Elasticities
6 c h a p t e r
WHAT IS THE PRICE ELASTICITY OF DEMAND?
In learning and applying the law of demand, we have established the basic fact that quantity demanded changes inversely with changes in price, ceteris paribus. But how much does quantity demanded change? The extent to which a change in price affects quantity demanded may vary considerably from product to product and over the various price ranges for the same product. The price elasticity of demand measures the responsiveness of quantity demanded to a change in price. Specifically, price elasticity is defined as the percentage change in quantity demanded divided by the percentage change in price, or Note that, following the law of demand, there is an inverse relationship between price and quantity demanded.
For this reason, the price elasticity of demand is, in theory, always negative. But in practice and for simplicity, this quantity is always expressed in absolute value terms—that is, as a positive number.
IS THE DEMAND CURVE ELASTIC OR INELASTIC?
It is important to understand the basic intuition behind elasticities. This can be easily understood by focusing on the percentage changes in quantity demanded and price.
Think of elasticity as an elastic rubber band. If the quantity demanded is very responsive to even a small change in price, we call it elastic. On the other hand, if even a huge change in price results in only a small change in quantity demanded, then the demand is said to be inelastic. For example, if a 10 percent increase in the price leads to a 50 percent reduction in the quantity demanded, we say that demand is elastic because the quantity demanded is very sensitive to the price change.
Demand is elastic in this case because a 10 percent change in price led to a larger (50 percent) change in quantity demanded.
Alternatively, if a 10 percent increase in the price leads to a 1 percent reduction in quantity demanded, we say that demand is inelastic because the quantity demanded did not respond much to the price reduction.
Demand is inelastic in this case because a 10 percent change in price led to a smaller (1 percent) change in quantity demanded.
TYPES OF DEMAND CURVES
Economists refer to a variety of demand curves based on the magnitude of their elasticity. A demand curve, or a portion of a demand curve, can be elastic, inelastic, or unit elastic.
Demand is elastic when the elasticity is greater than 1(ED . 1)—the quantity demanded changes proportionally more than the price changes. In this case, a given percentage increase in price, say 10 percent, leads to a larger percentage change in quantity demanded, say 20 percent, as seen in Exhibit 1(a). If the curve is perfectly elastic, the demand curve is horizontal. The elasticity coefficient is infinity because even the slightest change in price will lead to a huge change in quantity demanded— for example, a tiny increase in price will cause the quantity demanded to fall to zero. In Exhibit 1(b), a perfectly elastic demand curve (horizontal) is illustrated.
Demand is inelastic when the elasticity is less than 1—the quantity demanded changes proportionally less than the price changes. In this case, a given percentage (for example, 10 percent) change in price is accompanied with a smaller (for example,
ED 5
%DQD
%DP
5
1 percent
10 percent
5 .10
50 percent
5 5
Price Elasticity of Demand
s e c t i o n
6.1
_ What is price elasticity of demand?
_ How do we measure consumers’ responses to price changes?
_ What determines the price elasticity of demand?
104 CHAPTER SIX | Elasticities
Price elasticity of demand (ED)
Percentage change in quantity demanded
5 Percentage change in price
5 percent) reduction in quantity demanded, as seen in Exhibit 2(a). If the demand curve is perfectly inelastic, the quantity demanded is the same regardless of the price. The elasticity coefficient is zero because there is no response to a change in price. This is illustrated in Exhibit 2(b).
Price Elasticity of Demand 105
P1
Q2 Q1
P2
Demand ED _ _ _ .20 2 .10 %_ QD
10%_ P
20%
_QD
%_ P
Price Quantity
0
Demand
_ QD
1%_ P
Elastic Demand SECTION 6.1
EXHIBIT 1
A small percentage change in price leads to a larger percentage change in quantity demanded.
A small percentage change in price will change quantity demanded by an infinite amount.
10%.P
5%
ED _ _ _ .05 .5 .10 %_QD
%_ P P1
Q1 _ Q2
20%_ P
Inelastic Demand SECTION 6.1
EXHIBIT 2
A change in price leads to a smaller percentage change in quantity demanded.
The quantity demanded does not change regardless of the percentage change in price.
a. Elastic Demand (ED > 1) b. Perfectly Elastic Demand (ED = ‡) a. Inelastic Demand (ED < 1) b. Perfectly Inelastic Demand (ED = 0)
Goods for which ED equals one (ED 5 1) are said to be unit elastic demand. In this case, the quantity demanded changes proportionately to price changes. For example, a 10 percent increase in price will lead to a 10 percent reduction in quantity demanded. This is illustrated in Exhibit 3.
The price elasticity of demand is closely related to the slope of the demand curve. Generally speaking, the flatter the demand curve passing through a given point, the more elastic the demand. The steeper the demand curve passing through a given point, the less elastic the demand.
CALCULATING THE PRICE ELASTICITY OF DEMAND: THE MIDPOINT METHOD
To get a clear picture of exactly how the price elasticity of demand is calculated, consider the case for the compact disc (CD) market. Say the price of CDs increases from $19 to $21. If we take an average between the old price, $19, and the new price, $21, we can calculate an average price of $20. Exhibit 4 shows that as a result of the increase in the price of CDs, the quantity demanded has fallen from 82 million CDs to 78 million CDs per year. If we take an average between the old quantity demand, 82 million, and the new quantity demanded, 78 million, we have an average quantity demanded of 80 million CDs per year.
That is, the $2 increase in the price of CDs has led to a 4-million-CD reduction in quantity demanded.
How can we figure out the price elasticity of demand?
You might ask why we are using the average price and average quantity. The answer is that if we did not use the average amounts, we would come up with different values for the elasticity of demand depending on whether we moved up or down the demand curve. When the change in price and quantity are of significant magnitude, the exact meaning of the term percentage change requires clarification, and the terms price and quantity
must be defined more precisely. The issue thus is, should the percentage change be figured on the basis of price and quantity before or after the change has occurred? For example, a price rise from $10 to $15 constitutes a 50 percent change if the original price ($10) is used in figuring the percentage ($5/$10), or a 33 percent change if the price after the change ($15) is used ($5/$15). For small changes, the distinction is not important, but for large changes, it is. To avoid this confusion, economists often use this average technique.
106 CHAPTER SIX | Elasticities
D 10%_ P 10%
0 ED _ _ _ .10 1 .10 %_QD
Unit Elastic Demand
SECTION 6.1
EXHIBIT 3
The percentage change in quantity demanded is the same as the percentage change in price that caused it (ED 5 1).
If bus fares increase, will ridership fall a little or a lot?
It all depends on the price elasticity of demand. If the price elasticity of demand is elastic, a 50-cent price increase will lead to a relatively large reduction in bus travel as riders find viable substitutes. If the price elasticity of demand is inelastic, a 50-cent price increase will lead to a relatively small reduction in bus ridership as riders are not able to find good alternatives to bus transportation.
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Specifically, we are actually calculating the elasticity at a midpoint between the old and new prices and quantities.
Now to figure out the price elasticity of demand, we must first calculate the percentage change in price. To find the percentage change in price, we take the change in price (DP) and divide it by the average price (Pave). (Note: The Greek letter delta, D, means
“change in.”) Percentage change in price 5 DP/Pave
In our CD example, the original price was $19, and the new price is $21. The change in price (DP) is $2, and the average price (Pave) is $20. The percentage change in price can then be calculated as Percentage change in price 5 $2/$20
5 1/10 5 0.10 5 10 percent Next, we must calculate the percentage change in quantity demanded. To find the percentage change in quantity demanded, we take the change in quantity demanded (DQD) and divide it by the average quantity demanded (QD ave).
Percentage change in quantity demanded 5 DQD/QD ave
In our CD example, the original quantity demanded was 82 million, and the new quantity demanded is 78 million. The change in quantity demanded (DQD) is 4 million, and the average quantity demanded (QD ave) is 80 million. The percentage change in quantity demanded can then be calculated as Percentage change in quantity demanded 5
4 million/80 million 5 1/20 5 0.05 5 5 percent Because the price elasticity of demand is equal to the percentage change in quantity demanded divided by the percentage change in price, the price elasticity of demand for CDs between point A and point B can be shown as
1/20 1/10
5% 10%
5 .5
5 DQD/QD ave
DP/Pave
4 million/80 million $2/$20
Percentage change in quantity demanded Percentage change in price
Price Elasticity of Demand 107
82 80 78 $21
D Pave
Qave A B
Price per CD Quantity of CDs (millions per month)
0 $20 $19
. QD = 4 million
ED = .5 at midpoint between A and B
. P = $2
Calculating the Price Elasticity of Demand
EXHIBIT 4
Unlike most tangible items (such as specific types of food or cars), there are few substitutes for a physician and medical care when you have an emergency. Because the number of available substitutes is limited, the demand for emergency medical care is relatively inelastic.
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The price elasticity of demand is found with the formula
_QD/QD ave
_P/Pave
THE DETERMINANTS OF THE PRICE ELASTICITY OF DEMAND
As you have learned, the elasticity of demand for a specific good refers to movements along its demand curve as its price changes. A lower price will increase quantity demanded, and a higher price will reduce quantity demanded. But what factors will influence the magnitude of the change in quantity demanded in response to a price change? That is, what will make the demand curve relatively more elastic (where QD is responsive to price changes), and what will make the demand curve relatively less elastic (where QD is less responsive to price changes)?
For the most part, the price elasticity of demand depends on three factors: (1) the availability of close substitutes, (2) the proportion of income spent on the good, and (3) the amount of time that has elapsed since the price change.
Availability of Close Substitutes
Goods with close substitutes tend to have more elastic demands. Why? Because if the price of such a good increases, consumers can easily switch to other now relatively lower priced substitutes. There are many examples, such as butter and margarine, one brand of root beer as opposed to another, or different brands of gasoline, where the ease of substitution will make demand quite elastic for most individuals. Goods without close substitutes, such as insulin for diabetics, cigarettes for chain smokers, heroin for addicts, or emergency medical care for those with appendicitis or broken legs, tend to have inelastic demands.
The degree of substitutability can also depend on whether the good is a necessity or a luxury.
Goods that are necessities, like food, have no ready substitutes and thus tend to have lower elasticities than do luxury items, like jewelry.
When the demand for a good is broadly defined, it tends to be less elastic than when it is narrowly defined. For example, the elasticity of demand for food, a very broad category, tends to be inelastic because there are very few substitutes for food. But for a certain type of food, like pizza, a narrowly defined good, it is much easier to find a substitute—perhaps tacos, burgers, salads, burritos, or chili fries. That is, the demand for a particular type of food is more elastic because there are more and better substitutes than for food as an entire category.
Proportion of Income Spent on the Good
The smaller the proportion of income spent on a good, the lower its elasticity of demand. If the amount spent on a good relative to income is small, then the impact of a change in its price on one’s budget will also be small. As a result, consumers will respond less to price changes for these goods than for similar percentage changes in large-ticket items, where a price change could have a potentially large impact on the consumer’s budget. For example, a 50 percent increase in the price of salt will have a much smaller impact on consumers’ behavior than a similar percentage increase in the price of a new automobile.
Similarly, a 50 percent increase in the cost of private university tuition will have a greater impact on students’ (and sometimes parents’) budgets than a 50 percent increase in textbook prices.
Time
For many goods, the more time that people have to adapt to a new price change, the greater the elasticity of demand. Immediately after a price change, consumers may be unable to locate very good alternatives or easily change their consumption patterns. But
108 CHAPTER SIX | Elasticities
Q1 QSR QLR
DLR
DSR
Price of Gasoline Quantity of Gasoline
Short-Run and Long-Run Demand Curves
EXHIBIT 5
For many goods, like gasoline, price is much more elastic in the long run than in the short run because buyers have more time to find suitable substitutes or change their consumption patterns. In the short run, the increase in price from P1 to P2 has only a small effect on the quantity demanded for gasoline. In the long run, the effect of the price increase will be much larger.
the more time that passes, the more time consumers have to find or develop suitable substitutes and to plan and implement changes in their patterns of consumption.
For example, drivers may not respond immediately to an increase in gas prices, perhaps believing it to be temporary. However, if the price persists over a longer period, we would expect people to drive less, buy more fuel-efficient cars, move closer to work, carpool, take the bus, or even bike to work. So for many goods, especially nondurable goods (goods that do not last a long time), the short-run demand curve is generally less elastic than the long-run demand curve, as illustrated in Exhibit 5.
Total Revenue and the Price Elasticity of Demand 109
1. Price elasticity of demand measures the percentage change in quantity demanded divided by the percentage change in price.
2. If the demand for a good is price elastic in the relevant range, quantity demanded is very responsive to a price change.
If the demand for a good is relatively price inelastic, quantity demanded is not very responsive to a price change.
3. The price elasticity of demand depends on: (1) the availability of close substitutes, (2) the proportion of income spent on the good, and (3) the amount of time that buyers have to respond to a price change.
1. What question is the price elasticity of demand designed to answer?
2. How is the price elasticity of demand calculated?
3. What is the difference between a relatively price elastic demand curve and a relatively price inelastic demand curve?
4. What is the relationship between the price elasticity of demand and the slope at a given point on a demand curve?
5. What factors tend to make demand curves more price elastic?
6. Why would a tax on a particular brand of cigarettes be less ...
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