Wize AP Microeconomics Textbook > Elasticity

Cross Price Elasticity

Popular Courses

AP Exam Prep

0:00 / 0:00

Cross Price Elasticity of Demand

Cross price elasticity of demand tells us if two products are complements, substitutes or unrelated.

Cross Price Elasticity of Demand= %ΔQx%ΔPy = ΔQxΔPy⋅PyQx\boxed{\text{Cross\ Price\ Elasticity\ of\ Demand} =\ \frac{\%ΔQx}{\%ΔPy}\ =\ \frac{ΔQx}{ΔPy}\cdot\frac{Py}{Qx}}Cross Price Elasticity of Demand= %ΔPy%ΔQx​ = ΔPyΔQx​⋅QxPy​​

Substitutes and Complements
Substitutes: Cross price elasticity of demand is positive (>0)

Example: Coke and Pepsi. If the price of Pepsi increases, the demand for Coke will increase (positive relationship).

Complements: Cross price elasticity of demand is negative (<0) 

Example: Cars and gas. If the price of cars increase, the demand for gas will decrease (negative relationship).

Unrelated Products: Cross price elasticity of demand is equal to zero.

Example: Cars and oranges. If the price of cars increase, it will have no effect on the demand for oranges (no relationship).

0:00 / 0:00

Example: Cross Price Elasticity of Demand
The table below shows information about lemonade and cola:
  
a) What is the arc cross price elasticity of demand for lemonade with respect to the price of cola?

Arc Cross Price Elasticity of Demand= Average %ΔQxAverage %ΔPy\text{Arc Cross Price Elasticity of Demand}=\ \frac{Average\ \%ΔQx}{Average\ \%ΔPy}Arc Cross Price Elasticity of Demand= Average %ΔPyAverage %ΔQx​

The table only gives us quantity of lemonade so that means lemonade it good X and cola is good Y.

The price of cola only changes from 2015 to 2016 so those are the only two years we will look at.

Average % ΔQx (lemonade)=(New−Old)Average⋅100 = (25000−15000)20000⋅100 = 50%Average\ \%\ ΔQx\ \left(lemonade\right)=\frac{\left(New-Old\right)}{Average}\cdot100\ =\ \frac{\left(25000-15000\right)}{20000}\cdot100\ =\ 50\%Average % ΔQx (lemonade)=Average(New−Old)​⋅100 = 20000(25000−15000)​⋅100 = 50%

Average % ΔP (Cola)=(New−Old)Average⋅100 = (1.4−1)1.2⋅100 = 33.33%Average\ \%\ ΔP\ \left(Cola\right)=\frac{\left(New-Old\right)}{Average}\cdot100\ =\ \frac{\left(1.4-1\right)}{1.2}\cdot100\ =\ 33.33\%Average % ΔP (Cola)=Average(New−Old)​⋅100 = 1.2(1.4−1)​⋅100 = 33.33%

Arc Cross Price Elasticity of Demand= Average % ΔQxAverage % ΔPy= 50%33.33%=1.5\text{Arc Cross Price Elasticity of Demand}=\ \frac{Average\ \%\ ΔQx}{Average\ \%\ ΔPy}=\ \frac{50\%}{33.33\%}=1.5Arc Cross Price Elasticity of Demand= Average % ΔPyAverage % ΔQx​= 33.33%50%​=1.5

This means cola and lemonade are substitutes because the cross price elasticity is positive.

Practice: Cross Price Elasticity of Demand
The price of peaches at a market rises from $3.95 to $4.05 per kilo, and as a result the quantity of plums that consumers purchase increases from  4950 to 5050 kilos per week. The arc cross-price elasticity is