# cross price elasticity

John Christie
Rabina Sherchan

Cross-Price Elasticity is the measure of the responsiveness of the demand on the product under investigation compared to change in the price of a related good. Cross-price elasticity can be measured by the percentage change in the quantity demanded of one good divided by the percentage change in the price of a related good (Baye, 2006). The equation is Cross-price elasticity = (%ΔQ)/(%ΔP)

Examples

An example that can demonstrate this principle is the demand of SUV vehicles. When the price of gasoline increases, the demand for SUV decreases. This shows that the two products are complements. The amount that the demand for SUV decreases in relation to the gasoline increases is the measure of the Cross-Price Elasticity.

If goods are complements, like in the above example, the cross-price elasticity of demand will be less than zero. The negative cross-price elasticity in simple terms, signifies that there is inverse relationship between price of gasoline and demand for SUV. As one increases the other decreases and vice- versa.

A second example of cross-price elasticity can be seen between Nike and Adidas footwear. If the cross-price elasticity between these two is 2, 5% increase in the price of Nike will increase the demand for Adidas by 10%. When we see there is a direct relationship between the price of a good and the quantity demanded for the related good, they are substitue goods. Thus, for substitue goods, we have cross-price elasticity always greater than zero.

A third example of cross-price elasticity is between Coke and Pepsi. If the price of Coke increases by 10%, then the demand for Pepsi will increase by 20%. This results in a cross price elasticity between the two of 2. Like the example above, these two would be substitues since the cross-price elasticity is greater than zero.

Fourth example is for breakfast cereals manufactured by Wild Oats and General Mills. These are substitute goods as an increase in the price of one good will lead to an increase in demand for the rival product. Cross price elasticity here will be positive.

Below diagrams can help us understand the cross-price elasticity better.

Real world examples of Cross Price Elasticity:
 Product Under Investigation Comparison Product Price Elasticity US Domestic Tuna Imported Tuna 0.45 US Domestic Tuna Bread -0.33 US Domestic Tuna Ground Meat 0.3 Beer Wine 0.2 Beer Soft Drinks 0.3 Transit Automobiles 0.85 Transportation Recreation -0.05 Food Recreation 0.15 Clothing Food -0.18

Questions

1. Complementary goods have:
a) The same elasticities of demand
b) A positive cross-price elasticity of demand
c) A negative cross-price elasticity of demand
d) None of the above

The answer is C. When goods are complements the cross-price elasticity will be less than zero.

2. If tea and coffee are substitute goods, then the cross-price elasticity will be:
a) Positive
b) Negative
c) Equal to zero
d) None of the above

The answer is A. If two goods are substitutes then the cross-price elasticity will be greater than zero. For example if the price of coffee rises then the demand for tea will rise as consumers substitue it for coffee.

3. If the price of a GM cars fall by 8% and during the same time period the demand for a Ford car decreases by 2%. The cross-price elasticity of the demand for Ford cars is:
a) 0.5
b) 2.0
c) -0.25
d) 0.25

The answer is D. For cross-price elasticity it is the change in demand divided by the change in price (-2/-8). Also, the goods are substitues since the cross-price elasticity is greater than zero.

4) If the cross price elasticity between ketchup and mustard is 4, a 10% increase in the price of mustard will lead to a:
a) 40% drop in the quantity demanded of ketchup
b) 40% drop in the quantitiy demanded of mustard
c) 40% increase in the quantitiy demanded of ketchup
d) 40% increase in the quantity demanded of mustard

The correct answer is C. The cross-price elasticity is equal to the change in demand divided by the change in price. Since we know the cross-price elasticity equals 4 and price increases by 10% for mustard we can solve for the demand of ketchup. The equation would be 4=(X/10), and if we solve for X, which is the demand for ketchup, it would be 40%. Since the 40% is positive that means that there is an increase in the quantity demanded.

5) If the price of basketball tickets increases by 10%, the demand for hokey tickets increases by 20%. What is the the cross price elasticity of demand for hockey tickets?
a) 0.5
b) 2.0
c) -0.5
d) -2.0

The answer is C. For cross-price elasticity it is the change in demand divided by the change in price (20/10). Also, hockey tickets are a substitue for basketball tickets since the cross-price elasticity is greater than zero.

6) If computers and computer software are complementary goods. What should happen to the demand for computers if computer software prices increase?
a) Increase
b) Decrease
c) Remain The Same

The answer is B. Since the two goods are complements, and increase in the price of software will lead to a decrease in the demand for computers.

7) The equation for Cross-price elasticity is
a) (%ΔQ)/(%ΔP)
b) (%ΔP)/(%ΔQ)
c) P/Q
d) Q/P

8) For substitue goods, we have cross-price elasticity
a) Always less than zero
b) Always greater than zero
c) Always equal to zero
d) None of the above

The answer is B. There is a direct relationship between the price of a good and the quantity demanded for the related good when they are substitue goods. Increase in the price of one good will lead to an increase in demand for the other and thus cross price elasticity will always be positive.

9) Cross-price elasticity equals to zero for
a) Complementary goods
b) Substitute goods
c) Unrelated goods
d) None of the above

The answer is C. When there is no relationship between two products, the cross price elasticity of demand is zero.

References:

1. Managerial economics and Business Strategy, Michaeal R. Baye, Fourth Edition, Chapter 3
2. http://en.wikipedia.org/wiki/Cross_elasticity_of_demand
3. http://www.tutor2u.net/economics/content/topics/elasticity/cross_elasticity.htm
4. http://ingrimayne.com/econ/elasticity/OtherElast.html
5. http://64.233.167.104/search?q=cache:d3mTcOSVtLIJ:instruct1.cit.cornell.edu/courses/econ101jpw/slides/elasticity.ppt+cross+price+elasticity&hl=en&ct=clnk&cd=17&gl=us