PrinciplesofMacroeconomics-UNIT-2-Chapter5Reading.pdf

107 Chapter 5 | Elasticity

5 | Elasticity

Figure 5.1 Netflix On-Demand Media Netflix, Inc. is an American provider of on-demand Internet streaming media
to many countries around the world, including the United States, and of flat rate DVD-by-mail in the United States.
(Credit: modification of work by Traci Lawson/Flickr Creative Commons)

That Will Be How Much?

Imagine going to your favorite coffee shop and having the waiter inform you the pricing has changed. Instead
of $3 for a cup of coffee, you will now be charged $2 for coffee, $1 for creamer, and $1 for your choice of
sweetener. If you pay your usual $3 for a cup of coffee, you must choose between creamer and sweetener. If
you want both, you now face an extra charge of $1. Sound absurd? Well, that is similar to the situation Netflix
customers found themselves in—they faced a 60% price hike to retain the same service in 2011.

In early 2011, Netflix consumers paid about $10 a month for a package consisting of streaming video and
DVD rentals. In July 2011, the company announced a packaging change. Customers wishing to retain both
streaming video and DVD rental would be charged $15.98 per month, a price increase of about 60%. In
2014, Netflix also raised its streaming video subscription price from $7.99 to $8.99 per month for new U.S.
customers. The company also changed its policy of 4K streaming content from $9.00 to $12.00 per month that
year.

108 Chapter 5 | Elasticity

How would customers of the 18-year-old firm react? Would they abandon Netflix? Would the ease of access to
other venues make a difference in how consumers responded to the Netflix price change? We will explore the
answers to those questions in this chapter, which focuses on the change in quantity with respect to a change
in price, a concept economists call elasticity.

Introduction to Elasticity
In this chapter, you will learn about:

• Price Elasticity of Demand and Price Elasticity of Supply

• Polar Cases of Elasticity and Constant Elasticity

• Elasticity and Pricing

• Elasticity in Areas Other Than Price

Anyone who has studied economics knows the law of demand: a higher price will lead to a lower quantity demanded.
What you may not know is how much lower the quantity demanded will be. Similarly, the law of supply states that
a higher price will lead to a higher quantity supplied. The question is: How much higher? This chapter will explain
how to answer these questions and why they are critically important in the real world.

To find answers to these questions, we need to understand the concept of elasticity. Elasticity is an economics concept
that measures responsiveness of one variable to changes in another variable. Suppose you drop two items from a
second-floor balcony. The first item is a tennis ball. The second item is a brick. Which will bounce higher? Obviously,
the tennis ball. We would say that the tennis ball has greater elasticity.

Consider an economic example. Cigarette taxes are an example of a “sin tax,” a tax on something that is bad for you,
like alcohol. Governments tax cigarettes at the state and national levels. State taxes range from a low of 17 cents per
pack in Missouri to $4.35 per pack in New York. The average state cigarette tax is $1.69 per pack. The 2014 federal
tax rate on cigarettes was $1.01 per pack, but in 2015 the Obama Administration proposed raising the federal tax
nearly a dollar to $1.95 per pack. The key question is: How much would cigarette purchases decline?

Taxes on cigarettes serve two purposes: to raise tax revenue for government and to discourage cigarette consumption.
However, if a higher cigarette tax discourages consumption considerably, meaning a greatly reduced quantity of
cigarette sales, then the cigarette tax on each pack will not raise much revenue for the government. Alternatively,
a higher cigarette tax that does not discourage consumption by much will actually raise more tax revenue for the
government. Thus, when a government agency tries to calculate the effects of altering its cigarette tax, it must analyze
how much the tax affects the quantity of cigarettes consumed. This issue reaches beyond governments and taxes.
Every firm faces a similar issue. When a firm considers raising the sales price, it must consider how much a price
increase will reduce the quantity demanded of what it sells. Conversely, when a firm puts its products on sale, it must
expect (or hope) that the lower price will lead to a significantly higher quantity demanded.

5.1 | Price Elasticity of Demand and Price Elasticity of

Supply

By the end of this section, you will be able to:

• Calculate the price elasticity of demand

• Calculate the price elasticity of supply

Both the demand and supply curve show the relationship between price and the number of units demanded or
supplied. Price elasticity is the ratio between the percentage change in the quantity demanded (Qd) or supplied
(Qs) and the corresponding percent change in price. The price elasticity of demand is the percentage change in the
quantity demanded of a good or service divided by the percentage change in the price. The price elasticity of supply
is the percentage change in quantity supplied divided by the percentage change in price.

This OpenStax book is available for free at http://cnx.org/content/col12190/1.4

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109 Chapter 5 | Elasticity

We can usefully divide elasticities into three broad categories: elastic, inelastic, and unitary. An elastic demand or
elastic supply is one in which the elasticity is greater than one, indicating a high responsiveness to changes in price.
Elasticities that are less than one indicate low responsiveness to price changes and correspond to inelastic demand or
inelastic supply. Unitary elasticities indicate proportional responsiveness of either demand or supply, as Table 5.1
summarizes.

If . . . Then . . . And It Is Called . . .

% change in quantity > % change in price % change in quantity
% change in price

> 1 Elastic

% change in quantity = % change in price % change in quantity
% change in price

= 1 Unitary

% change in quantity < % change in price % change in quantity % change in price < 1 Inelastic Table 5.1 Elastic, Inelastic, and Unitary: Three Cases of Elasticity Before we delve into the details of elasticity, enjoy this article (http://openstaxcollege.org/l/Super_Bowl) on elasticity and ticket prices at the Super Bowl. ⎞ ⎠ ⎛ ⎝ To calculate elasticity along a demand or supply curve economists use the average percent change in both quantity and price. This is called the Midpoint Method for Elasticity, and is represented in the following equations: Q2 – Q1= Q2 + Q1 /2 % change in quantity × 100 = P2 – P1% change in price × 100⎞ ⎠ ⎛ ⎝P2 + P1 /2 The advantage of the Midpoint Method is that one obtains the same elasticity between two price points whether there is a price increase or decrease. This is because the formula uses the same base (average quantity and average price) for both cases. Calculating Price Elasticity of Demand Let’s calculate the elasticity between points A and B and between points G and H as Figure 5.2 shows. http://openstaxcollege.org/l/Super_Bowl 110 Chapter 5 | Elasticity Figure 5.2 Calculating the Price Elasticity of Demand We calculate the price elasticity of demand as the percentage change in quantity divided by the percentage change in price. First, apply the formula to calculate the elasticity as price decreases from $70 at point B to $60 at point A: 3,000 – 2,800% change in quantity = × 100(3,000 + 2,800)/2 200= 2,900 × 100 = 6.9 60 – 70% change in price = × 100(60 + 70)/2 –10= × 10065 = –15.4 Price Elasticity of Demand = 6.9% –15.4% = 0.45 6.9%Therefore, the elasticity of demand between these two points is which is 0.45, an amount smaller than one, –15.4% showing that the demand is inelastic in this interval. Price elasticities of demand are always negative since price and quantity demanded always move in opposite directions (on the demand curve). By convention, we always talk about elasticities as positive numbers. Mathematically, we take the absolute value of the result. We will ignore this detail from now on, while remembering to interpret elasticities as positive numbers. This means that, along the demand curve between point B and A, if the price changes by 1%, the quantity demanded will change by 0.45%. A change in the price will result in a smaller percentage change in the quantity demanded. For example, a 10% increase in the price will result in only a 4.5% decrease in quantity demanded. A 10% decrease in the price will result in only a 4.5% increase in the quantity demanded. Price elasticities of demand are negative numbers indicating that the demand curve is downward sloping, but we read them as absolute values. The following Work It Out feature will walk you through calculating the price elasticity of demand. This OpenStax book is available for free at http://cnx.org/content/col12190/1.4 http://cnx.org/content/col12190/1.4 111 Chapter 5 | Elasticity Finding the Price Elasticity of Demand Calculate the price elasticity of demand using the data in Figure 5.2 for an increase in price from G to H. Has the elasticity increased or decreased? Step 1. We know that: Price Elasticity of Demand = % change in quantity % change in price Step 2. From the Midpoint Formula we know that: = Q2 – Q1 × 100 Q2 + Q1)/2 ⎛ ⎝ % change in quantity = P2 – P1% change in price × 100 P2 + P1)/2 Step 3. So we can use the values provided in the figure in each equation: ⎛ ⎝ 1,600 – 1,800=% change in quantity × 100 ⎛ ⎝1,600 + 1,800)/2 –200= × 100 1,700 = –11.76 130 – 120% change in price = × 100 (130 + 120)/2 10= × 100 125 = 8.0 Step 4. Then, we can use those values to determine the price elasticity of demand: % change in quantity Price Elasticity of Demand = % change in price –11.76= 8 = 1.47 Therefore, the elasticity of demand from G to is H 1.47. The magnitude of the elasticity has increased (in absolute value) as we moved up along the demand curve from points A to B. Recall that the elasticity between these two points was 0.45. Demand was inelastic between points A and B and elastic between points G and H. This shows us that price elasticity of demand changes at different points along a straight-line demand curve. Calculating the Price Elasticity of Supply Assume that an apartment rents for $650 per month and at that price the landlord rents 10,000 units are rented as Figure 5.3 shows. When the price increases to $700 per month, the landlord supplies 13,000 units into the market. By what percentage does apartment supply increase? What is the price sensitivity? 112 Chapter 5 | Elasticity Figure 5.3 Price Elasticity of Supply We calculate the price elasticity of supply as the percentage change in quantity divided by the percentage change in price. Using the Midpoint Method, 13,000 – 10,000% change in quantity = × 100(13,000 + 10,000)/2 3,000= × 10011,500 = 26.1 $700 – $650% change in price = × 100⎛ ⎝$700 + $650)/2 50= × 100675 = 7.4 26.1%Price Elasticity of Supply = 7.4% = 3.53 Again, as with the elasticity of demand, the elasticity of supply is not followed by any units. Elasticity is a ratio of one percentage change to another percentage change—nothing more—and we read it as an absolute value. In this case, a 1% rise in price causes an increase in quantity supplied of 3.5%. The greater than one elasticity of supply means that the percentage change in quantity supplied will be greater than a one percent price change. If you're starting to wonder if the concept of slope fits into this calculation, read the following Clear It Up box. Is the elasticity the slope? It is a common mistake to confuse the slope of either the supply or demand curve with its elasticity. The slope is the rate of change in units along the curve, or the rise/run (change in y over the change in x). For example, in Figure 5.2, at each point shown on the demand curve, price drops by $10 and the number of units demanded increases by 200 compared to the point to its left. The slope is –10/200 along the entire demand curve and does not change. The price elasticity, however, changes along the curve. Elasticity between points A and B was 0.45 and increased to 1.47 between points G and H. Elasticity is the percentage change, which is a different calculation from the slope and has a different meaning. When we are at the upper end of a demand curve, where price is high and the quantity demanded is low, a small change in the quantity demanded, even in, say, one unit, is pretty big in percentage terms. A change This OpenStax book is available for free at http://cnx.org/content/col12190/1.4 http://cnx.org/content/col12190/1.4 113 Chapter 5 | Elasticity in price of, say, a dollar, is going to be much less important in percentage terms than it would have been at the bottom of the demand curve. Likewise, at the bottom of the demand curve, that one unit change when the quantity demanded is high will be small as a percentage. Thus, at one end of the demand curve, where we have a large percentage change in quantity demanded over a small percentage change in price, the elasticity value would be high, or demand would be relatively elastic. Even with the same change in the price and the same change in the quantity demanded, at the other end of the demand curve the quantity is much higher, and the price is much lower, so the percentage change in quantity demanded is smaller and the percentage change in price is much higher. That means at the bottom of the curve we'd have a small numerator over a large denominator, so the elasticity measure would be much lower, or inelastic. As we move along the demand curve, the values for quantity and price go up or down, depending on which way we are moving, so the percentages for, say, a $1 difference in price or a one unit difference in quantity, will change as well, which means the ratios of those percentages and hence the elasticity will change. 5.2 | Polar Cases of Elasticity and Constant Elasticity By the end of this section, you will be able to: • Differentiate between infinite and zero elasticity • Analyze graphs in to classify elasticity as constant unitary, infinite, or zero There are two extreme cases of elasticity: when elasticity equals zero and when it is infinite. A third case is that of constant unitary elasticity. We will describe each case. Infinite elasticity or perfect elasticity refers to the extreme case where either the quantity demanded (Qd) or supplied (Qs) changes by an infinite amount in response to any change in price at all. In both cases, the supply and the demand curve are horizontal as Figure 5.4 shows. While perfectly elastic supply curves are for the most part unrealistic, goods with readily available inputs and whose production can easily expand will feature highly elastic supply curves. Examples include pizza, bread, books, and pencils. Similarly, perfectly elastic demand is an extreme example. However, luxury goods, items that take a large share of individuals’ income, and goods with many substitutes are likely to have highly elastic demand curves. Examples of such goods are Caribbean cruises and sports vehicles. Figure 5.4 Infinite Elasticity The horizontal lines show that an infinite quantity will be demanded or supplied at a specific price. This illustrates the cases of a perfectly (or infinitely) elastic demand curve and supply curve. The quantity supplied or demanded is extremely responsive to price changes, moving from zero for prices close to P to infinite when prices reach P. Zero elasticity or perfect inelasticity, as Figure 5.5 depicts, refers to the extreme case in which a percentage change in price, no matter how large, results in zero change in quantity. While a perfectly inelastic supply is an extreme example, goods with limited supply of inputs are likely to feature highly inelastic supply curves. Examples include diamond rings or housing in prime locations such as apartments facing Central Park in New York City. Similarly, 114 Chapter 5 | Elasticity while perfectly inelastic demand is an extreme case, necessities with no close substitutes are likely to have highly inelastic demand curves. This is the case of life-saving drugs and gasoline. Figure 5.5 Zero Elasticity The vertical supply curve and vertical demand curve show that there will be zero percentage change in quantity (a) demanded or (b) supplied, regardless of the price. Constant unitary elasticity, in either a supply or demand curve, occurs when a price change of one percent results in a quantity change of one percent. Figure 5.6 shows a demand curve with constant unit elasticity. Constant unitary elasticity, in either a supply or demand curve, occurs when a price change of one percent results in a quantity change of one percent. Figure 5.6 shows a demand curve with constant unit elasticity. Using the midpoint method, you can calculate that between points A and B on the demand curve, the price changes by 28.6% and quantity demanded also changes by 28.6%. Hence, the elasticity equals 1. Between points B and C, price again changes by 28.6% as does quantity, while between points C and D the corresponding percentage changes are 22.2% for both price and quantity. In each case, then, the percentage change in price equals the percentage change in quantity, and consequently elasticity equals 1. Notice that in absolute value, the declines in price, as you step down the demand curve, are not identical. Instead, the price falls by $2.00 from A to B, by a smaller amount of $1.50 from B to C, and by a still smaller amount of $0.90 from C to D. As a result, a demand curve with constant unitary elasticity moves from a steeper slope on the left and a flatter slope on the right—and a curved shape overall. Notice that in absolute value, the declines in price, as you step down the demand curve, are not identical. Instead, the price falls by $23 from A to B, by a smaller amount of $1.50 from B to C, and by a still smaller amount of $.90 from C to D. As a result, a demand curve with constant unitary elasticity has a steeper slope on the left and a flatter slope on the right—and a curved shape overall. Figure 5.6 A Constant Unitary Elasticity Demand Curve A demand curve with constant unitary elasticity will be a curved line. Notice how price and quantity demanded change by an identical percentage amount between each pair of points on the demand curve. Unlike the demand curve with unitary elasticity, the supply curve with unitary elasticity is represented by a straight This OpenStax book is available for free at http://cnx.org/content/col12190/1.4 http://cnx.org/content/col12190/1.4 115 Chapter 5 | Elasticity line, and that line goes through the origin. In each pair of points on the supply curve there is an equal difference in quantity of 30. However, in percentage value, using the midpoint method, the steps are decreasing as one moves from left to right, from 28.6% to 22.2% to 18.2%, because the quantity points in each percentage calculation are getting increasingly larger, which expands the denominator in the elasticity calculation of the percentage change in quantity. Consider the price changes moving up the supply curve in Figure 5.7. From points D to E to F and to G on the supply curve, each step of $1.50 is the same in absolute value. However, if we measure the price changes in percentage change terms, using the midpoint method, they are also decreasing, from 28.6% to 22.2% to 18.2%, because the original price points in each percentage calculation are getting increasingly larger in value, increasing the denominator in the calculation of the percentage change in price. Along the constant unitary elasticity supply curve, the percentage quantity increases on the horizontal axis exactly match the percentage price increases on the vertical axis—so this supply curve has a constant unitary elasticity at all points. Figure 5.7 A Constant Unitary Elasticity Supply Curve A constant unitary elasticity supply curve is a straight line reaching up from the origin. Between each pair of points, the percentage increase in quantity supplied is the same as the percentage increase in price. 5.3 | Elasticity and Pricing By the end of this section, you will be able to: • Analyze how price elasticities impact revenue • Evaluate how elasticity can cause shifts in demand and supply • Predict how the long-run and short-run impacts of elasticity affect equilibrium • Explain how the elasticity of demand and supply determine the incidence of a tax on buyers and sellers Studying elasticities is useful for a number of reasons, pricing being most important. Let’s explore how elasticity relates to revenue and pricing, both in the long and short run. First, let’s look at the elasticities of some common goods and services. Table 5.2 shows a selection of demand elasticities for different goods and services drawn from a variety of different studies by economists, listed in of increasing elasticity. 116 Chapter 5 | Elasticity Goods and Services Elasticity of Price Housing 0.12 Transatlantic air travel (economy class) 0.12 Rail transit (rush hour) 0.15 Electricity 0.20 Taxi cabs 0.22 Gasoline 0.35 Transatlantic air travel (first class) 0.40 Wine 0.55 Beef 0.59 Transatlantic air travel (business class) 0.62 Kitchen and household appliances 0.63 Cable TV (basic rural) 0.69 Chicken 0.64 Soft drinks 0.70 Beer 0.80 New vehicle 0.87 Rail transit (off-peak) 1.00 Computer 1.44 Cable TV (basic urban) 1.51 Cable TV (premium) 1.77 Restaurant meals 2.27 Table 5.2 Some Selected Elasticities of Demand Note that demand for necessities such as housing and electricity is inelastic, while items that are not necessities such as restaurant meals are more price-sensitive. If the price of a restaurant meal increases by 10%, the quantity demanded will decrease by 22.7%. A 10% increase in the price of housing will cause only a slight decrease of 1.2% in the quantity of housing demanded. Read this article (http://openstaxcollege.org/l/Movietickets) for an example of price elasticity that may have affected you. This OpenStax book is available for free at http://cnx.org/content/col12190/1.4 http://openstaxcollege.org/l/Movietickets http://cnx.org/content/col12190/1.4 117 Chapter 5 | Elasticity Does Raising Price Bring in More Revenue? Imagine that a band on tour is playing in an indoor arena with 15,000 seats. To keep this example simple, assume that the band keeps all the money from ticket sales. Assume further that the band pays the costs for its appearance, but that these costs, like travel, and setting up the stage, are the same regardless of how many people are in the audience. Finally, assume that all the tickets have the same price. (The same insights apply if ticket prices are more expensive for some seats than for others, but the calculations become more complicated.) The band knows that it faces a downward-sloping demand curve; that is, if the band raises the ticket price and, it will sell fewer seats. How should the band set the ticket price to generate the most total revenue, which in this example, because costs are fixed, will also mean the highest profits for the band? Should the band sell more tickets at a lower price or fewer tickets at a higher price? The key concept in thinking about collecting the most revenue is the price elasticity of demand. Total revenue is price times the quantity of tickets sold. Imagine that the band starts off thinking about a certain price, which will result in the sale of a certain quantity of tickets. The three possibilities are in Table 5.3. If demand is elastic at that price level, then the band should cut the price, because the percentage drop in price will result in an even larger percentage increase in the quantity sold—thus raising total revenue. However, if demand is inelastic at that original quantity level, then the band should raise the ticket price, because a certain percentage increase in price will result in a smaller percentage decrease in the quantity sold—and total revenue will rise. If demand has a unitary elasticity at that quantity, then an equal percentage change in quantity will offset a moderate percentage change in the price—so the band will earn the same revenue whether it (moderately) increases or decreases the ticket price. If Demand Is . . . Then . . . Therefore . . . Elastic % change in Qd > % change in P A given % rise in P will be more than offset by a larger
% fall in Q so that total revenue (P × Q) falls.

Unitary % change in Qd = % change in P A given % rise in P will be exactly offset by an equal %
fall in Q so that total revenue (P × Q) is unchanged.

Inelastic % change in Qd < % change in P A given % rise in P will cause a smaller % fall in Q so that total revenue (P × Q) rises. Table 5.3 Will the Band Earn More Revenue by Changing Ticket Prices? What if the band keeps cutting price, because demand is elastic, until it reaches a level where it sells all 15,000 seats in the available arena? If demand remains elastic at that quantity, the band might try to move to a bigger arena, so that it could slash ticket prices further and see a larger percentage increase in the quantity of tickets sold. However, if the 15,000-seat arena is all that is available or if a larger arena would add substantially to costs, then this option may not work. Conversely, a few bands are so famous, or have such fanatical followings, that demand for tickets may be inelastic right up to the point where the arena is full. These bands can, if they wish, keep raising the ticket price. Ironically, https://seats.To 118 Chapter 5 | Elasticity some of the most popular bands could make more revenue by setting prices so high that the arena is not full—but those who buy the tickets would have to pay very high prices. However, bands sometimes choose to sell tickets for less than the absolute maximum they might be able to charge, often in the hope that fans will feel happier and spend more on recordings, T-shirts, and other paraphernalia. Can Businesses Pass Costs on to Consumers? Most businesses face a day-to-day struggle to figure out ways to produce at a lower cost, as one pathway to their goal of earning higher profits. However, in some cases, the price of a key input over which the firm has no control may rise. For example, many chemical companies use petroleum as a key input, but they have no control over the world market price for crude oil. Coffee shops use coffee as a key input, but they have no control over the world market price of coffee. If the cost of a key input rises, can the firm pass those higher costs along to consumers in the form of higher prices? Conversely, if new and less expensive ways of producing are invented, can the firm keep the benefits in the form of higher profits, or will the market pressure them to pass the gains along to consumers in the form of lower prices? The price elasticity of demand plays a key role in answering these questions. Imagine that as a consumer of legal pharmaceutical products, you read a newspaper story that a technological breakthrough in the production of aspirin has occurred, so that every aspirin factory can now produce aspirin more cheaply. What does this discovery mean to you? Figure 5.8 illustrates two possibilities. In Figure 5.8 (a), the demand curve is highly inelastic. In this case, a technological breakthrough that shifts supply to the right, from S0 to S1, so that the equilibrium shifts from E0 to E1, creates a substantially lower price for the product with relatively little impact on the quantity sold. In Figure 5.8 (b), the demand curve is highly elastic. In this case, the technological breakthrough leads to a much greater quantity sold in the market at very close to the original price. Consumers benefit more, in general, when the demand curve is more inelastic because the shift in the supply results in a much lower price for consumers. Figure 5.8 Passing along Cost Savings to Consumers Cost-saving gains cause supply to shift out to the right from S0 to S1; that is, at any given price, firms will be willing to supply a greater quantity. If demand is inelastic, as in (a), the result of this cost-saving technological improvement will be substantially lower prices. If demand is elastic, as in (b), the result will be only slightly lower prices. Consumers benefit in either case, from a greater quantity at a lower price, but the benefit is greater when demand is inelastic, as in (a). Aspirin producers may find themselves in a nasty bind here. The situation in Figure 5.8, with extremely inelastic demand, means that a new invention may cause the price to drop dramatically while quantity changes little. As a result, the new production technology can lead to a drop in the revenue that firms …