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Cross Elasticity of Demand
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SSC351 Study Guide

So far you learned that price and income play a role in determining elasticity of demand. They both are factors that determine the degree at which quantity demanded changes. For certain goods we saw relatively large changes in quantity demanded when price or income changes, while for certain other goods, the changes in quantity demanded are relatively small. Yet, for some goods the changes in price or income cause a correspondingly equal change in quantity demanded. In extreme cases, we saw no changes at all to quantity demanded regardless of price or income changes or an indefinite change even with the slightest change in price or income.

Now we are going to look at another factor that can determine the elasticity of demand. We will study how the price changes of one good, say good A, can affect the elasticity of demand of another related good, say good B. This is known as cross elasticity of demand.

In determining the cross elasticity of demand we will look at two different products. On one, we will look at the percentage change in price, and on the other we will study the percentage change in quantity as the result of the change in price of the former good. Please remember that the study of cross elasticity of demand is on related goods only, that is, either substitute or complementary goods.

How do we do this? First, calculate the change in price of product A using the following formula:

Change in Price

  (P1 + P2)/2

Then, calculate the change in quantity of product B using the following formula.

Change in Quantity

   (Q1 + Q2)/2

Lets use this example to complete the calculations:

The price of fountain pens (product A) increases from RM100 per unit to RM120 per unit. This price increase results in the decrease in demand for ink (product B), and the demand falls from 20 units to 16 units.

Change in price of product A                       = RM20

Change in Quantity Demanded of Product B = 4 units

The change in price is:

_____20____

(100 + 120)/2

0.10 (or 10%)

The change in quantity demanded is:

____4_____

(20 + 16)/2

0.22 (or 22%)

Here you see that a 10% increase in price of fountain pens resulted in a 22% fall in quantity demanded for ink. If you take the change in quantity demanded figure (0.22) and divides it with the change in price figure (0.10); you will get a figure of 2.2. What the 2.2 means is "a 1% increase in price of fountain pens results in a 2.2% decrease in quantity demanded for ink. (Since the change in quantity demanded is greater than 1, we say ink has a cross elastic demand).

The complete formula for calculating cross elasticity of demand is as follows:

Change in QD of Product B    divide by    Change in P of Product A

       (Q1 + Q2)/2                                            (P1 + P2)/2

After doing the appropriate calculations, make the appropriate conclusion. Pick any one below:

  1. The change in price of product A will cause a relatively larger change in the quantity demanded of product B. A 1% change in price of product A will result in a greater than 1% change in quantity demanded for product B. In this case, we say that the demand for product B is cross elastic.
  2. The change in price of product A will cause a relatively smaller change in the quantity demanded of product B. A 1% change in the price of product A will result in a smaller than 1% change in quantity demanded for product B. In this case, we say that the demand for product B is cross inelastic.
  3. The change in price of product A will cause a correspondingly equal change in quantity demanded of product B. A 1% change in the price of product A will result in an equal 1% change in quantity demanded for product B. In this case, we say the demand for product B is unit elastic.