# Elasticity in Economics: Practice Problems

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• 0:04 Formula for Elasticity
• 0:40 Price Elasticity
• 3:10 Income Elasticity
• 4:41 Cross Price Elasticity
• 6:05 Lesson Summary

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Lesson Transcript
Instructor: James Walsh

M.B.A. Veteran Business and Economics teacher at a number of community colleges and in the for profit sector.

Let's solve some elasticity problems. We will do one each for price elasticity, income elasticity and cross price elasticity. We will interpret what the answers mean at the end. All work will be shown and explained!

## Formula for Elasticity

Elasticity is a measure of the change in demand for a product or service related to changes in some other variable. That other variable can be price, income, or the price of some other product or service. Since you probably know that already, we're going to go to the mathematical calculation of different types of elasticity and how it's interpreted. All work will be shown.

The basic elasticity formula is:

Elasticity = the % change in quantity demanded / the % change in price or income

You need to remember this formula because it holds for all types of elasticity.

## Price Elasticity

Price elasticity measures the change in demand for a product or service to changes in its price. When the price of most things falls, people buy more. When they buy a greater percentage more than the percentage the price falls, demand is elastic and greater than 1 in the formula. That doesn't hold for all products, though; some have demand that is inelastic, meaning that demand doesn't rise at a greater rate than the price falls. The price elasticity for those products is less than 1.

When a boutique has a 20% off sale on clothing and sales go up by 30%, we can use the formula and find that elasticity is 30% / 20% = 1.5. That's more than 1, so demand for the retailer's clothing is elastic.

Real life doesn't always give us those percentages, though. All we usually have to work with are numbers. Let's look at a real life problem.

Gas prices spiked between 2004 and 2008. The table on your screen now shows gas prices and how much Americans consumed for those years, which you can see was 9,104 barrels per day at an average price of \$1.88 in 2004 and 8,989 barrels per day at an average price of \$3.29 in 2008. Consumption is the quantity demanded, so was demand for gasoline in those years elastic? Let's do the calculation and find out.

Year Avg. Price Consumption
2004 \$1.88 9,104 barrels per day
2008 \$3.29 8,989 barrels per day

Here are the steps:

#### Step 1: Calculate the % change in consumption.

(9,104 - 8,989) / 9,104
= 115 / 9,104
= 0.012

To make that decimal a percent, move the decimal point two places right and get 1.2%.

#### Step 2: Calculate the % change in price.

(3.29 - 1.88) / 3.29
= 1.41 / 3.29
= 0.428

Moving the decimal makes it 42.8%.

#### Step 3: Put the numbers into the elasticity formula.

1.2% / 42.8% = 0.028

You can ignore the negative sign if you get one; we're only interested in the number itself. Since that is less than 1, we can conclude that the demand for gas is inelastic. People may grumble about higher gas prices, but they don't buy much less to adjust.

## Income Elasticity

Beth owns the boutique in the example we did before. She's noticed that since a new medical center opened in her town, that sales seem a lot better. The medical center has created lots of good-paying jobs for doctors, nurses, and lab technicians, so the average income in her town has gone up. She looks around on the internet and finds that the average income in her town has gone from \$43,000 per year to \$49,000 per year since the medical center opened. She also knows that her monthly sales have increased from \$100,000 to \$120,000. She wonders if her sales are elastic related to income. We can use the formula to help her find out. Here are the steps:

#### Step 1: Calculate the % change in demand or sales.

(120,000 - 100,000) / 100,000
= 20,000 / 100,000
= 0.20
= 20%

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