Economists frequently want to summarize the way in which changes in one variable affect some other variable. For example, an economist might be interested in measuring how a change in the price of a good affects the quantity demanded or how a change in income affects total expenditures.
One problem that arises in attempting to develop such summary measures is that quite often the two variables are not measured in the same units. The quantity of apples purchased is measured in kilograms per week and the price of apples is measured in dollars per kilogram. We might then speak of an increase of 10 cents in the price of apples leading to a fall of 2 kilograms per week of apple purchases.
Similarly, we could speak of a fall in the price of oranges by 10 cents per dozen leading to an increase in orange purchases of half a dozen per week. However, there would now be no easy way to answer the question of whether apples are more or less responsive to price changes than are oranges. The problem exists because the commodities are measured in different units. As a solution economists have developed the concept of elasticity.
Elasticities are calculated as the percentage change in one variable
divided by the percentage change in another. The most common of such
calculations, price elasticity of demand (or demand elasticity), is a
measure of the responsiveness of quantity demanded to price changes:
The fact that demand curves slope downward implies that 
and 
have opposite signs. Thus, 
0. The usual
practice is to ignore the minus
sign and speak of demand elasticity as a positive number. Accordingly, the
numerical value of can vary
from zero to infinity.
When 
=
0 so that = 0, demand is
said to be perfectly inelastic.
When || < || so that < 1 demand is said to be inelastic.
When || = || so that = 1, demand is said to be unit elastic.
When || > || so that > 1 demand is said to be elastic.
When =
0 so that = infinity, demand
is said to be perfectly elastic.
Unlike the demand curves just presented, every point along a straight-line
demand curve with a non-zero, non-infinite slope is associated with a
different price elasticity. In fact, every possible value of from zero to infinity is
represented as we move from right to left along such a curve.
To provide a simple example of an elasticity calculation, suppose that a ten percent decrease in the price of yams causes a three percent increase in the quantity demanded. The elasticity of demand for yams is
Since this number is less than one, the demand for yams is inelastic.
What determines price elasticity? A commodity with close substitutes tends to have elastic demand; a commodity with no close substitutes tends to have inelastic demand. (Note that the more broadly defined is a commodity, the fewer close substitutes it tends to have; durable goods versus CD players, for example.)
