Price Elasticity of Demand

Definition

The price elasticity of demand, E_d is defined as the magnitude of:

proportionate change in quantity demanded

————————————————————————

proportionate change in price

Since the quantity demanded decreases when the price increases, this ratio is negative;
however, the absolute value usually is taken and E_d is reported as a positive number.

Because the calculation uses proportionate changes, the result is a unitless number and does not depend on the units
in which the price and quantity are expressed.

As an example calculation, take the case in which a product’s E_d is reported to be 0.5. Then, if the price were to increase by 10%, one would observe a decrease of approximately 5% in quantity demanded.

In the above example, we used the word “approximately” because the exact result depends on whether the initial point or the final point is used in the calculation. This matters because for a linear demand curve the price elasticity varies as one moves along the curve. For small changes in price and quantity the difference between the two results often is negligible, but for large changes the difference may be more significant. To deal with this issue, one can define the arc price elasticity of demand. The arc elasticity uses the average of the initial and final quantities and the average of the initial and final prices when calculating the proportionate change in each. Mathematically, the arc price elasticity of demand is defined as:
Q2 – Q1

———————–

( Q1 + Q2 ) / 2

——————————-

P2 – P1

———————–

( P1 + P2 ) / 2

where

        Q1  =  Initial quantity

        Q2  =  Final quantity

        P1  =  Initial price

        P2  =  Final price

Elastic versus Inelastic

E  > 1

In this case, the quantity demanded is relatively elastic, meaning that a price change will cause an even larger change in quantity demanded.
The case of E_d = infinity is referred to as perfectly elastic.
In this theoretical case, the demand curve would be horizontal.
For products having a high price elasticity of demand,
a price increase will result in a revenue decrease since
the revenue lost from the resulting decrease in quantity sold
is more than the revenue gained from the price increase.

E  < 1

In this case, the quantity demanded is relatively inelastic,
meaning that a price change will cause less of a change in quantity demanded.
The case of E_d = 0 is referred to as perfectly inelastic.
In this theoretical case, the demand curve would be vertical.
For products whose quantity demanded is inelastic,
a price increase will result in a revenue increase since the revenue lost
by the relatively small decrease in quantity is less than the revenue gained
from the higher price.

E  = 1

In this case, the product is said to have unitary elasticity; small changes in price do not affect the total revenue.

Factors Affecting the Price Elasticity of Demand

• Availability of substitutes: the more possible substitutes, the greater the elasticity.
  Note that the number of substitutes depends on how broadly one defines the product.