### Learning Objectives

- Define elasticity
- Explain the impact of elasticity on price changes

## Elasticity of Demand

The following video is a little long to watch, but it provides an excellent overview of elasticity and explains both the concept and the calculations in a simple, easy-to-follow way.

In review:

- Price elasticity measures the responsiveness of quantity demanded to a change in the product price
- The calculation for price elasticity is the percentage change in quantity demanded divided by the percentage change in price
- When the absolute value of the price elasticity is >1, the price is elastic and people are very sensitive to changes in price
- When the absolute value of the price elasticity is <1, the price is inelastic and people are insensitive to changes in price

With a good understanding of what elasticity means and how it is calculated, we can now investigate its impact on pricing strategies. In order to do this, we’ll look at a couple of examples and answer the following questions:

- How much of an impact do we think a price change will have on demand?
- How would we calculate the elasticity, and does it confirm our assumption?
- What impact does the elasticity have on the business or pricing objectives?

Please note: when we calculate elasticity, we will always use the *absolute value*, or the real number without regard to its sign (+/-). In other words, you can disregard the positive and negative signs and just pay attention to the real number.

## Example 1: The Student Parking Permit

How elastic is the demand for student parking passes at your institution? The answer to that question likely varies based on the profile of your institution, but we are going to explore a particular example. Let’s consider a community college campus where all of the students commute to class. Required courses are spread throughout the day and the evening, and most of the classes require classroom attendance (rather than online participation). There is a reasonable public transportation system with busses coming to and leaving campus from several lines, but the majority of students drive to campus. A student parking permit costs $40 per term. As the parking lots become increasingly congested, the college considers raising the price of the parking passes in hopes that it will encourage more students to carpool or to take the bus.

If the college increases the price of a parking permit from $40 to $48, will fewer students buy parking permits?

If you think that the change in price will cause many students to decide not to buy a permit, then you are suggesting that the demand is elastic—the students are quite sensitive to price changes. If you think that the change in price will not impact student permit purchases much, then you are suggesting that the demand is inelastic—student demand for permits is insensitive to price changes.

In this case, we can all argue that students are very sensitive to increases in costs *in general*, but the determining factor in their demand for parking permits is more likely to be the quality of alternative solutions. If the bus service does not allow students to travel between home, school, and work in a reasonable amount of time, many students will resort to buying a parking permit, even at the higher price. Because students don’t generally have extra money, they may grumble about a price increase, but many will still have to pay.

Let’s add some numbers and test our thinking. The college implements the proposed increase of $8. If we divide that by the original price ($40) then we can see that the price increase is 20% (8 / 40 = 0.20). Last year the college sold 12,800 student parking passes. This year, at the new price, the college sells 11,520 parking passes—which is a decrease of 10%, as shown below:

12,800 – 11,520 = 1,280

1,280 / 12,800 = 1 / 10 = 10%

Without doing any more math, we know that a 20% change in price resulted in a 10% change in demand. In other words, a large change in price created a comparatively smaller change in demand. This means that student demand is inelastic. Let’s test the math.

**% change in quantity demanded / % change in price = absolute value of price elasticity**

10% / 20% = 0.10 / 0.20 = 0.50

0.50 < 1

When the absolute value of the price elasticity is < 1, the demand is inelastic. In this example, student demand for parking permits is inelastic.

What impact does the price change have on the college and their goals for students? First, there are 1,280 fewer cars taking up parking places. If all of those students are using alternative transportation to get to school and this change has relieved parking-capacity issues, then the college may have achieved its goals. However, there’s more to the story: the price change also has an effect on the college’s revenue, as we can see below:

Year 1: 12,800 parking permits sold x $40 per permit = $512,000

Year 2: 11,520 parking permits sold x $48 per permit = $552,960

The college earned an additional $40,960 in revenue. Perhaps this can be used to expand parking or address other student transportation issues.

In this case, student demand for parking permits is inelastic. A significant change in price leads to a comparatively smaller change in demand. The result is lower sales of parking passes but more revenue.

Note: If you attend an institution that offers courses completely or largely online, the price elasticity for parking permits might be completely inelastic. Even if the institution gave away parking permits, you might not want one.

## Example 2: Helen’s Cookies

When we discussed break-even pricing, we used the example of a new cookie company that was selling its cookies for $2. In this example, let’s put the cookies in a convenience store, which has several options on the counter that customers can choose as a last-minute impulse buy. All of the impulse items range between $1 and $2 in price. In order to raise revenue, Helen (the baker, who has taken over the company,) decides to raise her price to $2.20.

If Helen increases the cookie price from $2.00 to $2.20—a 10% increase—will fewer customers buy cookies?

If you think that the change in price will cause many buyers to forego a cookie, then you are suggesting that the demand is elastic, or that the buyers are sensitive to price changes. If you think that the change in price will not impact sales much, then you are suggesting that the demand for cookies is inelastic, or insensitive to price changes.

Let’s assume that this price change does impact customer behavior. Many customers choose a $1 chocolate bar or a $1.50 doughnut over the cookie, or they simply resist the temptation of the cookie at the higher price. Before we do any math, this assumption suggests that the demand for cookies is elastic.

Adding in the numbers, we find that Helen’s weekly sales drop from 200 cookies to 150 cookies. This is a 25% change in demand on account of a 10% price increase. We immediately see that the change in demand is greater than the change in price. That means that demand is elastic. Let’s do the math.

% change in quantity demanded / % change in price

25% / 10% = 2.5

2.5 > 1

When the absolute value of the price elasticity is > 1, the demand is elastic. In this example, the demand for cookies is elastic.

What impact does this have on Helen’s objective to increase revenue? It’s not pretty.

Price 1: 200 cookies sold x $2.00 per cookie = $400

Price 2: 150 cookies sold x $2.20 = $330

She is earning less revenue because of the price change. What should Helen do next? She has learned that a small change in price leads to a large change in demand. What if she lowered the price slightly from her original $2.00 price? If the pattern holds, then a small reduction in price will lead to a large increase in sales. That would give her a much more favorable result.