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Chapter 3 Elasticities 47
Microeconomics
Chapter 3
Elasticities
Elasticity is a measure of the responsiveness of a variable to changes in price or any of the variable’s
determinants. In this chapter we will examine four kinds of elasticities, with numerous applications to important
economic problems.
3.1 Price elasticity of demand (PED)
Price elasticity of demand
Explain the concept of price elasticity of demand,
understanding that it involves responsiveness of quantity demanded to a change in price, along a given demand curve.
Understanding price elasticity
of demand ( PED )
According to the law of demand, there is a negative relationship between price and quantity demanded: the higher the price, the lower the quantity demanded, and vice versa, all other things equal. We now want to know by how much quantity responds to change in price.
Price elasticity of demand ( PED ) is a measure of the responsiveness of the quantity of a good demanded to changes in its price. PED is calculated along a given demand curve. In general, if there is a large responsiveness of quantity demanded, demand is referred to as being price elastic ; if there is a small responsiveness, demand is price inelastic.
The formula for PED
Calculate PED using the following equation.
percentage change in price
percentage change in quantity demanded PED =
Suppose we are considering price elasticity of demand ( PED ) for good X. The formula used to measure its PED is:
The sign of PED
State that the PED value is treated as if it were positive
although its mathematical value is usually negative.
Since price and quantity demanded are negatively (indirectly) related, the PED is a negative number. For any percentage increase in price (a positive denominator), there results a percentage decrease in quantity demand (a negative numerator), leading to a negative PED. Similarly, for a percentage price decrease the result will be a percentage price increase, again leading to a negative PED. However, the common practice is to drop the minus sign and consider PED as a positive number. (In mathematics this is called taking the absolute value.) This is done to avoid confusion when making comparisons between different values of PED. Using positive numbers, we can say, for example, that a PED of 3 is larger than a PED of 2. (Had we been using the minus sign, −2 would be larger than −3.)
price elasticity of demand (^) percentage change in price of good X
percentage change in quantity of good X demanded = PED =
If we abbreviate ‘change in’ by the Greek letter Δ, this formula can be rewritten as: PED =
%Δ Q x %Δ P x Simplifying, the above formula can be rewritten as:
PED =
Δ Q x Q x
× 100
Δ P x P x
× 100
Δ Q x Q x Δ P x P x
48 Section 1: Microeconomics
The use of percentages
Elasticity is measured in terms of percentages for two reasons:
- We need a measure of responsiveness that is independent of units. First, we want to be able to compare the responsiveness of quantity demanded of different goods; it makes little sense to compare units of oranges with units of computers or cars. Secondly, we want to be able to compare responsiveness across countries that have different currencies; an elasticity measured in terms of euros will not be comparable with an elasticity measured in yen or pounds. By computing changes in quantity and changes in price as percentages, we express them in common terms, thereby making it possible to compare responsiveness for different goods and across countries.
- It is meaningless to think of changes in prices or quantities in absolute terms (for example, a $ increase in price or a 20 unit decrease in quantity) because this tells us nothing about the relative size of the change. For example, a $15 price increase means something very different for a good whose original price is $100 than for a good whose original price is $5000. In the first case there is a 15% increase, and in the second there is a 0.3% increase. Using percentages to measure price and quantity changes allows us to put responsiveness into perspective.
The same arguments apply to all other elasticities we will consider.
Calculating PED
Calculate PED between two designated points on a
demand curve using the PED equation above.
We can now use the formula above to calculate PED. Suppose consumers buy 6000 DVD players when the price is $255 per unit, and they buy 5000 DVD players when the price is $300.
PED =
= = −1.33 or 1.
since we drop the minus sign. Therefore PED for DVD players is 1.33.^1
1 (a) Explain the meaning of price elasticity of demand. (b) Why do we say it measures responsiveness of quantity along a given demand curve? 2 Why do we treat PED as if it were positive, even though it is usually negative? 3 It is observed that when the price of pizzas is $16 per pizza, 100 pizzas are sold; when the price falls to $12 per pizza, 120 pizzas are sold. Calculate price elasticity of demand. 4 A 10% increase in the price of a particular good gives rise to an 8% decrease in quantity bought. What is the price elasticity of demand?
Test your understanding 3.
The range of values for PED
Explain, using diagrams and PED values, the concepts of
price elastic demand, price inelastic demand, unit elastic demand, perfectly elastic demand and perfectly inelastic demand.
The value of PED involves a comparison of two numbers: the percentage change in quantity demanded (the numerator in the PED formula) and the percentage change in price (the denominator). This comparison yields several possible values and range of values for PED. These are illustrated in Figure 3.1 and summarised in Table 3.1.
(^1) You may note that the value of this elasticity of demand depends on the choice of the initial price–quantity combination. In the calculation above, this was taken to be 300, 5000. If we had taken 255, 6000 as the initial price–quantity combination, we would get a PED value of 0.94. (You could calculate this as an exercise.) This difficulty can be overcome by use of the ‘midpoint formula’:
PED =
Δ Q x average Q x Δ P x average P x
.
In the previous example,
PED =
1000 5500 45
= 1.12, where 5500 = (5000^ +^ 6000) 2
and 277.5 = (255^ +^ 300) 2
i.e. we use the average of the two Q x values and the average of the two P x values instead of the initial Q x and initial P x.
50 Section 1: Microeconomics
- Demand is price elastic when PED > 1 (but less than infinity). The percentage change in quantity demanded is larger than the percentage change in price, so the value of PED is greater than one; quantity demanded is relatively responsive to price changes, and demand is price elastic. In Figure 3.1(b) the percentage change in quantity demanded (–10%) is larger than the percentage change in price (5%), therefore PED is greater than one.
In addition, there are three special cases:
- Demand is unit elastic when PED = 1. The percentage change in quantity demanded is equal to the percentage change in price, so PED is equal to one; demand is then unit elastic. Figure 3.1(c) shows a unit elastic demand curve, where the percentage change in quantity demanded (–5%) is equal to the percentage change in price (5%).
- Demand is perfectly inelastic when PED = 0. The percentage change in quantity demanded is zero; there is no change in quantity demanded, which remains constant at Q 1 no matter what happens to price; PED is then equal to zero and demand is perfectly inelastic. For example, a heroin addict’s quantity of heroin demanded is unresponsive to changes in the price of heroin. Figure 3.1(d) shows that a perfectly inelastic demand curve is vertical.
- Demand is perfectly elastic when PED = infinity. When a change in price results in an infinitely large response in quantity demanded, demand is perfectly elastic. As shown in Figure 3.1(e) the perfectly elastic demand curve is horizontal. At price P 1 , consumers will buy any quantity that is available. If price falls, buyers will buy all they can (an infinitely large response); if there is an increase in price, quantity demanded drops to zero. This apparently strange kind of demand will be considered in Chapter 7 (at higher level).
The numerical value of PED can therefore vary from zero to infinity. In general, the larger the value of PED , the greater the responsiveness of quantity demanded. PED for most goods and services is greater than zero and less than infinite, and other than exactly one. The cases of unit elastic, perfectly inelastic and perfectly elastic demand are rarely encountered in practice; however, they have important applications in economic theory.
units of good A
f e d c b a
PED = 4
PED = 1
PED = 0.
elastic portion of demand curve
inelastic portion of demand curve
P ($)
Figure 3.2 Variability ofPED along a straight-line demand curve
Variable PED and the straight-line
demand curve versus the slope
Explain why PED varies along a straight line demand curve
and is not represented by the slope of the demand curve.
When PED varies
Along any downward-sloping, straight-line demand curve , the PED varies (changes) as we move along the curve. This applies to all demand curves of the types shown in Figure 3.1 (a) and (b). It excludes unit elastic, perfectly inelastic and perfectly elastic demand curves (where PED = 1, PED = 0 and PED = infinity, respectively, and does not vary). We can see in Figure 3.2 that when price is low and quantity is high, demand is inelastic; as we move up the demand curve towards higher prices and lower quantities, demand becomes more and more elastic. The figure shows the PED values along different parts of the demand curve (you will be asked to do the PED calculations as an exercise – see Test your understanding 3.2). The reason behind the changing PED along a straight-line demand curve has to do with how PED is calculated. At high prices and low quantities, the percentage change in Q is relatively large (since the denominator of Δ Q / Q is small), while the percentage change in P is relatively small (because the denominator of Δ P / P is large). Therefore the value of PED , given by a large percentage change in Q divided by a small percentage change in P results in a large PED (elastic demand). At low prices and high quantities the opposite holds. The value of PED is
Chapter 3 Elasticities 51
given by a low percentage change in Q divided by a high percentage change in P , resulting in a low PED (elastic demand).
On any downward-sloping, straight-line demand curve, demand is price-elastic at high prices and low quantities, and price-inelastic at low price and large quantities. At the midpoint of the demand curve, there is unit elastic demand.
Therefore, the terms ‘elastic’ and ‘inelastic’ should not be used to refer to an entire demand curve (with the exception of the three special cases where PED is constant throughout the entire demand curve). Instead, they should be used to refer to a portion of the demand curve that corresponds to a particular price or price range.
The relationship between PED and the slope
(Higher level topic)
The varying PED along a straight-line demand curve should be contrasted with the slope , which is always constant along a straight line (see ‘Quantitative techniques’ chapter on the CD-ROM, page 28). In the special case of demand (and supply) functions, whose corresponding curves plot the dependent variable on the horizontal axis (in contrast to mathematical
convention), the slope is defined as Δ^ Q Δ P
, or the
horizontal change between two points on the curve divided by the vertical change between the same two points. A comparison of the slope with PED shows that the two should not be confused:
slope of demand curve =
Δ Q
Δ P
PED =
%Δ Q
%Δ P
Δ Q
Q
Δ P
P
Δ Q
Δ P
×
P
Q
= slope ×
P
Q
In these two expressions we can see why the slope is constant, while PED varies along a straight-line
demand curve. In a straight line, the ratio
Δ Q
Δ P
, or the
slope, does not change between any pairs of points on the line. However, PED is defined as the slope (which
is constant) times
P
Q
, which clearly changes as we
move along the demand curve, thus accounting for the changing PED. The slope of the demand curve measures the responsiveness of quantity demanded to changes in price in absolute terms, while PED measures the same responsiveness in percentage terms. PED is far
more useful as a measure of responsiveness for the reasons discussed on page 48. (See also the discussion in ‘Quantitative techniques’ chapter on the CD- ROM, page 28.)
PED should not be confused with the slope of a demand curve. Whereas the slope is constant for a linear (straight-line) demand curve, PED varies throughout its range.
Determinants of price elasticity of demand
Explain the determinants of PED, including the number
and closeness of substitutes, the degree of necessity, time and the proportion of income spent on the good.
We will now consider the factors that determine whether the demand for a good is elastic or inelastic.
Number and closeness of substitutes
The more substitutes a good (or service) has, the more elastic is its demand. If the price of a good with many substitutes increases, consumers can switch to other substitute products, therefore resulting in a relatively large drop (large responsiveness) in quantity demanded. For example, there are many brands of toothpaste, which are close substitutes for each other. An increase in the price of one, with the prices of others constant will lead consumers to switch to the others; hence demand for a specific toothpaste brand is price elastic. If a good or service has few or no substitutes, then an increase in price will bring forth a small drop in quantity demanded. An increase in the price of petrol (gasoline) is likely to lead to a relatively small decrease in quantity demanded, because there are no close substitutes; therefore, demand for petrol is price inelastic. Also important is the closeness of substitutes. For example, Coca-Cola®^ and Pepsi®^ are much closer substitutes than Coca-Cola and orange juice; we say that Coca-Cola and Pepsi have greater substitutability. The closer two substitutes are to each other, the greater the responsiveness of quantity demanded to a change in the price of the substitute, hence the greater the PED , because it is easier for the consumer to switch from one product to the other. A factor that affects the number of substitutes a good has is whether the good is defined broadly or narrowly. For example, fruit is a broad definition of a good if it is considered in relation to specific fruits such as oranges, apples, pears, and so on, which are narrowly defined. Note that a broad or narrow definition involves how goods are defined in relation to each other. If we had considered fruit in relation to
