Cross-price elasticity of demand

A measure of the responsiveness of one
variable (usually quantity demanded or
supplied) to a change in another variable
Most commonly used elasticity: price
elasticity of demand, defined as:
Price elasticity of demand
%change_ of _ quantity_ dem anded
%change_ of _ price
usually takes negative values
◦ when price grows, quantity demanded decreases
◦ when price decreases, quantity demanded increases
the exceptions:
◦ The Veblen effect is one of a family of theoretically
possible anomalies in the general theory of demand. It is
claimed that some types of high-status goods, such as
diamonds or luxury cars, are Veblen goods, in that
decreasing their prices decreases people's preference for
buying them because they are no longer perceived as
exclusive or high status products.[1] Similarly, a price
increase may increase that high status and perception of
exclusivity, thereby making the good even more
Giffen good
 the classic example given by Marshall is staple foods of inferior
 whose demand is driven by poverty, that makes their purchasers
unable to afford superior foodstuffs.
 As the price of the cheap staple food rises, they can no longer
afford to supplement their diet with better foods, and must
consume more of the staple food.
Marshall wrote in the 1895 edition of Principles of Economics:
As Mr. Giffen has pointed out, a rise in the price of bread makes
so large a drain on the resources of the poorer labouring families
and raises so much the marginal utility of money to them, that
they are forced to curtail their consumption of meat and the
more expensive farinaceous foods: and, bread being still the
cheapest food which they can get and will take, they consume
more, and not less of it.
Demand is said to be:
◦ elastic when Ed < -1,
◦ unit elastic when Ed = -1, and
◦ inelastic when Ed >-1.
Even small change of price results decreasing
of demand till zero
Customers buy the same amount of good,
regardless of good’s price
a price increase from $1 to $2 represents a 100%
increase in price,
a price increase from $2 to $3 represents a 50%
increase in price,
a price increase from $10 to $11 represents a 10%
increase in price.
Notice that, even though the price increases by $1
in each case, the percentage change in price
becomes smaller when the starting value is larger.
price _ elasticity _ of _ dem and
ΔQ - change of quantity demanded
Q – quantity demanded before price
ΔP – change of price
P – price before change
Suppose that quantity demanded falls from
60 to 40 when the price rises from $3 to $5.
The price elasticity of demand equls…
In this interval, demand is inelastic (since elasticity >- 1).
Total revenue = price times quantity
What happens to total revenue if the price
Ticket prices
Price elasticity
of demand
Total revenue
Price elasticity of demand =
%change_ of _ quantity_ dem anded
%change_ of _ price
A reduction in price will lead to:
◦ an increase in TR when demand is elastic.
◦ a decrease in TR when demand is inelastic.
◦ an unchanged level of total revenue when
demand is unit elastic.
different customers are charged different
prices for the same product, due to
differences in price elasticity of demand
higher prices for those customers who have
the most inelastic demand
lower prices for those customers who have a
more elastic demand.
Theatres usually charge three different prices
for a show. The prices target various age
groups, including youth, adults and seniors.
The prices fluctuate with the expected
income of each age category, with the highest
charge going to the adult population.
Some companies, such as firms selling
alcoholic beverages, produce similar products
but try to promote one as a prestige brand
with a much higher price.
Price elasticity of demand is relatively high
 close substitutes are available,
 the good or service is a large share of the
consumer's budget,
 a longer time period is considered,
 the customers are rather poor.
Price elasticity of demand is relatively low
 There are no close substitutes (e.g. electricity,
 Goods are necessities
 Customers are rather rich
 The good or service is a small share of the
consumer's budget
The cross-price elasticity of demand between
two goods j and k is defined as:
cross-price elasticity is positive if and only
if the goods are substitutes
cross-price elasticity is negative if and
only if the goods are complements.
A good is a normal good if income
elasticity > 0.
A good is an inferior good if income
elasticity < 0.
A good is a luxury good if income elasticity
> 1.
A good is a necessity good if income
elasticity < 1.
Example: land
Example: perfect competition
short run - period of time in which capital is
all inputs are variable in the long run
supply will be more elastic in the long run
than in the short run since firms can expand
or contract their capital in the long run.
równanie – equation
układ równań - simultaneous equations
ułamek – fraction
ułamek piętrowy – compound fraction
malejąca (rosnąca) funkcja – decreasing (increasing) function
funkcja liniowa – linear function
iloraz – quotient
iloczyn – product
różnica – difference
suma – sum
sumowanie – summation
dodatni – positive
ujemny – negative
licznik – numerator
mianownik - denominator
Czarny B. „Podstawy Ekonomii”, 2002
Wood, John C. (1993). Thorstein Veblen:
Critical Assessments, 352. London
Alfred Marshall, 1895. Principles of
Economics Bk.III,Ch.VI in paragraph III.VI.17

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