Suppose that a department store is selling a popular brand of dress shirt for $1

Question

Suppose that a department store is selling a popular brand of dress shirt for $109 each. During the first two weeks, the store sold 100 shirts, and in order to boost sale and clear the isles for new product, it declared a sale "buy one get one free". This resulted in sale of 500 shirts in one week, and the isles were cleared.

(a). Calculate the price elasticity of demand.

(b). Interpret your result. Specifically, what type of demand elasticity is it and what does the co-efficient of elasticity indicate when price went down?

Explanation / Answer

The Price Elasticity of Demand (commonly known as just price elasticity) measures the rate of response of quantity demanded due to a price change. The formula for the Price Elasticity of Demand (PEoD) is:

PEoD = (% Change in Quantity Demanded)/(% Change in Price)

Calculating the Price Elasticity of Demand

You may be asked the question "Given the following data, calculate the price elasticity of demand when the price changes from $9.00 to $10.00" Using the chart on the bottom of the page, I'll walk you through answering this question. (Your course may use the more complicated Arc Price Elasticity of Demand formula. If so you'll need to see the article on Arc Elasticity)

First we'll need to find the data we need. We know that the original price is $9 and the new price is $10, so we have Price(OLD)=$9 and Price(NEW)=$10. From the chart we see that the quantity demanded when the price is $9 is 150 and when the price is $10 is 110. Since we're going from $9 to $10, we have QDemand(OLD)=150 and QDemand(NEW)=110, where "QDemand" is short for "Quantity Demanded". So we have:

Price(OLD)=9
Price(NEW)=10
QDemand(OLD)=150
QDemand(NEW)=110

To calculate the price elasticity, we need to know what the percentage change in quantity demand is and what the percentage change in price is. It's best to calculate these one at a time.

Calculating the Percentage Change in Quantity Demanded

The formula used to calculate the percentage change in quantity demanded is:

[QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)

By filling in the values we wrote down, we get:

[110 - 150] / 150 = (-40/150) = -0.2667

We note that % Change in Quantity Demanded = -0.2667 (We leave this in decimal terms. In percentage terms this would be -26.67%). Now we need to calculate the percentage change in price.

Calculating the Percentage Change in Price

Similar to before, the formula used to calculate the percentage change in price is:

[Price(NEW) - Price(OLD)] / Price(OLD)

By filling in the values we wrote down, we get:

[10 - 9] / 9 = (1/9) = 0.1111

We have both the percentage change in quantity demand and the percentage change in price, so we can calculate the price elasticity of demand.

Final Step of Calculating the Price Elasticity of Demand

We go back to our formula of:

PEoD = (% Change in Quantity Demanded)/(% Change in Price)

We can now fill in the two percentages in this equation using the figures we calculated earlier.

PEoD = (-0.2667)/(0.1111) = -2.4005

When we analyze price elasticities we're concerned with their absolute value, so we ignore the negative value. We conclude that the price elasticity of demand when the price increases from $9 to $10 is 2.4005.

How Do We Interpret the Price Elasticity of Demand?

A good economist is not just interested in calculating numbers. The number is a means to an end; in the case of price elasticity of demand it is used to see how sensitive the demand for a good is to a price change. The higher the price elasticity, the more sensitive consumers are to price changes. A very high price elasticity suggests that when the price of a good goes up, consumers will buy a great deal less of it and when the price of that good goes down, consumers will buy a great deal more. A very low price elasticity implies just the opposite, that changes in price have little influence on demand.

Often an assignment or a test will ask you a follow up question such as "Is the good price elastic or inelastic between $9 and $10". To answer that question, you use the following rule of thumb:

Recall that we always ignore the negative sign when analyzing price elasticity, so PEoD is always positive. In the case of our good, we calculated the price elasticity of demand to be 2.4005, so our good is price elastic and thus demand is very sensitive to price changes.

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