Elasticity
Elasticity is a term used in business and economics to refer to responsiveness. The most common use of the term is
to characterize the responsiveness of consumers to a change in price. This is referred to as the “price elasticity of
demand,” but elasticity has other uses as well. “Income elasticity of demand” refers to the responsiveness of
consumers to a change in income. The “wage elasticity of the demand for labor” is essentially the same as the “price
elasticity of demand” except that the demanders are employers and the term “wage” is used analogously to “price.”
I.
Price elasticity of demand is the responsiveness of consumers to a change in price. If a small change in price
results in a large change in the quantity demanded, demand is said to be elastic. If a large change in price
results in only a small change in the quantity demanded, then the demand is said to be inelastic. The
following table summarizes price elasticity of demand. The wage elasticity of the demand for labor is
fundamentally identical to the price elasticity of demand.
Description
Graph
Examples
Change in
Q
Change in
P
#E# =
Elastic
A relatively small
change in price results
in a relatively large
change in quantity
demanded.
Vacation air fare,
specific brands of
items e.g., Pepsi,
Chevron gas,
Relatively
large
Relatively
small
#E# > 1
Unit
elastic
A change in price
results in an equal
change in the quantity
demanded.
Special case
Same
Same
#E# = 1
Inelastic
A relatively large
change in price results
in a relatively small
change in quantity
demanded.
Gas, electricity,
cigarettes, drugs,
health care, salt
Relatively
small
Relatively
large
#E# < 1
Perfectly
inelastic
Regardless of the
change in price,
consumers continue to
purchase the same
quantity of the good.
This is not realistic.
None
No change
Any
#E# = 0
Two similar formulas are used to calculate the price elasticity of demand. Since price and the quantity
demanded are negatively related, the numerical value for elasticity will always be negative. Because the sign
never changes, the sign is often ignored.
A.
Arc elasticity (or midpoint elasticity) calculates an average value for elasticity between two points on a
demand curve. In order to avoid differing results depending on the direction of the price change, this
formula calculates percent changes using the average or midpoint values for P and Q.
1.
The formula is
2.
Example: Suppose that when P = $2.10 consumers will buy 350 units per week. W hen the item
is on sale for P = $1.90 per unit, consumers buy 450 per week. Then,
Since *E* > 1, demand is elastic over this range of price and quantity. The percentage change in
quantity is two and a half times the percentage change in price (in terms of absolute value.)
B.
II.
Point elasticity calculates the value for elasticity at a single point on the demand curve. This
calculation uses the slope of the demand curve at the point of interest. W hen the demand curve is a
straight line, the slope at this point is the same as everywhere else on the demand curve and is easy to
find. W hen the demand curve is nonlinear, this calculation involves differential calculus to find the
slope of the demand curve at the point of interest.
1.
The derivation of the formula can be seen by beginning with a Formula
2.
Example: If the demand curve is represented by a straight line from (Q = 0, P = $10) to Q =
1000, P = $0.00), then the slope is -1/100. The point elasticity at (Q = 750, P = $2.50) is
(-100/1) (2.5/750) = -0.33.
Price elasticity of supply is the responsiveness of the quantity supplied to a change in price. The formulas for
the price elasticity of supply are identical to those for the price elasticity of demand with the single exception
that the quantity supplied rather than the quantity demanded is used. Since price and the quantity supplied
tend to be positively related, the price elasticity of supply tends to be positive, though there are possible
exceptions to this rule.
A.
Example: If the supply curve is represented by a straight that goes through the points (Q = 0, P =
$10.00) and (Q = 200, P = $110), then at (Q = 40, P = $30) the point elasticity of supply is
III.
IV.
Cross price elasticity of demand is the responsiveness of the demand for one good with respect to a change in
the price of another good. For example if the price of Pepsi declines we would expect that the amount of
Coke that consumers would want to buy would decrease. The cross price elasticity of demand measures the
magnitude of Coke consumers’ responsiveness to a change in the price of Pepsi. The sign of the cross price
elasticity of demand will depend on whether the two goods are substitutes or complements. If two goods are
substitutes like Pepsi and Coke, then an increase in the price of one good will cause an increase in the demand
for the other, so the cross price elasticity of demand will be positive. If two goods are complements like Pepsi
and hamburgers at a fast food restaurant, then a decrease in the price of one will tend to result in an increase in
the demand for the other, so the cross price elasticity will be negative.
A.
Formula: As with other elasticities, this elasticity can be calculated with a calculus-based formula that
will give a value for a specific price-quantity situation or a formula like the arc elasticity formulas
above that uses two distinct price-quantity situations. For our purposes, it is easier to use a an arc
elasticity-type formula. The following formula for cross price elasticity shows the responsiveness of
demand for good x as a result of a change in the price of good y.
B.
Example: Suppose that initially hotel customers are purchasing 450 meals per day in the hotel and the
daily room rate is $105. The hotel finds that when it lowers the room rate to $95, the number of meals
purchased increases to 550. The cross price elasticity of demand in this case is
Income elasticity of demand is the responsiveness of the demand for a good to a change in income. The
amount of most goods that people purchase increases with income. This positive relationship means that the
income elasticity of demand for most goods is positive and these goods are referred to as “normal” goods.
However, consumers may reduce purchases of some goods as their income increases. For example, as
incomes increase the usual response of consumers is to reduce their purchases of bus rides. This is because
they are more likely to be purchasing and traveling in their own cars as income rises. W hen the quantity of a
good demanded declines with increases in income, the good is referred to as an “inferior” good.
A.
Formula: As with the other formulas, the income elasticity of demand compares the relative change in
the quantity of the good with the relative change in something else - in this case, income. As with other
types of elasticities, one formula for income elasticity of demand calculates elasticity based on the
change between two distinct income-quantity situations, and another formula calculates the elasticity at
a specific income-quantity situation. The arc elasticity type formula is
B.
Example: Suppose that initially average household income is $34,000 and the average number of
airplane tickets purchased per household per year is 1.3. When average household income rose to
$36,000, the average number of airplane tickets purchased per household rose to 1.5. The income
elasticity of demand is