To determine whether the supply of a good is elastic, unit elastic, or inelastic, we compute a numerical value for the price elasticity of supply in a way similar to that used to calculate the price elasticity of demand. We use the formula:
• If the price elasticity of supply is greater than 1, supply is elastic.
• If the price elasticity of supply equals 1, supply is unit elastic.
• If the price elasticity of supply is less than 1, supply is inelastic.
Price elasticity of supply = Percentage change in quantity supplied Percentage change in price .
Fresh strawberries must be sold before they deteriorate, so their supply is inelastic.
FIGURE 5.6
Price Elasticity of Supply Calculation
$40 a bouquet and the quantity supplied is 6 million bouquets a month.
$80 a bouquet and the quantity supplied is 24 million bouquets a month.
percentage change in price equals ($40 $60) 100, which is 66.67 percent.
sup-plied is 18 million bouquets and 15 million bouquets, so the per-centage change in quantity sup-plied is (18 million 15 million) 100, which is 120 percent.
equals 120 percent 66.6 per-cent, which is 1.8.
,
Price (dollars per bouquet)
Quantity (millions of bouquets per month)
12 15
Let’s calculate the price elasticity of supply of roses. Suppose that in a nor-mal month, the price of roses is $40 a bouquet and 6 million bouquets are sup-plied. And suppose that in February, the price rises to $80 a bouquet and the quantity supplied increases to 24 million bouquets. Figure 5.6 illustrates the sup-ply of roses and summarizes the calculation. The figure shows the initial point at $40 a bouquet and the new point at $80 a bouquet. The price increases by $40 a bouquet and the average, or midpoint, price is $60 a bouquet, so the percent-age change in the price is 66.67 percent. The quantity supplied increases by 18 million bouquets and the average, or midpoint, quantity is 15 million bouquets, so the percentage change in the quantity supplied is 120 percent.
Using the above formula, you can see that the price elasticity of supply of roses is
The price elasticity of supply is 1.8 at the midpoint between the initial point and the new point on the supply curve. In this example, over this price range, the supply of roses is elastic.
Price elasticity of supply = 120 percent
66.67 percent = 1.8.
CHECKPOINT 5.2
Define the price elasticity of supply, and explain the factors that influence it and how to calculate it.
Practice Problems
A 10 percent increase in the price of a good increased the quantity supplied of the good by 1 percent after one month and by 25 percent after one year.
1. Is the supply of this good elastic, unit elastic, or inelastic? Is this good likely to be produced using factors of production that are easily obtained? What is the price elasticity of supply of this good?
2. What is the price elasticity of supply after one year? Has the supply of this good become more elastic or less elastic? Why?
In the News
Weak coal prices hit China’s third-largest coal miner
The chairman of Yanzhou Coal Mining, Wang Xin, reported that the demand for coal has fallen by 11.9 percent to 7.92 million tons from 8.99 million tons a year earlier, despite the price falling by 10.6 percent.
Source: Dow Jones, April 27, 2009 Calculate the price elasticity of supply of coal. Is the supply of coal elastic or inelastic?
Solutions to Practice Problems
1. The supply of a good is inelastic if the percentage increase in the quantity supplied is less than the percentage increase in price. In this example, a 10 percent price rise brings a 1 percent increase in the quantity supplied, so supply is inelastic. Because the quantity supplied increases by such a small percentage after one month, the factors of production that are used to pro-duce this good are more likely to be difficult to obtain.
The price elasticity of supply ⫽ Percentage change in the quantity supplied ⫼ Percentage change in the price. In this example, the price elasticity of supply equals 1 percent divided by 10 percent, or 0.1.
2. The price elasticity of supply ⫽ Percentage change in the quantity supplied ⫼ Percentage change in the price. After one year, the price elasticity of supply is 25 percent divided by 10 percent, or 2.5. The supply of the good has become more elastic over the year since the price rise. Possibly other producers have gradually started producing the good and with the passage of time more fac-tors of production can be reallocated.
Solution to In the News
The demand for coal decreased, so we can use these data to calculate the price elasticity of supply. The price elasticity of supply equals the percentage change in the quantity supplied divided by the percentage change in the price. The price elasticity of supply equals 11.9 percent divided by 10.6 percent, or 1.12. The quantity supplied fell by a larger percentage than the price, so the supply of coal is elastic, which is what a price elasticity of supply of 1.12 means.
MyEconLab
You can work these problems in Study Plan 5.2 and get instant feedback.
5.3 CROSS ELASTICITY AND INCOME ELASTICITY
Domino’s Pizza in Chula Vista has a problem. Burger King has just cut its prices.
Domino’s manager, Pat, knows that pizzas and burgers are substitutes. He also knows that when the price of a substitute for pizza falls, the demand for pizza decreases. But by how much will the quantity of pizza bought decrease if Pat maintains his current price?
Pat also knows that pizza and soda are complements. He knows that if the price of a complement of pizza falls, the demand for pizza increases. So he won-ders whether he might keep his customers by cutting the price he charges for soda. But he wants to know by how much he must cut the price of soda to keep selling the same quantity of pizza with cheaper burgers all around him.
To answer these questions, Pat needs to calculate the cross elasticity of demand. Let’s examine this elasticity measure.