cross price elasticity(1)

7/30/2019 Cross Price Elasticity(1)

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TOPIC 7: ELASTICITY

Measuring Responsiveness

ECON-200

CSCCSelloane Asiamah


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Cross Price Elasticity (Exy) Measures how much demand of

Good X changes when the price of Good Y changes. How sensitiveis the demand for a good to changes in the price of a related good?

Changes in the price of a related good is a DEMAND SHIFTER!

RECALL: When the price of a good changes, it can SHIFT theDEMAND of RELATED GOOD (this is 1 of the 5 demand shifters!)

Assuming Good X & Y are related, they can either be:

1. SUBSTITUTES (can replace each other to fulfill the same want)

2. COMPLEMENTS (are used together in consumption)

3. Cross Price Elasticity


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ExyRELATED GOODS

HOW CONSUMERS RESPOND DEPENDS ON WHETHER THE GOOD IS A SUBSTITUTE

or A COMPLEMENT GOOD!

1. SUBSTITUTE GOOD:Price of Y INCREASES then Qd for Y DECREASES (Y is relatively more expensive)Since Good X can be substituted for Good Y, when Qd for Y decreases then people

buy more X andDEMAND for X INCREASES

Py Dx

Price of YDECREASES then Qd for Y INCREASES (Y is relatively cheaper than X)Since Good Y can be substituted for Good X, when Qd for Y increases, people are

buying less X and .DEMAND for X DECREASES

Py Dx


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ExyRELATED GOODS

HOW CONSUMERS RESPOND DEPENDS ON WHETHER THE GOOD IS A SUBSTITUTE

or A COMPLEMENT GOOD!

2. COMPLEMENT GOOD:Price of Y INCREASES then Qd for Y DECREASES. Since Good Y is used togetherwith Good X, when Qd for Y decreases then people will also buy less X and

DEMAND for X DECREASES

Py Dx

Price of YDECREASES then Qd for Y INCREASES. Since Good Y is used togetherwith Good X, when Qd for Y increases, people will also buy more X and

DEMAND for X INCREASES

Py Dx


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To calculate how sensitive demand for X is to changes in the

price of Y, we must calculate the Cross Price Elasticity usingthis formula:

Exy = % change in Demand for X

% change in Price of Y

Cross Price Elasticity


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Again you can calculate your % changes using eitherthe point method or Arc (midpoint) method

New value Original value

Original value

New value Original valueNew + Original

2

Calculating % Change

POINT METHOD

ARC METHOD


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Calculating Exy

Try it using the point method:

1. The price of hotdogs increases from $3 to $3.60. As aresult, the demand for hotdog buns decreases from 12units to 8 units (complements).

Exy = % change in Dx = 8 - 12

% change in Py 12

$3.60 - $3.00$3.00

Calculating, you should have an Exy value = -1.67

=

- 412

$0.60

$3.00


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Do not ignore the sign!!!

Unlike your Ep coefficient, do NOT ignore the negativesign on your Exy coefficient.

When Exy is negative, then you have goods that are

complements!

When the Price of hotdogs INCREASED, people bought

less hotdogs and the Demand for hotdog buns DECREASED

because you use them together.

*Since Py increased and Dx decreased (Negative/inverserelationship) therefore Exy is negative!


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Calculating ExyTry it using the point method:

2. Assume Burger King increased the price of their burgerfrom $3.50 to $4.00. Down the street, Wendys realizes

that they are selling more burgers. Usually they sell 70burgers per day and now they are selling 100 (substitute

goods)

Exy = % change in Dx = 100 70 = 30

% change in Py 70 70

$4.00 - $3.50 $0.50

$3.50 $3.50

Calculating, you should have an Exy value = 3


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Do not ignore the sign!!!

When Exy is positive, then you have substitute goods.

When the Price of Burger King burgers INCREASED,

people bought less burgers from BK and went downthe street to Wendys. As a result, Wendys

experienced an INCREASE in the Demand for their

burgers because they are substitutes!

*When Py increased and Dx increased (Positiverelationship) therefore Exy is positive!


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Interpreting Exy

What does the Exy coefficient tell us?

Example 1.

Exy = - 1.67

This is the cross price elasticity of hotdog buns and hotdog buns.

This means that a 1% change in the price of hotdogs leads to a

1.67% change in demand for hotdog buns!

Because Exy is negative, they are complements!

Negative Exy means that the price of good Y (hotdogs) and

the demand for good X (buns) move in opposite directions.

When Py increases, Dx decreases (and vice versa)


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Interpreting ExyWhat does the Exy coefficient tell us?

Example 2.

Exy = 3

This is the cross price elasticity of Burger King burgers and

Wendys burgers.

This means that a 1% change in the price of Burger King burgers

leads to a 3% change in demand for Wendys burgers!

Because Exy is positive, they are substitutes!

Positive Exy means that the price of good Y (Burger King) and

the demand for good X (Wendys) move in the same direction.

When Py increases, Dx increases (and vice versa)


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Good Y will always be the good that has a change in price

Good X is the related good its demand is reacting to thechange in the price of Good Y.

Example:

Initially, chips are priced at $3 and pretzels are priced at $4. At

these prices, people buy 5 bags of chips and 4 bags of pretzels.

The price of chips increases to $4 but the price of pretzels does

NOT change! Your Exy would find the change in the demand for

pretzels when the price of chips increases. FIND EXY!

Chips QDc Pretzels QDp

$3 5 $4 4

$4 3 $4 7


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SOLUTION:

Py is the price of chips since it was the good with the price

change. Dx is the demand for pretzels its price did not

change but the demand changed (in reaction to the change in

the price of chips!

Using theARC method:

Exy = % change in Dx =

% change in Py

7 4(7+4)/2

$4-$3($4+$3)/2

=

0.540.28

Exy for chips and pretzels = 1.92Since its positive, they are substitutes.

Interpretation of Exy = A 1% change in the price of chips leads

to a 1.92% change in the demand for pretzels.

= 1.92

cross price elasticity(1)

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