# What is Cross Price Elasticity?

Definition: Cross price elasticity measures how a change in the price of one good affects the quantity demanded of another good when these goods are either substitutes or complements.

## What Does Cross Price Elasticity Mean?

What is the definition of cross price elasticity? The quantity demanded of a good in the market depends on its sale price but also on the prices of other goods related to it. When two goods are substitutes, like butter and margarine, when the price of butter increases, the demand for margarine is likely to increase. In this case, butter and margarine have a positive cross price elasticity. When two goods are complements, like gasoline and cars, if the price of gas increases, the demand for cars is likely to decrease. In this case, gasoline and cars have a negative cross price elasticity.

CPE EA,B = [(Qf – Qi)/ (Qf + Qi) / 2] / [(Pf-Pi) / (Pf + Pi) /2 ]

Where,

1. Qf = the final quantity demanded of good A
2. Qi = the initial quantities demanded of good A
3. Pf = the final price of good B
4. Pi = the initial price demanded of good B

Let’s look at an example.

## Example

Mary goes to the grocery shop to buy 3 packs of margarine and 1 pack of butter. Last week, the price of margarine was \$5, and today the price of margarine is \$7. So, Mary decides to buy 4 packs of butter, which sell for less than \$3 each. Because the products are substitutes, the increase in the price of margarine leads to an increase in the quantity demanded for butter.

Assuming that butter is product A and margarine is product B, the CPE for margarine and butter is:

CPE EA,B = [(Qf – Qi)/ (Qf + Qi) / 2] / [(Pf-Pi) / (Pf + Pi) /2 ] = [(4-1)/(4+1)/2] / [(7-5)/(7+5)/2] = (3/2.5)/(2/6) = 1.2/0.33 = 3.64

Then, Mary goes to buy gas. She doesn’t want to use the car so much when doing errands because last week the cost of gas was \$3.5 per gallon, and her tank fills up with 6 gallons. So, she has in mind to put 4 gallons of gas, and leave the car at home for the rest of the day. However, when she arrives at the gas station, she sees that the price of gas dropped to \$3.0. So, Mary decides to fill her tank up and use the car the entire day. Because the products are complements, the decrease in the price of gas leads to an increase in the use of car.

Assuming that car is product A and gas is product B, the cross price elasticity for car and gas is:

CPE EA,B = [(Qf – Qi)/ (Qf + Qi) / 2] / [(Pf-Pi) / (Pf + Pi) /2 ] = [(6-4)/(6+4)/2] / [(3-3.5)/(3+3.5)/2] = (2/5)/(-0.5/3.25) = 0.4/-015 = -2.67

## Summary Definition

Define Cross Price Elasticity: CPE means the degree to which one good’s change in price will affect another good’s demand.

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