CED = Cross Elasticity of Demand

Definition:

CROSS ELASTICITY OF DEMAND measures the proportionate change in the quantity demanded of good A caused by a change in the price of good B.

Price is only one of the factors that can change the demand for a good. Others include

changes in taste and fashion
changes in income
anticipated price changes
changes in climate

changes in the price of other goods

We can see that one of the elements which could cause a change in quantity demanded is a change in price of another good.

In order for this to be true there must be some relationship between the goods. The goods must be capable of being used one in conjunction with the other, or else the goods are goods which may serve more or less the same purpose.

Goods which may be used with each other are said to be goods which are in Joint Demand, or Complementary Goods.
Goods which may be used for similar purposes are called Competitive (or Substitute) Goods.

The formula for calculating CROSS ELASTICITY OF DEMAND is almost the same as that for calculating PRICE ELASTICITY OF DEMAND:-

P1a + P2a Qb

----------- X ----

Q1b + Q2b Pa

where "a" represents one good and "b" represents a different good that is either a complement to, or a substitute for, good a.

You can use the Arc Elasticity Calculator to
calculate Cross Elasticity of Demand

Substitute Goods Complementary Goods

Substitute Goods

Examples of Substitute Goods
Butter and Margarine
Tapes and Compact Disks
Cars and Motorbikes
Matches and Lighters
Paint Brushes and Paint Rollers
Apples and Bananas

This is how to establish the demand elasticity of bananas in respect of a price change in apples.

Price of Apples Quantity of Bananas demanded

10p 4 kilos per week

15p 5 kilos per week.

Apply the CED formula

10 + 15 +1 25 +1

--------X --- = --- X ---

4 + 5 +5 9 +5

= 25 � 45 = +0.55

Apples and Bananas are substitute goods.

When the price of apples goes up, all other things being equal, the demand for apples will fall. Given that we still want an intake of fruit, we could expect that the demand for bananas (which have not had a price change) will increase.

An increase in the price of apples has caused an increase in the demand for bananas.

A plus by a plus gives us a plus.

The CROSS ELASTICITY OF DEMAND sign for Substitute Goods is Positive

If we are talking about Cross Elasticity of Demand and the sign is positive, this means that the goods in question are Substitute Goods

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Complementary Goods

Examples of Complementary Goods
Bread and Butter
Tapes and Tape Recorders
Cars and Petrol
Cigarettes and Matches
Paint and Paint Brushes
Cereals and Milk
DVDs and DVD Players

Now let us have a look at what happens to the quantity demanded of DVDs demanded when there is a change in the price of DVD Players.

Price of DVD Players Quantity of DVDs sold per week

�200 5000

�150 8000

Apply the CED formula

200 + 150 +3000 350 +3000

-------------- X ------- = ------ X -------

5000 + 8000 -50 13000 -50

= 1,050,000 1050

------------ X ------

-650,000 -650

= 1050 � -650 = -1.615 or 1.615 in absolute terms.

Note that as the price of the DVD Players went down, the quantity of DVDs demanded rose. This would appear to be logical. As the price of the DVD Players fell, more DVD Players would be demanded, and therefore more DVDs will be bought to be played on the increased number of DVD Players.

As the price of DVD Players went down (minus), the quantity demanded of DVDs went up (plus).

A minus by a plus in our formula will have to give a minus, or negative, answer.

The CROSS ELASTICITY OF DEMAND sign for Complementary Goods is Negative

If we are talking about Cross Elasticity of Demand and the sign is negative, this means that the goods in question are Complementary Goods

Once again, the importance of the sign becomes evident. The sign in CROSS ELASTICITY OF DEMAND will show whether the good in question is a substitute or a complement. Having established that, however, ignore the sign and measure the elasticity in the usual way. In the examples above, the apples and bananas had inelastic demand, while the CD Players and the CDs had an elastic demand.

Examination Tip:

Don't try to remember that the sign for Complementary Goods in CROSS ELASTICITY OF DEMAND is Negative and that the sign for Substitute Goods is Positive. Under examination pressures, students very often get them confused. Instead of remembering them (possibly incorrectly), work out the cold logic of the examples. If the price of one breakfast cereal goes up, the demand for it will fall. Given that we would still want to put a cereal in our bowls in the mornings, the demand for its substitute will rise. Therefore substitutes have a positive sign.

If the price of cigarettes goes up (ignoring the addictive element of the nicotine), the demand for cigarettes should fall, and so also would the demand for matches to light them. Complementary Goods must, therefore, have a negative sign.

Don't Try To Remember It - Analyse It!!!

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