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Price elasticity of demand is a measurement of the change in the consumption of a product in relation to a change in its price. Expressed mathematically, it is:
Price Elasticity of Demand = Percentage Change in Quantity Demanded / Percentage Change in Price
Economists use price elasticity to understand how supply and demand for a product change when its price changes.
- Price elasticity of demand is a measurement of the change in consumption of a product in relation to a change in its price.
- A good is elastic if a price change causes a substantial change in demand or supply.
- A good is inelastic if a price change does not cause demand or supply to change very much.
- The availability of a substitute for a product affects its elasticity. If there are no good substitutes and the product is necessary, demand won’t change when the price goes up, making it inelastic.
Economists have found that the prices of some goods are very inelastic. That is, a reduction in price does not increase demand much, and an increase in price does not hurt demand either. For example, gasoline has little price elasticity of demand. Drivers will continue to buy as much as they have to, as will airlines, the trucking industry, and nearly every other buyer.
Other goods are much more elastic, so price changes for these goods cause substantial changes in their demand or their supply.
Not surprisingly, this concept is of great interest to marketing professionals. It could even be said that their purpose is to create inelastic demand for the products they market. They achieve that by identifying a meaningful difference in their products from any others that are available.
If the quantity demanded of a product changes greatly in response to changes in its price, it is elastic. That is, the demand point for the product is stretched far from its prior point. If the quantity purchased shows a small change after a change in its price, it is inelastic. The quantity didn’t stretch much from its prior point.
The more easily a shopper can substitute one product for another, the more the price will fall. For example, in a world in which people like coffee and tea equally, if the price of coffee goes up, people will have no problem switching to tea, and the demand for coffee will fall. This is because coffee and tea are considered good substitutes for each other.
The more discretionary a purchase is, the more its quantity of demand will fall in response to price increases. That is, the product demand has greater elasticity.
Say you are considering buying a new washing machine, but the current one still works; it's just old and outdated. If the price of a new washing machine goes up, you’re likely to forgo that immediate purchase and wait until prices go down or the current machine breaks down.
The less discretionary a product is, the less its quantity demanded will fall. Inelastic examples include luxury items that people buy for their brand names. Addictive products are quite inelastic, as are required add-on products, such as ink-jet printer cartridges.
One thing all of these products have in common is that they lack good substitutes. If you really want an Apple iPad, a Kindle Fire won’t do. Addicts are not dissuaded by higher prices, and only HP ink will work in HP printers (unless you disable HP cartridge protection).
The length of time that the price change lasts also matters. Demand response to price fluctuations is different for a one-day sale than for a price change that lasts for a season or a year.
Clarity of time sensitivity is vital to understanding the price elasticity of demand and for comparing it with different products. Consumers may accept a seasonal price fluctuation rather than change their habits.
As a rule of thumb, if the quantity of a product demanded or purchased changes more than the price changes, the product is considered to be elastic. (For example, the price goes up by 5%, but the demand falls by 10%.)
If the change in quantity purchased is the same as the price change (say, 10%/10% = 1), the product is said to have unit (or unitary) price elasticity.
Finally, if the quantity purchased changes less than the price (say, -5% demanded for a +10% change in price), then the product is deemed inelastic.
To calculate the elasticity of demand, consider this example: Suppose that the price of apples falls by 6% from $1.99 a bushel to $1.87 a bushel. In response, grocery shoppers increase their apple purchases by 20%. The elasticity of apples is thus: 0.20/0.06 = 3.33. The demand for apples is quite elastic.
Price elasticity of demand is the ratio of the percentage change in quantity demanded of a product to the percentage change in price. Economists employ it to understand how supply and demand change when a product’s price changes.
If a price change for a product causes a substantial change in either its supply or demand, it is considered elastic. Generally, it means that there are acceptable substitutes for the product. Examples would be cookies, luxury automobiles, and coffee.
If a price change for a product doesn’t lead to much if any change in its supply or demand, it is considered inelastic. Generally, it means that the product is considered to be a necessity or a luxury item with addictive constituents. Examples would be gasoline, milk, and iPhones.
By the end of this section, you will be able to:
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.
Elasticities can be usefully divided 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 summarized in Table 1.
| [latex]\%\;change\;in\;quantity > \%\;change\;in\;price[/latex] | [latex]\frac{\%\;change\;in\;quantity}{\%\;change\;in\;price)} > 1[/latex] | Elastic |
| [latex]\%\;change\;in\;quantity = \%\;change\;in\;price[/latex] | [latex]\frac{\%\;change\;in\;quantity}{\%\;change\;in\;price)} = 1[/latex] | Unitary |
| [latex]\%\;change\;in\;quantity < \%\;change\;in\;price[/latex] | [latex]\frac{\%\;change\;in\;quantity}{\%\;change\;in\;price)} < 1[/latex] | Inelastic |
| Table 1. Elastic, Inelastic, and Unitary: Three Cases of Elasticity |
Before we get into the nitty gritty of elasticity, enjoy this article on elasticity and ticket prices at the Super Bowl.
To calculate elasticity, instead of using simple percentage changes in quantity and price, 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:
[latex]\begin{array}{r @{{}={}} l}\%\;change\;in\;quantity & \frac { { Q }_{ 2 }-{ Q }_{ 1 } }{ ({ Q }_{ 2 }+{ Q }_{ 1 })/2 } \times 100 \\[1em] \%\;change\;in\;price & \frac { { P }_{ 2 }-{ P }_{ 1 } }{ ({ P }_{ 2 }+{ P }_{ 1 })/2 } \times 100 \end{array}[/latex]
The advantage of the is 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 for both cases.
Let’s calculate the elasticity between points A and B and between points G and H shown in Figure 1.
First, apply the formula to calculate the elasticity as price decreases from $70 at point B to $60 at point A:
[latex]\begin{array}{r @{{}={}} l}\%\;change\;in\;quantity & \frac { { 3,000 }-{ 2,800 } }{ ({ 3,000 }+{ 2,800 })/2 } \times 100 \\[1em] & \frac { 200 }{ 2,900 } \times 100 \\[1em] & = 6.9 \\[1em] \%\;change\;in\;price & \frac { { 60 }-{ 70 } }{ ({ 60 }+{ 70 })/2 } \times 100 \\[1em] & \frac { -10 }{ 65 } \times 100 \\[1em] & -15.4 \\[1em] Price\;Elasticity\;of\;Demand & \frac { 6.9\% }{ -15.4\% } \\[1em] & 0.45 \end{array}[/latex]
Therefore, the elasticity of demand between these two points is [latex]\frac { 6.9\% }{ -15.4\% }[/latex] which is 0.45, an amount smaller than one, 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. So 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 are read as absolute values. The following Work It Out feature will walk you through calculating the price elasticity of demand.
Calculate the price elasticity of demand using the data in Figure 1 for an increase in price from G to H. Has the elasticity increased or decreased?
Step 1. We know that:
[latex]Price\;Elasticity\;of\;Demand = \frac { \%\;change\;in\;quantity }{ \%\;change\;in\;price }[/latex]
Step 2. From the Midpoint Formula we know that:
[latex]\begin{array}{r @{{}={}} l}\%\;change\;in\;quantity & \frac { { Q }_{ 2 }-{ Q }_{ 1 } }{ ({ Q }_{ 2 }+{ Q }_{ 1 })/2 } \times 100 \\[1em] \%\;change\;in\;price & \frac { { P }_{ 2 }-{ P }_{ 1 } }{ ({ P }_{ 2 }+{ P }_{ 1 })/2 } \times 100 \end{array}[/latex]
Step 3. So we can use the values provided in the figure in each equation:
[latex]\begin{array}{r @{{}={}} l}\%\;change\;in\;quantity & \frac { { 1,600 }-{ 1,800 } }{ ({ 1,600 }+{ 1,800 })/2 } \times 100 \\[1em] & \frac { -200 }{ 1,700 } \times 100 \\[1em] & -11.76 \\[1em] \%\;change\;in\;price & \frac { { 130 }-{ 120 } }{ ({ 130 }+{ 120 })/2 } \times 100 \\[1em] & \frac { 10 }{ 125 } \times 100 \\[1em] & 8.0 \end{array}[/latex]
Step 4. Then, those values can be used to determine the price elasticity of demand:
[latex]\begin{array}{r @{{}={}} l}Price\;Elasticity\;of\;Demand & \frac { \%\;change\;in\;quantity }{ \%\;change\;in\;price } \\[1em] & \frac { -11.76 }{ 8 } \\[1em] & 1.47 \end{array}[/latex]
Therefore, the elasticity of demand from G to 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.
Assume that an apartment rents for $650 per month and at that price 10,000 units are rented as shown in Figure 2. When the price increases to $700 per month, 13,000 units are supplied into the market. By what percentage does apartment supply increase? What is the price sensitivity?
Using the Midpoint Method,
[latex]\begin{array}{r @{{}={}} l}\%\;change\;in\;quantity & \frac { { 13,000 }-{ 10,000 } }{ ({ 13,000 }+{ 10,000 })/2 } \times 100 \\[1em] & \frac { 3,000 }{ 11,500 } \times 100 \\[1em] & 26.1 \\[1em] \%\;change\;in\;price & \frac { { \$700 }-{ \$650 } }{ ({ \$700 }+{ \$650 })/2 } \times 100 \\[1em] & \frac { 50 }{ 675 } \times 100 \\[1em] & 7.4 \\[1em] Price\;Elasticity\;of\;Demand & \frac { 26.1\% }{ 7.4\% } \\[1em] & 3.53 \end{array}[/latex]
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 is read 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.
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 1, each point shown on the demand curve, price drops by $10 and the number of units demanded increases by 200. So 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 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.
So, 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 will change.
Price elasticity measures the responsiveness of the quantity demanded or supplied of a good to a change in its price. It is computed as the percentage change in quantity demanded (or supplied) divided by the percentage change in price. Elasticity can be described as elastic (or very responsive), unit elastic, or inelastic (not very responsive). Elastic demand or supply curves indicate that quantity demanded or supplied respond to price changes in a greater than proportional manner. An inelastic demand or supply curve is one where a given percentage change in price will cause a smaller percentage change in quantity demanded or supplied. A unitary elasticity means that a given percentage change in price leads to an equal percentage change in quantity demanded or supplied.
Self-Check Questions
- From the data shown in Table 2 about demand for smart phones, calculate the price elasticity of demand from: point B to point C, point D to point E, and point G to point H. Classify the elasticity at each point as elastic, inelastic, or unit elastic.
Points P Q A 60 3,000 B 70 2,800 C 80 2,600 D 90 2,400 E 100 2,200 F 110 2,000 G 120 1,800 H 130 1,600 Table 2. - From the data shown in Table 3 about supply of alarm clocks, calculate the price elasticity of supply from: point J to point K, point L to point M, and point N to point P. Classify the elasticity at each point as elastic, inelastic, or unit elastic.
Point Price Quantity Supplied J $8 50 K $9 70 L $10 80 M $11 88 N $12 95 P $13 100 Table 3.
Review Questions
- What is the formula for calculating elasticity?
- What is the price elasticity of demand? Can you explain it in your own words?
- What is the price elasticity of supply? Can you explain it in your own words?
Critical Thinking Questions
- Transatlantic air travel in business class has an estimated elasticity of demand of 0.40 less than transatlantic air travel in economy class, with an estimated price elasticity of 0.62. Why do you think this is the case?
- What is the relationship between price elasticity and position on the demand curve? For example, as you move up the demand curve to higher prices and lower quantities, what happens to the measured elasticity? How would you explain that?
Problems
- The equation for a demand curve is P = 48 – 3Q. What is the elasticity in moving from a quantity of 5 to a quantity of 6?
- The equation for a demand curve is P = 2/Q. What is the elasticity of demand as price falls from 5 to 4? What is the elasticity of demand as the price falls from 9 to 8? Would you expect these answers to be the same?
- The equation for a supply curve is 4P = Q. What is the elasticity of supply as price rises from 3 to 4? What is the elasticity of supply as the price rises from 7 to 8? Would you expect these answers to be the same?
- The equation for a supply curve is P = 3Q – 8. What is the elasticity in moving from a price of 4 to a price of 7?
elastic demand when the elasticity of demand is greater than one, indicating a high responsiveness of quantity demanded or supplied to changes in price elastic supply when the elasticity of either supply is greater than one, indicating a high responsiveness of quantity demanded or supplied to changes in price elasticity an economics concept that measures responsiveness of one variable to changes in another variable inelastic demand when the elasticity of demand is less than one, indicating that a 1 percent increase in price paid by the consumer leads to less than a 1 percent change in purchases (and vice versa); this indicates a low responsiveness by consumers to price changes inelastic supply when the elasticity of supply is less than one, indicating that a 1 percent increase in price paid to the firm will result in a less than 1 percent increase in production by the firm; this indicates a low responsiveness of the firm to price increases (and vice versa if prices drop) price elasticity the relationship between the percent change in price resulting in a corresponding percentage change in the quantity demanded or supplied price elasticity of demand percentage change in the quantity demanded of a good or service divided the percentage change in price price elasticity of supply percentage change in the quantity supplied divided by the percentage change in price unitary elasticity when the calculated elasticity is equal to one indicating that a change in the price of the good or service results in a proportional change in the quantity demanded or supplied