Measuring Cross Price Elasticity of Demand: Proportionate Method
Learning
Contents:
· Computation of Cross Price Elasticity using Proportionate Method or Percentage method
Cross Price Elasticity of Demand
(Proportionate or Percentage Method)
Cross price elasticity
of demand tells us the relationship between price of one good and its impact on
the quantity demand for another good. The effect of price of one good on the
demand for another good is measured by cross price elasticity of demand. Therefore,
it measures the percentage change in quantity demand in response to a
percentage change in the price of another good. It is measured by its
coefficient XED. Mathematically, it is
calculated as,
Computation
of Cross Price Elasticity using Proportionate Method or Percentage method
1. If a 12 percent rise in the price of burger decreases the quantity of burger demanded by 22 percent and increases the quantity of hot dog demanded by 14 percent, calculate the cross-price elasticity of demand between burger and hot dog. Also state their relationship.
Solution:
Following
information is given:
|
Percentage increase in demand of Hot Dog
=14% |
|
Percentage increase in price of Burger
=12% |
|
XED=? |
Interpretation:
The calculated value of
cross-price elasticity of demand (XED) is 1.17 shows that a 100% increase in
price of Burger caused 117% increase in the demand for Hot Dog showing that
demand is very elastic and they are very substitutable to each other.
2.
If a 5 percent rise in the price of coffee increases the quantity of tea
demanded by 2 percent and decreases the quantity of coffee demanded by 1
percent, calculate the cross-price elasticity of demand.
Solution:
Following
information is given:
|
Percentage increase in demand of Tea
=1% |
|
Percentage increase in price of Coffee =2% |
|
XED=? |
Interpretation:
The calculated value of
cross-price elasticity of demand (XED) is 0.4 shows that a 1% increase in price
of Coffee caused 2% increase in the demand for Tea showing that demand is inelastic
and they are somewhat substitutable to each other.
3.
If the cross elasticity of demand between peanut butter and milk is -1.11, then
are peanut butter and milk substitutes or complements? Explain it.
Solution:
The value of cross elasticity of demand is -1.11 indicating that Peanut butter and milk are highly complements because a negative cross price elasticity of demand means that as the price of milk goes up, the demand for peanut butter goes down. This would indicate that when the price of milk goes up, we buy less milk and we are also buying less peanut butter (so we must buy these together -- they are complements).
Solution:
Following
information is given:
Interpretation
The calculated value of
cross-price elasticity of demand (XED) is 2.664 shows that a 12.5% increase in
price of X caused 33.3% increase in the demand for Y showing that demand is
very elastic and they are very substitutable to each other.
5.
The owners of a pizza outlets find that when their competitor, a burger outlets,
decreases the price of their burger from ₹2 to ₹1.80, the number of pizza
slices that they sell each week decreases from 400 to 380, because of the
decreased price of burgers. Determine the cross elasticity for the pizza
slices.
Solution:
Following
information is given:
Interpretation
The calculated value of
cross-price elasticity of demand (XED) is 0.5 shows that a 10% fall in price of
burger caused 5 % fall in the demand for pizza slices showing that demand is less
elastic and they are somewhat substitutable to each other.
6.
Suppose Laziz Pizza and Dominos are two pizza outlets where consumers prefer to
go. Due to rising costs, Laziz Pizza increases its price by 10 percent and consumers
do not like the price increase and they switch to Dominos, thereby increasing its
demand by 8 percent. Calculate the cross price elasticity and tells whether the
good is substitute or complement? Also tell their relationship.
Solution:
Following
information is given:
|
Percentage increase in demand of
Dominos =8%
|
|
Percentage increase in price of Laziz
Pizza =10% |
|
XED=? |
Interpretation
The calculated value of cross-price elasticity of demand (XED) is 0.8 shows that a 10% fall in price of Laziz Pizza caused 5 % fall in the demand for Dominos pizza showing that demand is less elastic and they are somewhat substitutable to each other.
7. Suppose
the price of Mac Book increases from $1000 to $1500 and quantity demand of Sony
VIAO increases from 200 units to 220 units. Calculate its cross price
elasticity of demand.
Solution:
Following
information is given:
8.
Suppose, when the price of wine falls by 10%, the quantity of beer demanded
decreases by 5%. Calculate the Cross price elasticity of demand. Also state
what type of good are they and their relationship.
Solution:
Following
information is given:
|
Percentage fall in price of Wine =10% |
|
Percentage fall in quantity demanded
of Beer =5% |
|
XED=? |
Interpretation:
The calculated value of
cross-price elasticity of demand (XED) is 0.5 shows that a 10% fall in price of
wine caused 5 % fall in the demand for Beer showing that demand is less elastic
and they are somewhat substitutable to each other.
9.
The cross-price elasticity of demand for Burger Bun and patty is equal to -1.5.
So, what is the relationship between burger bun and patty? (Complements /
Substitutes). Suppose that the price of patty increases by 10%. What is the
percentage change in the quantity demanded of Burger Bun?
Solution:
Following
information is given:
|
Percentage increase in price of patty
=10%
|
|
Percentage change in quantity demanded
of Burger Bun =? |
|
XED=-1.5 |
Interpretation:
The cross price elasticity
of demand is -1.5 that implies that 10% increase in price of the patty caused
15% fall in the demand of Burger Bun. The demand is very elastic and both the
goods are highly complementary to each other.
10.
In this example, we are trying to understand the relationship between price and
demand of two amusement parks, say Appu Ghar and Adventure Island. Suppose that
Adventure Island increases its daily ticket price from ₹110 to ₹140. As a
result, demand at Appu Ghar increases from 10,000 to 11,500. Calculate the
cross price elasticity of demand.
Solution:
Following
information is given:
Interpretation:
The cross price elasticity
of demand is 0.53 that implies that 28% increase in price of the Adventure
Island Tickets caused 15% rise in the demand of Appu Ghar Tickets showing that
the demand is less elastic and they are somewhat substitutable to each other.
Let’s
try some questions
Choose
the Correct Answer
1. A bakery is indulged in the
production of cakes and the price of cakes increases by 13 percent. At the same
time, demand for vanilla essence syrup decreases by 4 percent. This is because baker needs vanilla essence
syrup in order to make cake. What will be the cross price elasticity of demand?
a. 0.30
b.
0.25
c.
0.45
d. 0.10
2. Suppose the cross-price elasticity of
shirts with respect to trousers is −1/5. If the price of trousers goes up by
10% the quantity of shirts demanded ________
a. increased by15 percent.
b.
increased by25 percent.
c.
decreased by15 percent.
d. decreased by30 percent.
3. When the price of beef goes up by 10%
the quantity of chicken demanded rises by 5%. Then the cross-price elasticity
of chicken with respect to beef is ____ .
a. 0.5
b.
-2.0
c.
2.0
d.
-0.5
3. When the price of apples goes up from
$2 to $ 2.50. As a result, quantity demanded of pears rises from 30 units to 50
units Determine the cross-price elasticity of demand .
a. 0.5
b.
-2.0
c.
2.7
d. -0.5
Answer Key
|
1.a |
2.c |
|
3.a |
4.c |
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