Price Elasticity
The Price
Elasticity of Demand (commonly known as just price elasticity) measures the
rate of response of quantity demanded due to a price change. The formula for
the Price Elasticity of Demand (PEoD) is:
PEoD = (%
Change in Quantity Demanded)/(% Change in Price)
Price
elasticities are almost always negative, although analysts tend to ignore the
sign even though this can lead to ambiguity. Only goods which do not conform to
the law of demand,
such as Veblen and Giffen goods, have a
positive price elasticity.
Income Elasticity
The Income
Elasticity of Demand measures the rate of response of quantity demand due to a
raise (or lowering) in a consumers income. The formula for the Income
Elasticity of Demand (IEoD) is given by:
IEoD = (%
Change in Quantity Demanded)/(% Change in Income)
Cross Elasticity
cross
elasticity of demand or cross-price elasticity of demand measures the
responsiveness of the demand for a good to a change
in the price of another good. It is measured as the percentage change in demand
for the first good that occurs in response to a percentage change in price of
the second good. For example, if, in response to a 10% increase in the price of
fuel, the demand of new cars that are fuel inefficient decreased by 20%, the
cross elasticity of demand would be: 
. A negative cross elasticity denotes two
products that are complements, while a positive cross elasticity denotes two
substitute products. These two key relationships may go against one's
intuition, but the reason behind them is fairly simple: assume products A and B
are complements, meaning that an increase in the demand for A is caused by an
increase in the quantity demanded for B. Therefore, if the price of product B
decreases, then the demand curve for product A shifts to the right, increasing
A's demand, resulting in a negative value for the cross elasticity of demand.
The exact opposite reasoning holds for substitutes.
The cross
elasticity of demand for substitute goods will always be positive, because the
demand for one good will increase if the price for the other good increases.
For example, if the price of coffee increases (but everything else stays the
same), the quantity demanded for tea (a substitute beverage) will increase as
consumers switch to an alternative. On the other hand, the coefficient for
compliments will be negative. For example, if the price of coffee increases
(but everything else stays the same), the quantity demanded for coffee stir
sticks will drop as consumers will purchase fewer sticks. If the coefficient is
0, then the two goods are not related.