluded that higher taxes would have little effect. Does the consultants’ testimony make economic sense?

The consultants are almost certainly right that peer influence is the most important determinant of teen smoking. But that does not imply that a higher tax on cigarettes would have little impact on adolescent smoking rates. Because most teenagers have little money to spend at their own discretion, cigarettes constitute a significant share of a typical teenage smoker’s budget. The price elasticity of demand is thus likely to be far from negligible. For at least some teenage smokers, a higher tax would make smoking unaffordable. And even among those who could afford the higher prices, at least some others would choose to spend their money on other things rather than pay the higher prices.

Do high cigarette prices discourage teen smoking?

Given that the tax would affect at least *some* teenage smokers, the consultants’ argument begins to unravel. If the tax deters even a small number of smokers directly through its effect on the price of cigarettes, it will also deter others indirectly, by reducing the number of peer role models who smoke. And those who refrain because of these indirect effects will in turn no longer influence others to smoke, and so on. So even if the direct effect of higher cigarette taxes on teen smoking is small, the cumulative effects may be extremely large. The mere fact that peer pressure may be the primary determinant of teen smoking therefore does not imply that higher cigarette taxes will have no significant impact on the number of teens who smoke.

**The Economic Naturalist 4.2**

**Why was the luxury tax on yachts such a disaster?**

In 1990, Congress imposed a luxury tax on yachts costing more than $100,000, along with similar taxes on a handful of other luxury goods. Before these taxes were imposed, the Joint Committee on Taxation estimated that they would yield more than $31 million in revenue in 1991. However, the tax actually generated only a bit more than half that amount, $16.6 million.__ ^{1}__ Several years later, the Joint Economic Committee estimated that the tax on yachts had led to a loss of 7,600 jobs in the U.S. boating industry. Taking account of lost income taxes and increased unemployment benefits, the U.S. government actually came out $7.6 million behind in fiscal 1991 as a result of its luxury taxes—almost $39 million worse than the initial projection. What went wrong?

Why did the luxury tax on yachts backfire?

The 1990 law imposed no luxury taxes on yachts built and purchased outside the United States. What Congress failed to consider was that foreign-built yachts are almost perfect substitutes for yachts built and purchased in the United States. And, no surprise, when prices on domestic yachts went up because of the tax, yacht buyers switched in droves to foreign models. A tax imposed on a good with a high price elasticity of demand stimulates large rearrangements of consumption but yields little revenue. Had Congress done the economic analysis properly, it would have predicted that this particular tax would be a big loser. Facing angry protests from unemployed New England shipbuilders, Congress repealed the luxury tax on yachts in 1993.

**A GRAPHICAL INTERPRETATION OF PRICE ELASTICITY**

For small changes in price, price elasticity of demand is the proportion by which quantity demanded changes divided by the corresponding proportion by which price changes. This formulation enables us to construct a simple expression for the price elasticity of demand for a good using only minimal information about its demand curve.

Look at __Figure 4.3__. *P* represents the current price of a good and *Q* the quantity demanded at that price. Δ*P* represents a small change in the current price, and the resulting change in quantity demanded is given by Δ*Q*. The expression Δ*P*/*P* will then stand for the proportion by which price changes and Δ*Q*/*Q* will stand for the corresponding proportion by which quantity changes. These two expressions, along with our definition of the price elasticity of demand (Equation 4.1), give us the formula for price elasticity:

**FIGURE 4.3 A Graphical Interpretation of Price Elasticity of Demand.**Price elasticity of demand at any point along a straight-line demand curve is the ratio of price to quantity at that point times the reciprocal of the slope of the demand curve.(4.2)

Suppose, for example, that 20 units were sold at the original price of 100 and that when price rose to 105, quantity demanded fell to 15 units. Neglecting the negative sign of the quantity change, we would then have Δ*Q*/*Q* = 5/20 and Δ*P*/*P* = 5/100 which yields ∈ = (5/20)/(5/100) = 5.

One attractive feature of this formula is that it has a straightforward graphical interpretation. Thus, if we want to calculate the price elasticity of demand at point *A* on the demand curve shown in __Figure 4.3__, we can begin by rewriting the right-hand side of Equation 4.2 as (*P*/*Q*) × (Δ*Q*/Δ*P*). And since the slope of the demand curve is equal to Δ*P*/Δ*Q*, Δ*Q*/Δ*P* is the reciprocal of that slope: Δ*Q*/Δ*P* = 1/slope. The price elasticity of demand at point *A*, denoted ∈* _{A}*, therefore has the following simple formula:

(4.3)

To demonstrate how convenient this graphical interpretation of elasticity can be, suppose we want to find the price elasticity of demand at point *A* on the demand curve in __Figure 4.4__. The slope of this demand curve is the ratio of its vertical intercept to its horizontal intercept: 20/5 = 4. So 1/slope = 1/4. (Actually, the slope is −4, but we again ignore the minus sign for convenience since price elasticity of demand always has the same sign.) The ratio *P*/*Q* at point *A* is 8/3, so the price elasticity at point *A* is equal to (*P*/*Q*) × (1/slope) = (8/3) × (1/4) = 2/3. This means that when the price of the good is 8, a 3 percent reduction in price will lead to a 2 percent\ increase in quantity demanded.

**FIGURE 4.4 Calculating Price Elasticity of Demand.**The price elasticity of demand at *A* is given by (*P*/*Q*) × (1/slope) = (8/3) × (1/4) = 2/3.

**CONCEPT CHECK 4.2**

What is the price elasticity of demand when *P* = 4 on the demand curve in __Figure 4.4__?

**EXAMPLE 4.2The Relationship between Elasticity and Slope**

**For the demand curves D_{1} and D_{2} shown in Figure 4.5, calculate the price elasticity of demand when P = 4. What is the price elasticity of demand on D_{2} when P = 1?**

**FIGURE 4.5 Price Elasticity and the Steepness of the Demand Curve.**When price and quantity are the same, price elasticity of demand is always greater for the less steep of two demand curves.

These elasticities can be calculated easily using the formula ∈ = (*P*/*Q*) × (1/slope). The slope of *D*_{1} is the ratio of its vertical intercept to its horizontal intercept: 12/6 = 2. So (1/slope) is 1/2 for *D*_{1}. Similarly, the slope of *D*_{2} is the ratio of its vertical intercept to its horizontal intercept: 6/12 = 1/2. So the reciprocal of the slope of *D*_{2} is 2. For both demand curves, *Q* = 4 when *P* = 4, so (*P*/*Q*) = 4/4 = 1 for each. Thus the price elasticity of demand when *P* = 4 is (1 ) × (1/2) = 1/2 for *D*_{1} and (1 ) × (2) = 2 for *D*_{2}. When *P* = 1, *Q* = 10 on *D*_{2}, so (*P*/*Q*) = 1/10. Thus price elasticity of demand = (1/10) × (2) = 1/5 when *P* = 1 on *D*_{2}.

This example illustrates a general rule: If two demand curves have a point in common, the steeper curve must be the less price-elastic of the two with respect to price at that point. However, this does not mean that the steeper curve is less elastic at *every* point. Thus, we saw that at *P* = 1, price elasticity of demand on *D*_{2} was only 1/5, or less than half the corresponding elasticity on the steeper *D*_{1} at *P* = 4.

**PRICE ELASTICITY CHANGES ALONG A STRAIGHT-LINE DEMAND CURVE**

As a glance at our elasticity formula makes clear, price elasticity has a different value at every point along a straight-line demand curve. The slope of a straight-line demand curve is constant, which means that 1/slope is also constant. But the price–quantity ratio *P*/*Q* declines as we move down the demand curve. The elasticity of demand thus declines steadily as we move downward along a straight-line demand curve.

Since price elasticity is the percentage change in quantity demanded divided by the corresponding percentage change in price, this pattern makes sense. After all, a price movement of a given absolute size is small in percentage terms when it occurs near the top of the demand curve, where price is high, but large in percentage terms when it occurs near the bottom of the demand curve, where price is low. Likewise, a quantity movement of a given absolute value is large in percentage terms when it occurs near the top of the demand curve, where quantity is low, and small in percentage terms when it occurs near the bottom of the curve, where quantity is high.

The graphical interpretation of elasticity also makes it easy to see why the price elasticity of demand at the midpoint of any straight-line demand curve must always be 1. Consider, for example, the price elasticity of demand at point *A* on the demand curve *D* shown in __Figure 4.6__. At that point, the ratio *P*/*Q* is equal to 6/3 = 2. The slope of this demand curve is the ratio of its vertical intercept to its horizontal intercept, 12/6 = 2. So (1/slope) = 1/2 (again, we neglect the negative sign for simplicity). Inserting these values into the graphical elasticity formula yields ∈* _{A}* = (

**FIGURE 4.6 Elasticity at the Midpoint of a Straight-Line Demand Curve.**The price elasticity of demand at the midpoint of any straight-line demand curve always takes the value 1.

This result holds not just for __Figure 4.6__, but also for any other straight-line demand curve.__ ^{2}__ A glance at the formula also tells us that since

**FIGURE 4.7 Price Elasticity Regions along a Straight-Line Demand Curve.**Demand is elastic on the top half, unit elastic at the midpoint, and inelastic on the bottom half of a straight-line demand curve.

**TWO SPECIAL CASES**

There are two important exceptions to the general rule that elasticity declines along straight-line demand curves. First, the horizontal demand curve in __Figure 4.8__(a) has a slope of zero, which means that the reciprocal of its slope is infinite. Price elasticity of demand is thus infinite at every point along a horizontal demand curve. Such demand curves are said to be __perfectly elastic__.

**FIGURE 4.8 Perfectly Elastic and Perfectly Inelastic Demand Curves.**The horizontal demand curve (a) is perfectly elastic, or infinitely elastic, at every point. Even the slightest increase in price leads consumers to desert the product in favor of substitutes. The vertical demand curve (b) is perfectly inelastic at every point. Consumers do not, or cannot, switch to substitutes even in the face of large increases in price.

Second, the demand curve in __Figure 4.8__(b) is vertical, which means that its slope is infinite. The reciprocal of its slope is thus equal to zero. Price elasticity of demand is thus exactly zero at every point along the curve. For this reason, vertical demand curves are said to be __perfectly inelastic__.

*RECAP*

**CALCULATING PRICE ELASTICITY OF DEMAND**

The price elasticity of demand for a good is the percentage change in the quantity demanded that results from a 1 percent change in its price. Mathematically, the elasticity of demand at a point along a demand curve is equal to (*P*/*Q*) × (1/slope), where *P* and *Q* represent price and quantity and (1/slope) is the reciprocal of the slope of the demand curve at that point. Demand is elastic with respect to price if the absolute value of its price elasticity exceeds 1; inelastic if price elasticity is less than 1; and unit elastic if price elasticity is equal to 1.

**ELASTICITY AND TOTAL EXPENDITURE**

Sellers of goods and services have a strong interest in being able to answer questions like “Will consumers spend more on my product if I sell more units at a lower price or fewer units at a higher price?” As it turns out, the answer to this question depends critically on the price elasticity of demand. To see why, let’s first examine how the total amount spent on a good varies with the price of the good.

The total daily expenditure on a good is simply the daily number of units bought times the price for which it sells. The market demand curve for a good tells us the quantity that will be sold at each price. We can thus use the information on the demand curve to show how the total amount spent on a good will vary with its price.

To illustrate, let’s calculate how much moviegoers will spend on tickets each day if the demand curve is as shown in __Figure 4.9__ and the price is $2 per ticket (a). The demand curve tells us that at a price of $2 per ticket, 500 tickets per day will be sold, so total expenditure at that price will be $1,000 per day. If tickets sell not for $2 but for $4 apiece, 400 tickets will be sold each day (b), so total expenditure at the higher price will be $1,600 per day.

**FIGURE 4.9 The Demand Curve for Movie Tickets.**An increase in price from $2 to $4 per ticket increases total expenditure on tickets.

Note that the total amount consumers spend on a product each day must equal the total amount sellers of the product receive. That is to say, the terms ** total expenditure** and

**Total expenditure** = **Total revenue:** The dollar amount that consumers spend on a product (*P* × *Q*) is equal to the dollar amount that sellers receive.

It might seem that an increase in the market price of a product should always result in an increase in the total revenue received by sellers. Although that happened in the case we just saw, it needn’t always be so. The law of demand tells us that when the price of a good rises, people will buy less of it. The two factors that govern total revenue—price and quantity—will thus always move in opposite directions as we move along a demand curve. When price goes up and quantity goes down, the product of the two may go either up or down.

Note, for example, that for the demand curve shown in __Figure 4.10__ (which is the same as the one in __Figure 4.9__), a rise in price from $8 per ticket (a) to $10 per ticket (b) will cause total expenditure on tickets to go down. Thus people will spend $1,600 per day on tickets at a price of $8, but only $1,000 per day at a price of $10.

**FIGURE 4.10 The Demand Curve for Movie Tickets.**An increase in price from $8 to $10 per ticket results in a fall in total expenditure on tickets.

The general rule illustrated by __Figures 4.9__ and __4.10__ is that a price increase will produce an increase in total revenue whenever it is greater, in percentage terms, than the corresponding percentage reduction in quantity demanded. Although the two price increases (from $2 to $4 and from $8 to $10) were of the same absolute value—$2 in each case—they are much different when expressed as a percentage of the original price. An increase from $2 to $4 represents a 100 percent increase in price, whereas an increase from $8 to $10 represents only a 25 percent increase in price. And although the quantity reductions caused by the two price increases were also equal in absolute terms, they too are very different when expressed as percentages of the quantities originally sold. Thus, although the decline in quantity demanded was 100 tickets per day in each case, it was just a 20 percent reduction in the first case (from 500 units to 400 in __Figure 4.9__) but a 50 percent reduction in the second (from 200 units to 100 in __Figure 4.10__). In the second case, the negative effect on total expenditure of the 50 percent quantity reduction outweighed the positive effect of the 25 percent price increase. The reverse happened in the first case: The 100 percent increase in price (from $2 to $4) outweighed the 20 percent reduction in quantity (from 5 units to 4 units).

The following example provides further insight into the relationship between total revenue and price.

**EXAMPLE 4.3Elasticity and Total Expenditure**

**For the demand curve shown in Figure 4.11, draw a separate graph showing how total expenditure varies with the price of movie tickets.**

**FIGURE 4.11 The Demand Curve for Movie Tickets.**

The first step in constructing this graph is to calculate total expenditure for each price shown in the graph and record the results, as in __Table 4.2__. The next step is to plot total expenditure at each of the price points on a graph, as in __Figure 4.12__. Finally, sketch the curve by joining these points. (If greater accuracy is required, you can use a larger sample of points than the one shown in __Table 4.2__.)

**FIGURE 4.12 Total Expenditure as a Function of Price.**For a good whose demand curve is a straight line, total expenditure reaches a maximum at the price corresponding to the midpoint of the demand curve.

Note in __Figure 4.12__ that as the price per ticket increases from $0 to $6, total expenditure increases. But as the price rises from $6 to $12, total expenditure decreases. Total expenditure reaches a maximum of $1,800 per day at a price of $6.

The pattern observed in the preceding example holds true in general. For a straight-line demand curve, total expenditure is highest at the price that lies on the midpoint of the demand curve.

Bearing in mind these observations about how expenditure varies with price, let’s return to the question of how the effect of a price change on total expenditure depends on the price elasticity of demand. Suppose, for example, that the business manager of a rock band knows he can sell 5,000 tickets to the band’s weekly summer concerts if he sets the price at $20 per ticket. If the elasticity of demand for tickets is equal to 3, will total ticket revenue go up or down in response to a 10 percent increase in the price of tickets?

Total revenue from tickets sold is currently ($20/ticket) × (5,000 tickets/week) = $100,000 per week. The fact that the price elasticity of demand for tickets is 3 implies that a 10 percent increase in price will produce a 30 percent reduction in the number of tickets sold, which means that quantity will fall to 3,500 tickets per week. Total expenditure on tickets will therefore fall to (3,500 tickets/week) × ($22/ticket) = $77,000 per week, which is significantly less than the current spending total.

What would have happened to total expenditure if the band manager had *reduced* ticket prices by 10 percent, from $20 to $18? Again assuming a price elasticity of 3, the result would have been a 30 percent increase in tickets sold—from 5,000 per week to 6,500 per week. The resulting total expenditure would have been ($18/ticket) × (6,500 tickets/week) = $117,000 per week, significantly more than the current total.

These examples illustrate the following important rule about how price changes affect total expenditure for an elastically demanded good:

**Rule 1:** When price elasticity of demand is greater than 1, changes in price and changes in total expenditure always move in opposite directions.

Let’s look at the intuition behind this rule. Total expenditure is the product of price and quantity. For an elastically demanded product, the percentage change in quantity will be larger than the corresponding percentage change in price. Thus the change in quantity will more than offset the change in revenue per unit sold.

Now let’s see how total spending responds to a price increase when demand is *inelastic* with respect to price. Consider a case like the one just considered except that the elasticity of demand for tickets is not 3 but 0.5. How will total expenditure respond to a 10 percent increase in ticket prices? This time the number of tickets sold will fall by only 5 percent to 4,750 tickets per week, which means that total expenditure on tickets will rise to (4,750 tickets/week) × ($22/ticket) = $104,500 per week, or $4,500 per week more than the current expenditure level.

In contrast, a 10 percent price reduction (from $20 to $18 per ticket) when price elasticity is 0.5 would cause the number of tickets sold to grow by only 5 percent, from 5,000 per week to 5,250 per week, resulting in total expenditure of ($18/ticket) × (5,250 tickets/week) = $94,500 per week, significantly less than the current total.

As these examples illustrate, the effect of price changes on total expenditure when demand is inelastic is precisely the opposite of what it was when demand was elastic:

**Rule 2:** When price elasticity of demand is less than 1, changes in price and changes in total expenditure always move in the same direction.

Again, the intuition behind this rule is straightforward. For a product whose demand is inelastic with respect to price, the percentage change in quantity demanded will be smaller than the corresponding percentage change in price. The change in revenue per unit sold (price) will thus more than offset the change in the number of units sold.

The relationship between elasticity and the effect of a price change on total revenue is summarized in __Figure 4.13__, where the symbol ∈ is used to denote elasticity.

**FIGURE 4.13 Elasticity and the Effect of a Price Change on Total Expenditure.**

Recall that in the example with which we began this chapter, an increase in the price of drugs led to an increase in the total amount spent on drugs. That will happen whenever the demand for drugs is inelastic with respect to price, as it was in that example. Had the demand for drugs instead been elastic with respect to price, the drug supply interruption would have led to a reduction in total expenditure on drugs.

**INCOME ELASTICITY AND CROSS-PRICE ELASTICITY OF DEMAND**

The elasticity of demand for a good can be defined not only with respect to its own price but also with respect to the prices of substitutes or complements, or even to income. For example, the elasticity of demand for peanuts with respect to the price of cashews—also known as the ** cross-price elasticity of demand** for peanuts with respect to cashew prices—is the percentage by which the quantity of peanuts demanded changes in response to a 1 percent change in the price of cashews. The

Unlike the elasticity of demand for a good with respect to its own price, these other elasticities may be either positive or negative, so it is important to note their algebraic signs carefully. The income elasticity of demand for inferior goods, for example, is negative, whereas the income elasticity of demand for normal goods is positive. When the cross-price elasticity of demand for two goods is positive—as in the peanuts/cashews example—the two goods are substitutes. When it is negative, the two goods are complements. The elasticity of demand for tennis racquets with respect to court rental fees, for example, is less than zero.

**CONCEPT CHECK 4.3**

If a 10 percent increase in income causes the number of students who choose to attend private universities to go up by 5 percent, what is the income elasticity of demand for private universities?

*RECAP*

**CROSS-PRICE AND INCOME ELASTICITIES**

When the cross-price elasticity of demand for one good with respect to the price of another good is positive, the two goods are substitutes; when the cross-price elasticity of demand is negative, the two goods are complements. A normal good has positive income elasticity of demand and an inferior good has negative income elasticity of demand.

**THE PRICE ELASTICITY OF SUPPLY**

On the buyer’s side of the market, we use price elasticity of demand to measure the responsiveness of quantity demanded to changes in price. On the seller’s side of the market, the analogous measure is ** price elasticity of supply.** It is defined as the percentage change in quantity supplied that occurs in response to a 1 percent change in price. For example, if a 1 percent increase in the price of peanuts leads to a 2 percent increase in the quantity supplied, the price elasticity of supply of peanuts would be 2.

The mathematical formula for price elasticity of supply at any point is the same as the corresponding expression for price elasticity of demand:

(4.4)

where *P* and *Q* are the price and quantity at that point, Δ*P* is a small change in the initial price, and Δ*Q* the resulting change in quantity.

As with the corresponding expression for price elasticity of demand, Equation 4.4 can be rewritten as (*P*/*Q*) × (Δ*Q*/Δ*P*). And since (Δ*Q*/Δ*P*) is the reciprocal of the slope of the supply curve, the right-hand side of Equation 4.4 is equal to (*P*/*Q*) × (1/slope)—the same expression we saw in Equation 4.3 for price elasticity of demand. Price and quantity are always positive, as is the slope of the typical supply curve, so price elasticity of supply will be a positive number at every point.

Consider the supply curve shown in __Figure 4.14__. The slope of this supply curve is 2, so the reciprocal of this slope is 1/2. Using the formula, this means that the price elasticity of supply at *A* is (8/2) × (1/2) = 2. The corresponding expression at *B* is (10/3) × (1/2) = 5/3, a slightly smaller value.

**FIGURE 4.14 A Supply Curve for Which Price Elasticity Declines as Quantity Rises.**For the supply curve shown, (1/slope) is the same at every point, but the ratio *P*/*Q* declines as *Q* increases. So elasticity = (*P*/*Q*) × (1/slope) declines as quantity increases.

**CONCEPT CHECK 4.4**

For the supply curve shown in __Figure 4.14__, calculate the elasticity of supply when *P* = 6.

Not all supply curves, however, have the property that price elasticity declines as quantity rises. Consider, for example, the supply curve shown in __Figure 4.15__. Because the ratio *P*/*Q* is the same at every point along this supply curve, and because the slope of the supply curve is also constant, price elasticity of supply will take exactly the same value at every point along this curve. At *A*, for example, price elasticity of supply = (*P*/*Q*) × (1/slope) = (4/12) × (12/4) = 1. Similarly, at *B* price elasticity of supply = (5/15) × (12/4) = 1 again.

**FIGURE 4.15 Calculating the Price Elasticity of Supply Graphically.**Price elasticity of supply is (*P*/*Q*) × (1/slope), which at *A* is (4/12) × (12/4) = 1, exactly the same as at *B.* The price elasticity of supply is equal to 1 at any point along a straight-line supply curve that passes through the origin.

Indeed, the price elasticity of supply will always be equal to 1 at any point along a straight-line supply curve that passes through the origin. The reason is that for movements along any such line, both price and quantity always change in exactly the same proportion.

On the buyer’s side of the market, two important polar cases are demand curves with infinite price elasticity and zero price elasticity. As the next two examples illustrate, analogous polar cases exist on the seller’s side of the market.

**EXAMPLE 4.4Perfectly Inelastic Supply**

**What is the elasticity of supply of land within the borough limits of Manhattan?**

Land in Manhattan sells in the market for a price, just like aluminum or corn or automobiles or any other product. And the demand for land in Manhattan is a downward-sloping function of its price. For all practical purposes, however, its supply is completely fixed. No matter whether its price is high or low, the same amount of it is available in the market. The supply curve of such a good is vertical, and its price elasticity is zero at every price. Supply curves like the one shown in __Figure 4.16__ are said to be __perfectly inelastic__.

**FIGURE 4.16 A Perfectly Inelastic Supply Curve.**Price elasticity of supply is zero at every point along a vertical supply curve.

**EXAMPLE 4.5Perfectly Elastic Supply**

**What is the elasticity of supply of lemonade?**

Suppose that the ingredients required to bring a cup of lemonade to market and their respective costs are as follows:

If these proportions remain the same no matter how many cups of lemonade are made, and the inputs can be purchased in any quantities at the stated prices, draw the supply curve of lemonade and compute its price elasticity.

Since each cup of lemonade costs exactly 14¢ to make, no matter how many cups are made, the marginal cost of lemonade is constant at 14¢ per cup. And since each point on a supply curve is equal to marginal cost (see __Chapter 3__, *Supply and Demand*), this means that the supply curve of lemonade is not upward-sloping but is instead a horizontal line at 14¢ per cup (__Figure 4.17__). The price elasticity of supply of lemonade is infinite.

**FIGURE 4.17 A Perfectly Elastic Supply Curve.**The elasticity of supply is infinite at every point along a horizontal supply curve.

Whenever additional units of a good can be produced by using the same combination of inputs, purchased at the same prices, as have been used so far, the supply curve of that good will be horizontal. Such supply curves are said to be __perfectly elastic__.

**DETERMINANTS OF SUPPLY ELASTICITY**

The two preceding examples suggest some of the factors that govern the elasticity of supply of a good or service. The lemonade case was one whose production process was essentially like a cooking recipe. For such cases, we can exactly double our output by doubling each ingredient. If the price of each ingredient remains fixed, the marginal cost of production for such goods will be constant—and hence their horizontal supply curves.

The Manhattan land example is a contrast in the extreme. The inputs that were used to produce land in Manhattan—even if we knew what they were—could not be duplicated at any price.

The key to predicting how elastic the supply of a good will be with respect to price is to know the terms on which additional units of the inputs involved in producing that good can be acquired. In general, the more easily additional units of these inputs can be acquired, the higher price elasticity of supply will be. The following factors (among others) govern the ease with which additional inputs can be acquired by a producer.

**Flexibility of Inputs**

To the extent that production of a good requires inputs that are also useful for the production of other goods, it is relatively easy to lure additional inputs away from their current uses, making supply of that good relatively elastic with respect to price. Thus the fact that lemonade production requires labor with only minimal skills means that a large pool of workers could shift from other activities to lemonade production if a profitable opportunity arose. Brain surgery, by contrast, requires elaborately trained and specialized labor, which means that even a large price increase would not increase available supplies, except in the very long run.

**Mobility of Inputs**

If inputs can be easily transported from one site to another, an increase in the price of a product in one market will enable a producer in that market to summon inputs from other markets. For example, the supply of agricultural products is made more elastic with respect to price by the fact that thousands of farm workers are willing to migrate northward during the growing season. The supply of entertainment is similarly made more elastic by the willingness of entertainers to hit the road. Cirque performers, lounge singers, comedians, and dancers often spend a substantial fraction of their time away from home.

For most goods, the price elasticity of supply increases each time a new highway is built, or when the telecommunications network improves, or indeed when any other development makes it easier to find and transport inputs from one place to another.

**Ability to Produce Substitute Inputs**

The inputs required to produce finished diamond gemstones include raw diamond crystal, skilled labor, and elaborate cutting and polishing machinery. In time, the number of people with the requisite skills can be increased, as can the amount of specialized machinery. The number of raw diamond crystals buried in the earth is probably fixed in the same way that Manhattan land is fixed, but unlike Manhattan land, rising prices will encourage miners to spend the effort required to find a larger proportion of those crystals. Still, the supply of natural gemstone diamonds tends to be relatively inelastic because of the difficulty of augmenting the number of diamond crystals.

The day is close at hand, however, when gemstone makers will be able to produce synthetic diamond crystals that are indistinguishable from real ones. Indeed, there are already synthetic crystals that fool even highly experienced jewelers. The introduction of a perfect synthetic substitute for natural diamond crystals would increase the price elasticity of supply of diamonds (or, at any rate, the price elasticity of supply of gemstones that look and feel just like diamonds).

**Time**

Because it takes time for producers to switch from one activity to another, and because it takes time to build new machines and factories and train additional skilled workers, the price elasticity of supply will be higher for most goods in the long run than in the short run. In the short run, a manufacturer’s inability to augment existing stocks of equipment and skilled labor may make it impossible to expand output beyond a certain limit. But if a shortage of managers was the bottleneck, new MBAs can be trained in only two years. Or if a shortage of legal staff is the problem, new lawyers can be trained in three years. In the long run, firms can always buy new equipment, build new factories, and hire additional skilled workers.

The conditions that gave rise to the perfectly elastic supply curve for lemonade in the example we discussed earlier are satisfied for many other products in the long run. If a product can be copied (in the sense that any company can acquire the design and other technological information required to produce it), and if the inputs needed for its production are used in roughly fixed proportions and are available at fixed market prices, then the long-run supply curve for that product will be horizontal. But many products do not satisfy these conditions, and their supply curves remain steeply upward-sloping, even in the very long run.

**The Economic Naturalist 4.3**

**Why are gasoline prices so much more volatile than car prices?**

Automobile price changes in the United States usually occur just once a year, when manufacturers announce an increase of only a few percentage points. In contrast, gasoline prices often fluctuate wildly from day to day. As shown in __Figure 4.18__, for example, the highest daily gasoline prices in California’s two largest cities were three times higher than the lowest daily prices in 2001 and early 2002. Why this enormous difference in volatility?

**FIGURE 4.18 Gasoline Prices in Two California Cities.**Source: Oil Price Information Service, www.opisnet.com.

With respect to price volatility, at least two important features distinguish the gasoline market from the market for cars. One is that the short-run price elasticity of demand for gasoline is much smaller than the corresponding elasticity for cars. The other is that supply shifts are much more pronounced and frequent in the gasoline market than in the car market. (See __Figure 4.19__.)

**FIGURE 4.19 Greater Volatility in Gasoline Prices Than in Car Prices.**Gasoline prices are more volatile prices because supply shifts are larger and more frequent in the gasoline market (a) than in the car market (b) and also because supply and demand are less elastic in the short run in the gasoline market.

Why are the two markets different in these ways? Consider first the difference in price elasticities of demand. The quantity of gasoline we demand depends largely on the kinds of cars we own and the amounts we drive them. In the short run, car ownership and commuting patterns are almost completely fixed, so even if the price of gasoline were to change sharply, the quantity we demand would not change by much. In contrast, if there were a sudden dramatic change in the price of cars, we could always postpone or accelerate our next car purchases.

To see why the supply curve in the gasoline market experiences larger and more frequent shifts than the supply curve in the car market, we need only examine the relative stability of the inputs employed by sellers in these two markets. Most of the inputs used in producing cars—steel, glass, rubber, plastics, electronic components, labor, and others—are reliably available to car makers. In contrast, the key input used in making gasoline—crude oil—is subject to profound and unpredictable supply interruptions.

Why are gasoline prices so much less stable than automobile prices?

This is so in part because much of the world’s supply of crude oil is controlled by OPEC, a group of oil-exporting countries that has sharply curtailed its oil shipments to the United States on several previous occasions. Even in the absence of formal OPEC action, however, large supply curtailments often occur in the oil market—for example, whenever producers fear that political instability might engulf the major oil-producing countries of the Middle East.

Note in __Figure 4.18__ the sharp spike in gasoline prices that occurred just after the terrorist attacks on the World Trade Center and Pentagon on September 11, 2001. Because many believed that the aim of these attacks was to provoke large-scale war between Muslim societies and the West, fears of an impending oil supply interruption were perfectly rational. Similar oil price spikes occurred in the early months of 2011, when political upheaval in several Middle Eastern countries threatened to disrupt oil supplies. Such fears alone can trigger a temporary supply interruption, even if war is avoided. The prospect of war creates the expectation of oil supply cutbacks that would cause higher prices in the future, which leads producers to withdraw some of their oil from current markets (in order to sell it at higher prices later). But once the fear of war recedes, the supply curve of gasoline reverts with equal speed to its earlier position. Given the low short-run price elasticity of demand for gasoline, that’s all it takes to generate the considerable price volatility we see in this market.

Price volatility is also common in markets in which demand curves fluctuate sharply and supply curves are highly inelastic. One such market was California’s unregulated market for wholesale electricity during the summer of 2000. The supply of electrical generating capacity was essentially fixed in the short run. And because air conditioning accounts for a large share of demand, several spells of unusually warm weather caused demand to shift sharply to the right. Price at one point reached more than four times its highest level from the previous summer.

**UNIQUE AND ESSENTIAL INPUTS: THE ULTIMATE SUPPLY BOTTLENECK**

Fans of professional basketball are an enthusiastic bunch. Directly through their purchases of tickets and indirectly through their support of television advertisers, they spend literally billions of dollars each year on the sport. But these dollars are not distributed evenly across all teams. A disproportionate share of all revenues and product endorsement fees accrues to the people associated with consistently winning teams, and at the top of this pyramid generally stands the National Basketball Association’s championship team.

Consider the task of trying to produce a championship team in the NBA. What are the inputs you would need? Talented players, a shrewd and dedicated coach and assistants, trainers, physicians, an arena, practice facilities, means for transporting players to away games, a marketing staff, and so on. And whereas some of these inputs can be acquired at reasonable prices in the marketplace, many others cannot. Indeed, the most important input of all—highly talented players—is in extremely limited supply. This is so because the very definition of talented player is inescapably relative—simply put, such a player is one who is better than most others.

Given the huge payoff that accrues to the NBA championship team, it is no surprise that the bidding for the most talented players has become so intense. If there were a long list of players with the potential to boost a team’s winning percentage substantially, the Golden State Warriors wouldn’t have agreed to pay Steph Curry a salary of more than $34 million a year. But, of course, the supply of such players is extremely limited. There are many hungry organizations that would like nothing better than to claim the NBA championship each year, yet no matter how much each is willing to spend, only one can succeed. The supply of NBA championship teams is perfectly inelastic with respect to price even in the very long run.

Sports champions are by no means the only important product whose supply elasticity is constrained by the inability to reproduce unique and essential inputs. In the movie industry, for example, although the supply of movies starring Robert Downey Jr. is not perfectly inelastic, there are only so many films he can make each year. Because his films consistently generate huge box office revenues, scores of film producers want to sign him for their projects. But because there isn’t enough of him to go around, his salary per film is $50 million.

In the long run, unique and essential inputs are the only truly significant supply bottleneck. If it were not for the inability to duplicate the services of such inputs, most goods and services would have extremely high price elasticities of supply in the long run.

**SUMMARY**

· The price elasticity of demand is a measure of how strongly buyers respond to changes in price. It is the percentage change in quantity demanded that occurs in response to a 1 percent change in price. The demand for a good is called elastic with respect to price if the absolute value of its price elasticity is more than 1, inelastic if its price elasticity is less than 1, and unit elastic if its price elasticity is equal to 1. *(LO1)*

· Goods such as salt, which occupy only a small share of the typical consumer’s budget and have few or no good substitutes, tend to have low price elasticity of demand. Goods like new cars of a particular make and model, which occupy large budget shares and have many attractive substitutes, tend to have high price elasticity of demand. Price elasticity of demand is higher in the long run than in the short run because people often need time to adjust to price changes. *(LO1)*

· The price elasticity of demand at a point along a demand curve also can be expressed as the formula ∈ = (Δ*Q*/*Q*)/(Δ*P*/*P*). Here, *P* and *Q* represent price and quantity at that point and Δ*Q* and Δ*P* represent small changes in price and quantity. For straight-line demand curves, this formula can also be expressed as ∈ = (*P*/*Q*) × (1/slope). These formulations tell us that price elasticity declines in absolute terms as we move down a straight-line demand curve. *(LO2)*

· A cut in price will increase total spending on a good if demand is elastic but reduce it if demand is inelastic. An increase in price will increase total spending on a good if demand is inelastic but reduce it if demand is elastic. Total expenditure on a good reaches a maximum when price elasticity of demand is equal to 1. *(LO3)*

· Analogous formulas are used to define the elasticity of demand for a good with respect to income and the prices of other goods. In each case, elasticity is the percentage change in quantity demanded divided by the corresponding percentage change in income or price. *(LO4)*

· Price elasticity of supply is defined as the percentage change in quantity supplied that occurs in response to a 1 percent change in price. The mathematical formula for the price elasticity of supply at any point is (Δ*Q*/*Q*)/(Δ*P*/*P*), where *P* and *Q* are the price and quantity at that point, Δ*P* is a small change in the initial price, and Δ*Q* is the resulting change in quantity. This formula also can be expressed as (*P*/*Q*) × (1/slope), where (1/slope) is the reciprocal of the slope of the supply curve. *(LO5)*

· The price elasticity of supply of a good depends on how difficult or costly it is to acquire additional units of the inputs involved in producing that good. In general, the more easily additional units of these inputs can be acquired, the higher price elasticity of supply will be. It is easier to expand production of a product if the inputs used to produce that product are similar to inputs used to produce other products, if inputs are relatively mobile, or if an acceptable substitute for existing inputs can be developed. And like the price elasticity of demand, the price elasticity of supply is greater in the long run than in the short run. *(LO5)*

**KEY TERMS**

__cross-price elasticity of demand__

__elastic__

__income elasticity of demand__

__inelastic__

__perfectly elastic demand__

__perfectly elastic supply__

__perfectly inelastic demand__

__perfectly inelastic supply__

__price elasticity of demand__

__price elasticity of supply__

__total expenditure__

__total revenue__

__unit elastic__

**REVIEW QUESTIONS**

1. 1.Why does a consumer’s price elasticity of demand for a good depend on the fraction of the consumer’s income spent on that good? *(LO1)*

2. 2.Why does the price elasticity of demand for a good decline as we move down along a straight-line demand curve? *(LO2)*

3. 3.Under what conditions will an increase in the price of a product lead to a reduction in total spending for that product? *(LO3)*

4. 4.Why do economists pay little attention to the algebraic sign of the elasticity of demand for a good with respect to its own price, yet pay careful attention to the algebraic sign of the elasticity of demand for a good with respect to another good’s price? *(LO4)*

5. 5.Why is supply elasticity higher in the long run than in the short run? *(LO5)*

**PROBLEMS**

1. 1.Is the demand for a particular brand of car, like a Chevrolet, likely to be more or less price-elastic than the demand for all cars? Explain. *(LO1)*

2. 2.Among the following groups—senior executives, junior executives, and students—which is likely to have the most and which is likely to have the least price-elastic demand for membership in the Association of Business Professionals? *(LO1)*

3. 3.Calculate the price elasticity of demand (in absolute value) at points *A*, *B*, *C*, *D*, and *E* on the demand curve below. *(LO2)*

4. 4.Suppose, while rummaging through your uncle’s closet, you found the original painting of *Dogs Playing Poker*, a valuable piece of art. You decide to set up a display in your uncle’s garage. The demand curve to see this valuable piece of art is as shown in the diagram. What price should you charge if your goal is to maximize your revenues from tickets sold? On a graph, show the inelastic and elastic regions of the demand curve. *(LO2, LO3)*

5. 5.The schedule below shows the number of packs of bagels bought in Davis, California, each day at a variety of prices. *(LO2, LO3)*

a. Graph the daily demand curve for packs of bagels in Davis.

b. Calculate the price elasticity of demand at the point on the demand curve at which the price of bagels is $4 per pack.

c. If all bagel shops increased the price of bagels from $4 per pack to $5 per pack, what would happen to total revenues?

d. Calculate the price elasticity of demand at a point on the demand curve where the price of bagels is $1 per pack.

e. If bagel shops increased the price of bagels from $1 per pack to $2 per pack, what would happen to total revenues?

6. 6.*At point *A* on the demand curve shown, by what percentage will a 1 percent increase in the price of the product affect total expenditure on the product? *(LO3)*

7. 7.*Suppose that, in an attempt to induce citizens to conserve energy, the government enacted regulations requiring that all air conditioners be more efficient in their use of electricity. After this regulation was implemented, government officials were then surprised to discover that people used even more electricity than before. Using the concept of price elasticity, explain how this increase might have occurred. *(LO1, LO4)*

8. 8.A 2 percent increase in the price of milk causes a 4 percent reduction in the quantity demanded of chocolate syrup. What is the cross-price elasticity of demand for chocolate syrup with respect to the price of milk? Are the two goods complements or substitutes? *(LO4)*

9. 9.What are the respective price elasticities of supply at *A* and *B* on the supply curve shown in the accompanying figure? *(LO5)*

10. 10.The price elasticity of supply for basmati rice (an aromatic strain of rice) is likely to be which of the following? *(LO5)*

a. Higher in the long run than in the short run because farmers cannot easily change their decisions about how much basmati rice to plant once the crop has been planted.

b. High because consumers have many other kinds of rice and other staple foods to choose from.

c. Low in both the long run and the short run because rice farming requires only unskilled labor.

d. High in both the long run and the short run because the inputs required to produce basmati rice can easily be duplicated.

11. 11.Suppose that the ingredients required to bring a slice of pizza to market and their respective costs are as listed in the table:

If these proportions remain the same no matter how many slices are made, and the inputs can be purchased in any quantities at the stated prices, draw the supply curve of pizza slices and compute its price elasticity. *(LO5)*

**ANSWERS TO CONCEPT CHECKS**

1. 4.1In response to a 5 percent reduction in the price of ski passes, the quantity demanded increased by 20 percent. The price elasticity of demand for ski passes is thus (20 percent)/(5 percent) = 4, and that means that at the initial price of $400, the demand for ski passes is elastic with respect to price. *(LO1)*

2. 4.2At point *A* in the accompanying diagram, *P*/*Q* = 4/4 = 1. The slope of this demand curve is 20/5 = 4, so ∈ = 1 × (1/slope) = 1/4. *(LO2)*

3. 4.3Income elasticity = percentage change in quantity demanded/percentage change in income = 5 percent/ 10 percent = 0.5. *(LO4)*

4. 4.4For the supply curve below, *Q* = 1 when *P* = 6, so elasticity of supply = (*P*/*Q*) × (1/slope) = (6) × (1/2) = 3. *(LO5)*

**APPENDIX**

The Midpoint Formula

**S**uppose you encounter a question like the following on a standardized test in economics:

At a price of 3, quantity demanded of a good is 6, while at a price of 4, quantity demanded is 4. What is the price elasticity of demand for this good?

Let’s attempt to answer this question by using the formula ∈ = (Δ*Q*/*Q*)(Δ*P*/*P*). In __Figure 4A.1__, we first plot the two price–quantity pairs given in the question and then draw the straight-line demand curve that connects them. From the graph, it is clear that Δ*P* = 1 and Δ*Q* = 2. But what values do we use for *P* and *Q*? If we use *P* = 4 and *Q* = 4 (point *A*), we get an elasticity of 2. But if we use *P* = 3 and *Q* = 6 (point *B*), we get an elasticity of 1. Thus, if we reckon price and quantity changes as proportions of their values at point *A* we get one answer, but if we compute them as proportions of their values at point *B* we get another. Neither of these answers is incorrect. The fact that they differ is merely a reflection of the fact that the elasticity of demand differs at every point along a straight-line demand curve.

**FIGURE 4A.1 Two Points on a Demand Curve.**

Strictly speaking, the original question (“What is the price elasticity of demand for this good?”) was not well posed. To have elicited a uniquely correct answer, it should have been “What is the price elasticity of demand at point *A*?” or “What is the price elasticity of demand at point *B*?” Economists have nonetheless developed a convention, which we call the *midpoint formula*, for answering ambiguous questions like the one originally posed. If the two points in question are (*Q _{A}*,

(4A.1)

The midpoint formula thus sidesteps the question of which price–quantity pair to use by using averages of the new and old values. The formula reduces to

(4A.2)

For the two points shown in __Figure 4A.1__, the midpoint formula yields ∈ = [2/(4 + 6)]/[1/(4 + 3)] = 1.4, which lies between the values for price elasticity at *A* and *B*.

We will not employ the midpoint formula again in this text. Hereafter, all questions concerning elasticity will employ the measure discussed in the text of this chapter, which is called *point elasticity*.

^{1}For an alternative view, see Dennis Zimmerman, “The Effect of the Luxury Excise Tax on the Sale of Luxury Boats,” Congressional Research Service, February 10, 1992.

^{2}To see why, note that at the midpoint of any such curve, *P* is exactly half the vertical intercept of the demand curve and *Q* is exactly half the horizontal intercept. Since the ratio of the vertical intercept to the horizontal intercept is the slope of the demand curve, the ratio (*P*/*Q*) must also be equal to the slope of the demand curve. And this means that (1/slope) will always be equal to (*Q*/*P*). Thus, the product (*P*/*Q*) × (1/slope) = (*P*/*Q*) × (*Q*/*P*) will always be exactly 1 at the midpoint of any straight-line demand curve.

* Denotes more difficult problem.