The price elasticity of demand measures the responsiveness of quantity demanded to a change in price, with all other factors held constant.

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

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

For

a

the

is

*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

For

a

by

from

*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.

Some products that initially have a low degree of necessity are habit forming and can become “necessities” to some consumers.

products that consume a large portion of the purchaser’s budget tend to have greater elasticity.