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The price elasticity of demand measures the responsiveness of quantity demanded to a change in price,
with all other factors held constant.
Definition
The price elasticity of demand, Ed is defined as the magnitude of:
proportionate change in quantity demanded
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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 Ed 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 Ed 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 are 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
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( Q1 + Q2 ) / 2
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P2 - P1
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( 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 Ed = 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 Ed = 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 Influencing the Price Elasticity of Demand
The price elasticity of demand for a particular demand curve is influenced by the following factors:
Availability of substitutes: the greater the number of substitute products, the greater the elasticity.
Degree of necessity or luxury: luxury products tend to have greater elasticity than necessities. Some products that initially have a low degree of necessity are habit forming and can become "necessities" to some consumers.
Proportion of income required by the item: products requiring a larger portion of the consumer's income tend to have greater elasticity.
Time period considered: elasticity tends to be greater over the long run because consumers have more time to adjust their
behaviour to price changes. Permanent or temporary price change: a one-day sale will result in a different response than a permanent price decrease of the same magnitude.
Price points: decreasing the price from £2.00 to £1.99 may result in greater increase in quantity demanded than decreasing it from £1.99 to £1.98.
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