C H A P T E R

F O U R

Elasticity C H A P T E R

O U T L I N E

Price Elasticity of Demand Determinants of Price Elasticity Price Elasticity Graphically Applications of Price Elasticity Elasticity of Supply Income Elasticity Cross-elasticity of Demand

W

hat’s ahead...This chapter focuses on how consumers respond to a change in the price of any particular good. Such responsiveness is called price elasticity of demand. We begin by showing how the seller’s total revenue is directly tied to elasticity. Next, we use the idea of elasticity to analyze four popular myths that are widely held by the general public. Finally, we see how elasticity is also used in the contexts of supply, income, and interproduct comparisons. A QUESTION OF RELEVANCE…

Have you ever noticed that most people make some purchases seemingly without thinking about it, yet agonize, sometimes for days, over the purchase of other things? Do you realize that there may well be a dozen or so different prices paid by people who board the same plane for a transcontinental flight? We are all aware that almost everything we purchase in Canada is taxed. It may seem clear that an increase in the GST is simply passed on to the consumer, while the retailer and producer are nothing more than disinterested bystanders. But do consumers really pay these taxes, or is it possible that the supplier shares some of the burden? Do the ticket scalpers you see outside the buildings of high-profile events like playoff hockey games or a Celine Dion concert always make a profit from the resale of the tickets they hold? Although these questions seem unrelated, they have a common link that we will explore in this chapter.

120

CHAPTER 4

Elasticity

I

total revenue: the total amount of income a firm receives from its sales; formally, it is price multiplied by the quantity of the product sold.

f a business raises the price of its product, will its revenue rise? Most people instinctively answer “yes” to this question. However, such an answer is correct only under certain conditions. You will recall that Chapter 2 introduced the law of demand and established the inverse relationship between price and quantity. Thus we know that a decrease in the price of, say, an airline ticket from Toronto to Montreal would result in an increase in the quantity of tickets sold. Obviously, this would be beneficial to consumers, but what we have not yet discussed is whether this would or would not be beneficial to the airline company selling the tickets. What is involved here is whether the airline would receive more or less total revenue as a result of selling more tickets at a lower price per ticket. Total revenue (TR), not to be confused with total profit, is simply the total dollar value of selling some quantity of an item at a certain price. Formally, it is:

TR = P  Q price elasticity of demand: the responsiveness of quantity demanded to a change in price.

Here, P stands for the price of the product and Q stands for the quantity sold. The effect of lowering price by itself will decrease total revenue. At the same time, however, the lower price will result in the quantity sold going up, and this will tend to increase total revenue. So what will be the net effect of these opposing pressures? The answer to this question depends on the concept economists call price elasticity of demand. The dictionary defines elasticity as “the state of being elastic or flexible,” and our focus is on the flexibility of consumers’ reactions to a change in price.

Price Elasticity of Demand Price elasticity of demand, which for the time being we will simply call elasticity, can also be defined as a measure of how much quantity demanded changes as a result of a change in price. The measurement of elasticity is obtained by taking the percentage change in quantity and dividing it by the percentage change in price. Note that we use percentage changes because price is expressed in dollars and quantity in units, so that using just the absolute change in quantity divided by the absolute change in price would not work. Also, showing elasticity in percentage terms means that we can ignore the units in which the quantity is measured. Let’s look at some hypothetical data, shown in Table 4.1. T A B L E 4 . 1 Demand for Airline Tickets I Vancouver to Edmonton

Vancouver to Calgary

Price

Quantity of Tickets

Total Revenue

Price

Quantity of Tickets

Total Revenue

$650 550

1000 1100

$650 000 605 000

$650 550

1000 1250

$650 000 687 500

Suppose the Vancouver to Edmonton ticket price is $650 and the quantity of tickets sold per day is 1000. This would yield total revenue to the airline of: $650  1000  $650 000. Next, assume that the price of a ticket falls to $550. As a result, the quantity of tickets sold rises to 1100. Total revenue, however, actually drops to: $550  1100  $605 000. In contrast, for the Vancouver to Calgary flight the same price change

Elasticity

elasticity coefficient: a number that measures the responsiveness of quantity demanded to a change in price.

CHAPTER 4

121

results in quantity rising from 1000 to 1250. As a result, total revenue also rises to: $550  1250  $687 500. From these examples we can conclude that the effect on total revenue can vary greatly, depending on how quantity responds to a price change. It also means that one cannot predict the effect on total revenue of a price decrease without knowing how responsive the quantity demanded will be. This is what is meant by the concept of elasticity. Let’s use the same information in Table 4.1 to do some calculations of elasticity. To obtain what is called the elasticity coefficient we use the general equation mentioned above, where elasticity is symbolized by the Greek upper-case letter epsilon, the subscript  indicates that it is the price elasticity of demand that is being referred to, and ∆ means “change in”:

 =

% ∆ quantity demanded % ∆ price

This basic equation can be expanded as follows:

 =

∆ Qd  100 average Qd ∆P average P

 100

To obtain the elasticity coefficient in the Vancouver to Edmonton example, we first need to determine the percentage change in quantity as the quantity changes from the original 1000 to the new 1100. The absolute increase is 100, and we need to put this 100 over a base to get the percentage increase. This raises the question of whether that base should be the original 1000 or the new 1100. Since 100 ÷ 1000 is 0.1 and 100 ÷ 1100 is 0.09, it clearly does make a difference as to which base is chosen. To resolve this question we take the average of the original base and the new base, which, in this case, is:

1000  1100 2

 1050

(Using averages ensures that we get the same result if the quantity goes down from $1100 to $1000 or up from $1000 to $1100.) Thus, the percentage change in quantity is the absolute change of 100 divided by the average base of 1050 multiplied by 100. Let’s show this explicitly:

% ∆ Qd 

100 1050

 100  9.5%

The 9.5 percent result is the numerator in the above equation. Next we calculate the percentage change in price by dividing the absolute change of $100 by the average of the original and new prices. The percentage change in the price is:

% ∆ Price 

$100 $600

 100  16.7%

Actually, the technical answer is –16.7 percent, but, with appropriate apologies to mathematicians, we simply ignore the minus sign. The reason economists do this is that price and quantity always move in opposite directions, and thus any calculation of price elasticity of demand would result in a negative coefficient. We can now obtain the elasticity coefficient:

122

CHAPTER 4

Elasticity

 = inelastic demand: quantity demanded that is not very responsive to a change in price.

% ∆ Q 9.5% = = 0.57 % ∆ P 16.7%

So, the Vancouver to Edmonton market has an elasticity coefficient of 0.57, which is less than 1 and is referred to as inelastic demand. This means that the quantity demanded is not very responsive to a price change. Specifically, a 1 percent change in price leads to only a 0.57 percent change in quantity. Note that because the demand is inelastic, total revenue will fall as a result of the decrease in price. In the calculation above we saw that total revenue decreases from the original $650 000 to $605 000. We are now able to make our first generalization involving elasticity: If demand is inelastic and price falls, then total revenue will also fall.

Let’s make the same calculation using the figures in the Vancouver to Calgary example. Here the absolute change in quantity is 250 and the average base is:

1000  1250 = 1125 2 Next is the following calculation: 250 = 22.2% 1125 To obtain the denominator we put the absolute change in price, $100, over the average base of: $650  $550 = $600 2 This gives a denominator of: 100 600

= 16.7%

Thus, the elasticity coefficient is:

elastic demand: quantity demanded that is quite responsive to a change in price.

22.2% = 1.32 16.7% The Vancouver to Calgary market, therefore, has an elasticity coefficient of 1.32, which is greater than 1 and is referred to as elastic demand. Here, the quantity demanded is much more responsive to a change in price. A 1 percent change in price leads to a 1.32 percent change in quantity demanded. Since the increase in quantity, which pushes total revenue up, is stronger than the decrease in price, which pushes total revenue down, we would expect that the net effect will be an increase in total revenue and this is verified by our earlier calculation of total revenue increasing from the original $650 000 to $687 500. We can now make our second generalization about elasticity: If demand is elastic and price falls, then total revenue will rise.

Do we get the same kind of result if the price increases instead of decreases? Let’s examine this by going to Table 4.2, in which we see price increasing from the original $650 to $750.

Elasticity

CHAPTER 4

123

S E L F - T E S T 1. Shown below are three sets of prices and their related quantities. Calculate the elasticity coefficients for each set.

Set I Set II Set III

Price

Quantity

$1.50 2.00 120.00 100.00 18.50 22.50

200 100 1600 1800 48 40

T A B L E 4 . 2 Demand for Airline Tickets II Vancouver to Edmonton

Vancouver to Calgary

Price

Quantity

Total Revenue: C

Price

Quantity

Total Revenue: D

$650 750

1000 900

$650 000 675 000

$650 750

1000 750

$650 000 567 500

We see from Table 4.2 that a $100 price increase in each market ($650 to $750) results in a decrease in the number of tickets sold for the Vancouver to Edmonton flights of only 100, but for the Vancouver to Calgary flights the decrease is 250. You should be able to verify that the elasticity coefficient in the Vancouver to Edmonton market is 0.74 and in the Vancouver to Calgary market is 2. These figures are different from the coefficients calculated previously, and there is a lesson in this. Moving up or down a demand curve results in the elasticity coefficient changing because the average base changes. Recall that the elasticity coefficient in the Vancouver to Edmonton example was 0.57 in the $550–$650 price range (Table 4.1), whereas it is 0.74 in the $650–$750 price range (Table 4.2). This, despite the fact that the absolute change in price is $100 and the absolute change in quantity is 100 tickets in both cases. However, the two average bases are not the same. The average quantity in the first instance is 1050 but only 950 in the second. Similarly, the average price is $600 in the first instance but $700 in the second. S E L F - T E S T 2. Below are two sets of prices and their related quantities. Calculate the elasticity coefficients for each set.

Set I Set II

Price

Quantity

$9 8 2 1

1 2 8 9

In each set the change in price is $1 and the change in quantity is 1 unit. Why aren’t the coefficients the same?

124

CHAPTER 4

Elasticity

Despite the difference in elasticity coefficients at different price ranges, one thing remains consistent: the Vancouver to Edmonton market is an example of inelastic demand, and the Vancouver to Calgary market is an example of elastic demand. We saw earlier that if price decreases and demand is inelastic, then total revenue would fall. Thus, if price were to rise, we would expect the opposite, a rise in total revenue, and this is exactly what we get as total revenue increases from $650 000 to $675 000. Similarly, Table 4.1 indicated that if price falls and demand is elastic, we would experience an increase in total revenue. Thus, we would expect that a price rise in combination with elastic demand would cause a decrease in total revenue, and this is exactly what happens in Table 4.2, as total revenue falls from $650 000 to $567 500. Table 4.3 summarizes the effect of elasticity on total revenue as a result of a price change. T A B L E 4 . 3 Relationship Between Price and Total Revenue Elasticity Coefficient

Price

Total Revenue

inelastic (1)

falls rises falls rises

falls rises rises falls

We could also summarize the effects of a price change by saying that: If the demand is inelastic, price and total revenue move in the same direction. If the demand is elastic, price and total revenue move in opposite directions.

S E L F - T E S T 3. What would happen to total revenue in each of the circumstances below: A)  > 1 and price falls? B)  < 1 and price rises? C)  < 1 and price falls? D)  > 1 and price rises?

4. Suppose that the price of four different products all increased by 20 percent. Given the elasticity coefficients shown below, what is the percentage change in the quantity of each product? A)  = 4. B)  = 0.5. C)  = 1. D)  = 0.

Determinants of Price Elasticity Before we examine the determinants of elasticity, let’s identify some commodities that typically have elastic demands and some that typically have inelastic demands (see Table 4.4).

Elasticity

CHAPTER 4

125

T A B L E 4 . 4 Examples of Products with Different Elasticities of Demand Commodities That Have Elastic Demands

Commodities That Have Inelastic Demands

fresh tomatoes (4.60) movies (3.41) lamb (2.65) restaurant meals (1.63) china and tableware (1.54) automobiles (1.14)

household electricity (0.13) eggs (0.32) car repairs (0.36) food (0.58) household appliances (0.63) tobacco (0.86)

Source: H.S. Houthakker and Lester D. Taylor, Consumer Demand in the United States (Cambridge, MA: Harvard University Press, 1970).

A major determinant of elasticity is the availability of close substitutes. For example, in most people’s eyes almost any other vegetable is a substitute for tomatoes. Home videos and other forms of entertainment are substitutes for movies, whereas pork and beef are close substitutes for lamb. The substitute for a restaurant meal is to cook at home. Many households find that the substitute for furniture or china and tableware is to simply make do with less of what many consider to be non-essential items. Automobiles have the least elastic demand of those on our list because many people do not consider public transit or bicycling to be a close substitute. A clear conclusion comes out of all this. The more substitutes available for any particular commodity, the greater is the elasticity of demand for that commodity. A D D E D

D I M E N S I O N

What Is a Necessity? It is not uncommon for people to think of products as either luxuries or necessities. There is then a temptation to conclude that luxury products are elastic in demand, whereas necessities must be inelastic. While there is undoubtedly validity in this rule of thumb, we must be careful. To some, wine with a meal is an absolute necessity, while to others it

is a seldom-bought luxury. What is a bottle of brandy—a necessity for evening relaxation or a luxury used only in holiday times? What really matters when we are talking about the elasticity of demand is that normally we are looking at market elasticity, that is, the preferences of the majority of people.

Let’s now go through the list of commodities that have inelastic demands. Candles can be used as a substitute for electric light, but this is not an attractive option to most people. Eggs are an essential ingredient in baking and cooking. The only real substitutes for auto repairs are to repair the car yourself or to buy a new one, and both of these options are impractical most of the time. Food, as a category, has no substitutes. To the users of tobacco, this item involves an addiction for which there is simply no substitute. To most families, significant price swings in household appliances such as a hot-water heater will not change the quantity demanded much. Before leaving this discussion of the availability of substitutes, we should note that a great deal depends on how the commodity in question is defined. The demand for food is an example of a broadly defined category and as such it is highly inelastic, since there is no substitute for food. Yet the elasticity of demand for any one food item, such as green beans, is much more elastic because there are many close substitutes. As another example, the elasticity of demand for housing in general is quite low because all of us have to live somewhere whereas, the elasticity of demand for home ownership is much greater since there is the alternative of renting.

126

CHAPTER 4

Elasticity

A second determinant of elasticity is the percentage of household income spent on the commodity. In general, we can say the larger the percentage of one’s income that is spent on a particular commodity, the more elastic is the demand for that commodity. For this reason the elasticity of demand for a high-priced automobile or for a topof-the-line stereo system will be high. On the other hand, the elasticity of demand for ordinary spices or hand soap will tend to be inelastic simply because the total percentage of a household’s budget that is spent on such items is small and the price change will have little impact on our budgets. The third determinant of elasticity involves the amount of time that has elapsed since the price change. The classic example here is that of gasoline. When the OPEC oil embargo of l973 resulted in the halting of (most) oil shipments to North America, the price of gasoline increased fourfold in just 18 months. Measurements of elasticity made over this period of time indicated a very inelastic demand. This was because in the immediate aftermath of such a price shock, very few close substitutes to gasoline were available. This fact became much less true as time wore on, and a number of substitutes were developed. The most significant of these was the development and marketing of much more fuel-efficient automobiles that became increasingly popular in the later 1970s. In addition, given enough time to adjust, people moved closer to their place of employment and the established patterns of driving long distances for a holiday or for a casual visit were changed. Subsequent measurements of the elasticity of demand for gasoline over a time period of 5 or 10 years after the price shock showed elasticity coefficients that were much higher than those taken in the first 18 months. All of this can lead us to conclude that the elasticity of demand tends to be greater the longer the time period involved. In summary, the demand for a product is more elastic: • the more substitutes there are available • the larger the percentage of one’s income that is spent on the product • the longer the time period involved E - C O N O M I C S A New Way of Shopping Wired magazine reports that the following scenario is not far off. Imagine yourself walking into a supermarket and instead of picking a shopping cart to hold your purchases you pick up your Personal Digital Assistant (PDA). This new electronic device allows you to walk up and down the aisles and obtain your individually tailored price for every item you pass. But this initially-quoted price is just the starting point of the process. You could, for example, “have a conversation” with a tube of toothpaste by saying something like: “I understand that the price for one is $2.89 but what if I buy six units?” The response might be: “$2.73 for six and $2.59 for twelve.” You would then indicate your choice and move on without

actually picking up any toothpaste. When your shopping was done, you would proceed to a checkout area where your goods would be waiting for you, along with your bill. After several shopping experiences like this, the store would have a very good idea of what you buy and in what quantities. In short, it would know your demand elasticity for scores of products. Having this knowledge, the store could then pattern individual prices for each item and for each customer. Currently, obtaining such information is very expensive for the seller and can only be applied to large groups of people; e.g. young families, older singles, etc. The PDA will change all that by personalizing each customer’s preferences.

Price Elasticity Graphically What we need to do next is to take this concept of elasticity and give it graphical representation. We will start with Figure 4.1.

Elasticity

CHAPTER 4

127

F I G U R E 4 . 1 The Demand for Airline Tickets: Vancouver to Edmonton

Price elasticity of demand = 0.57

Price per ticket

$650

550

When the price of an airline ticket from Vancouver to Edmonton is $650, 1000 tickets per day are sold. If the price falls to $550, then the quantity demanded rises to 1100 tickets.

D

1000 1100 Quantity of tickets per day

Using the data from Table 4.1, Figure 4.1 shows that a price decrease of $100 in the Edmonton fare results in an increase in the quantity demanded of 100 tickets. You may recall that the elasticity coefficient in this case is 0.57. This indicates that demand is inelastic. This is reflected in the relatively steep demand curve in Figure 4.1. Contrast this demand curve with the one in Figure 4.2. F I G U R E 4 . 2 The Demand for Airline Tickets: Vancouver to Calgary

Price elasticity of demand = 1.32

Price per ticket

$650

When the price of an airline ticket from Vancouver to Calgary is $650, 1000 tickets per day are sold. If the price falls to $550, the quantity demanded rises to 1250 tickets.

550 D

1000

1250

Quantity of tickets per day

In Figure 4.2, using the Vancouver to Calgary data from Table 4.1, the demand curve plots out an increase of 250 tickets demanded as a result of a $100 decrease in price. This is an elastic demand. Notice that the demand curve is not as steep as was the one in Figure 4.1 but is, instead, relatively shallow. Does this mean that all demand

128

CHAPTER 4

Elasticity

curves that appear steep are inelastic and all that appear shallow are elastic—that is, is there a relationship between the slope of the demand curve and elasticity? We must be very careful here because the technical answer is no, but the practical answer is maybe. To sort this out, let us go to Figure 4.3. F I G U R E 4 . 3 A Constant-Slope Demand Curve $10

a

9

b

7

Price

Both of the movements a to b and c to d involve a change in price of $2 and a change in quantity of 2 units. Yet, the elasticity coefficient for the a to b movement is much larger than that for the c to d movement. Since the slope of this demand curve is constant and the elasticity is not, we can conclude that slope and elasticity are not the same concepts.

=4

Elasticity is not the same thing as slope

5

c

3

 = 0.25

d

1 1

3

5

7

9

10

Quantity

You may recall from high school math that the slope of any straight line is equal to the rise over run. Note in the demand curve in Figure 4.3 that an increase in price of $1 always results in a quantity decrease of 1. Thus the slope of the demand curve is constant and equal to 1 (again the negative sign is ignored). Is elasticity also constant? Let’s calculate the elasticity coefficient for a movement along the curve first for point a to b and then for point c to d. Movement a to b would yield a coefficient of:

 =

% ∆Q 2/2  100 100% = = =4 % ∆P 2/8  100 25%

On the other hand, movement from point c to d would yield:

 =

2/8  100 25% = = 0.25 2/2  100 100%

Quite clearly the elasticity coefficient is different at different points on the demand curve. Thus, it must be concluded that slope and elasticity are not the same thing. One final note: the changes in price and quantity in Figure 4.3 are rather large. Technically, elasticity can be measured for very small changes — in the extreme at a single point by multiplying the inverse of the slope by the ratio P/Q. S E L F - T E S T 5. Imagine that elasticity coefficients were recently measured in Canada over a period of one year for the following products. Indicate whether you think such a measurement would be elastic (>1) or inelastic (1 and not yet 1 and price falls. b) If elasticity is >1 and price rises. c) If elasticity is