Price Elasticity of Demand

Price elasticity of demand measures the responsiveness of buyers to a price change. If the price of gasoline increases by 10%, how will this affect the amount of gasoline purchased? Will the amount purchased decrease by more than 10%? Will the amount purchased decrease by less than 10%? Will the amount purchased decrease by exactly 10%? Or will the amount purchased not change at all? Once we know the price elasticity of demand, we can answer these questions, because price elasticity of demand measures the relationship between the percentage change in the amount purchased and the percentage change in the price.

To calculate price elasticity of demand, we need to have price and quantity demanded data. A demand schedule and its corresponding demand curve give us the data. How do we know the location and shape of a product’s demand curve?

The Derivation of a Demand Curve

Economists who estimate the shape and the location of a product’s demand curve, usually look at the following:

1. Historical data.
Price and quantity data show how consumers have responded to past changes in the price and quantity demanded of the product. Price and quantity demanded changes must be looked at in isolation of other variables. Prices may change, but so may other variables, such as buyers’ incomes and prices of related products. It is, therefore, important to estimate price and quantity demanded changes assuming other variables remain constant (ceteris paribus).
2. Surveys.
You can simply ask consumers how they would respond to a future change in the price of the product. This may not always be accurate, because consumers don’t always know in advance how they will respond to a price change. However, data from surveys allow economists to estimate the location and slope of a demand curve. When we know the location and the slope (the angle) of a product’s demand curve, we can determine its price elasticity of demand.

The Formula for Price Elasticity of Demand

The law of demand states that as the price of a product decreases, quantity demanded increases, and vice versa. Elasticity measures how much less people buy of that product when the price rises, and vice versa.

We calculate price elasticity of demand by looking at the ratio of

 e = The percentage change in quantity demanded divided by the percentage change in the price of the product Or abbreviated: e = % change in Q / % change in P Where: 1. The % change in Q = the change in quantity demanded / the average of the two quantities demanded. And: 2. The % change in P = the change in price / the average of the two prices.

The above formula for calculating percentages is called the “arc” formula. There are other ways to calculate percentages, but the arc formula is the most accurate and most commonly used in economics.

Examples of how to Use the Formula for Price Elasticity of Demand

Let’s look at several examples to see how to use the formula in the previous paragraph.

Example 1
Problem: Let’s say that a department store sells pillows, and that in a typical week, buyers purchase 6 pillows when the price is \$21. After the department store decreases its price to \$19, it observes that buyers now purchase 10 pillows per week. Given these changes, what is the price elasticity of demand for the department store’s pillows?

Solution: Remember that elasticity = (the change in quantity demanded / the average of the two quantities demanded) / (the change in the price / the average of the two prices).

The change in the quantity demanded is 10 pillows minus 6 pillows, or 4. The average of these quantities is 8 (the sum of the two quantities (6 plus 10) divided by 2).

The change in the prices is \$21 minus \$19, or \$2. The average of the two prices is \$20 (the sum of the two prices (\$19 + \$21) divided by 2).

Therefore:

e = ((10 – 6) /8) / ((\$21 – \$19) / \$20)

= (4 / 8) / (\$2 / \$20)

= (.5) / (.1) = 5.

Therefore, the price elasticity of demand for the above product is 5.

The 5 means that the percentage change in the amount purchased is 5 times greater than the percentage change in the price. In other words, buyers are very sensitive to this price change. When the pillows decreased in price, buyers responded strongly. The price decreased by only 10% (.1), but the amount purchased increased by 50% (.5).

Officially, the above number is -5 (negative 5), because the price decreased, while the quantity purchased increased. Because price elasticity of demand is always a negative number, we leave out the negative sign and express price elasticity of demand as its positive, or absolute, value.

Example 2
Problem: A grocery store observes that at \$2/gallon, buyers purchase 800 gallons of milk per day. At \$3/gallon, buyers purchase 700 gallon of milk per day. What is the price elasticity of demand for milk?

Solution:
1. The change in quantity demanded = 100
2. The average quantity demanded = 750
3. The change in price = \$1
4. The average price = \$2.50
5. So, e = (100 / 750) / (\$1 / \$2.50)
= (.133) / (.4)
= .3325

So the price elasticity of demand for milk given the above data is .3325. This means that if milk increases in price by 40% (.4), then the quantity demanded of milk decreases by 13.3% (.133). Relatively speaking, buyers are not very sensitive to a price change.

Example 3
Problem: A movie theater observes that at \$6 per movie ticket, 1,800 people attend the movie each week. At \$4.80 per movie ticket, 2,600 people attend the movie each week. What is the price elasticity of demand for movie tickets?

 Solution: e = (800 / 2,200) / (\$1.20 / \$5.40) = (.3636) / (.2222) = 1.636

Example 4

Problem: Let’s compute the price elasticity of demand for concert tickets. Suppose that for a concert, the price of a ticket is \$15 and 25,000 people are in attendance. For another, nearly identical concert, the organizers charge \$17 and 24,000 fans attend. What is the price elasticity of demand for concert tickets?

Solution: Using the formula for price elasticity of demand, we get
e = (1,000 / 24,500) / (\$2 / \$16) = (.0408) / (.125) = .3264

So the elasticity in this example is .33 (rounded), or 33%. This means that when concert tickets increase in price by 12.5% (.125), we can expect 4.08% (.0408) fewer people to attend. So when the price increases by 100%, then we can expect 33% fewer people to purchase tickets (assuming the price elasticity remains constant over that range).

Video Explanation
For an explanation of price elasticity of demand and examples of calculations, please watch the following video: