Computing the Price Elasticity of Demand

Computing the Price Elasticity of Demand
1. The formula used to calculate the price elasticity of demand is:
Price elasticity of demand = .Percentage change in price
                                    Percentage change in quantity demanded

a. If the price elasticity of demand is greater than 1 (the numerator is larger than the denominator), demand is elastic.
b. If the price elasticity of demand is equal to 1 (the numerator equals the denominator), demand is unit elastic.
c. If the price elasticity of demand is less than 1 (the numerator is less than the denominator), demand is inelastic.
2. Slope and elasticity
The slope of a demand curve measures the responsiveness of quantity demanded to a change in price, but it is not a units-free measure of this responsiveness and cannot be used to compare the demand curves of different goods.
3. A units-free measure
The percentage change in price and the percentage change in quantity demanded (the denominator and numerator of the elasticity formula) are independent of the units of measurement. As a result, the elasticity formula produces a units-free measure of responsiveness.

Elasticity Along a Linear Demand Curve
Along a straight-line demand curve, the slope is constant, but the elasticity changes.
1. At the midpoint of a linear demand curve, the elasticity equals 1 and demand is unit elastic.
2. Above the midpoint of a linear demand curve, elasticity is greater than 1 and demand is elastic.
3. Below the midpoint of a linear demand curve, elasticity is less than 1 and demand is inelastic.

Total Revenue and Price Elasticity of Demand
1. Total revenue from the sale of a good equals (the price of the good)  (the quantity of the good sold).
2. The total revenue test is a method of estimating the price elasticity of demand because the impact of a change in price on total revenue depends on the elasticity of demand.
a. If elasticity is greater than 1, an increase in price decreases total revenue. Price and total revenue change in opposite directions.
b. If elasticity equals 1, an increase in price does not change total revenue.
c. If elasticity is less than 1, an increase in price increases total revenue. Price and total revenue change in the same direction.
Your Expenditure and Your Elasticity of Demand
When the price of a good increases, your expenditure on that good depends on the elasticity of your demand for that good.
a. If your demand is elastic, your expenditure on the good decreases when the price rises.
b. If your demand is unit elastic, your expenditure on the good does not change when the price rises.
c. If your demand is inelastic, your expenditure on the good increases when the price rises.

The Price Elasticity of Demand

The price elasticity of demand is a measure of the extent to which the quantity demanded of a good changes when the price of the good changes and all other influences on buyers’ plans remain the same.

A. Percentage Change in Price

1. The midpoint method uses the average of the initial price and new price in the denominator when calculating a percentage change. Because the average price is the same between two prices regardless of whether the price falls or rises, the percentage change in price calculated by the midpoint method is the same for a price rise and a price fall. 

a. Using the midpoint formula, the percentage change in price equals

B. Percentage Change in Quantity Demanded

Use the midpoint method when calculating the percentage change in quantity.

1. Minus Sign

Because a change in price causes an opposite change in quantity demanded, for the price elasticity of demand we focus on the magnitude of the change by using the absolute value.

C. Elastic and Inelastic Demand

The price elasticity of demand falls into three categories:

1. Elastic demand—when the percentage change in the quantity demanded exceeds the percentage change in price (which means the elasticity is greater than 1).

2. Unit elastic demand—when the percentage change in the quantity demanded equals the percentage change in price (which means the elasticity equals 1).

3. Inelastic demand—when the percentage change in the quantity demanded is less than the percentage change in price (which means the elasticity is less than 1).

4. There are two extreme cases:

a. Perfectly elastic demand—when the quantity demanded changes by a very large percentage in response to an almost zero percentage change in price.

b. Perfectly inelastic demand—when the quantity demanded remains constant as the price changes