CPEoD = (% Change in Quantity Demand for Good X)/(% Change in Price for Good Y)
Calculating the Cross-Price Elasticity of DemandYou're given the question: "With the following data, calculate the cross-price elasticity of demand for good X when the price of good Y changes from $9.00 to $10.00." Using the chart on the bottom of the page, we'll answer this question.
We know that the original price of Y is $9 and the new price of Y is $10, so we have Price(OLD)=$9 and Price(NEW)=$10. From the chart we see that the quantity demanded of X when the price of Y is $9 is 150 and when the price is $10 is 190. Since we're going from $9 to $10, we have QDemand(OLD)=150 and QDemand(NEW)=190. You should have these four figures written down:
To calculate the cross-price elasticity, we need to calculate the percentage change in quantity demanded and the percentage change in price. We'll calculate these one at a time.
Calculating the Percentage Change in Quantity Demanded of Good XThe formula used to calculate the percentage change in quantity demanded is:
[QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)
By filling in the values we wrote down, we get:
[190 - 150] / 150 = (40/150) = 0.2667
So we note that % Change in Quantity Demanded = 0.2667 (This in decimal terms. In percentage terms this would be 26.67%).
Calculating the Percentage Change in Price of Good YThe formula used to calculate the percentage change in price is:
[Price(NEW) - Price(OLD)] / Price(OLD)
We fill in the values and get:
[10 - 9] / 9 = (1/9) = 0.1111
We have our percentage changes, so we can complete the final step of calculating the cross-price elasticity of demand.
Final Step of Calculating the Cross-Price Elasticity of DemandWe go back to our formula of:
CPEoD = (% Change in Quantity Demanded of Good X)/(% Change in Price of Good Y)
We can now get this value by using the figures we calculated earlier.
CPEoD = (0.2667)/(0.1111) = 2.4005
We conclude that the cross-price elasticity of demand for X when the price of Y increases from $9 to $10 is 2.4005.
How Do We Interpret the Cross-Price Elasticity of Demand?The cross-price elasticity of demand is used to see how sensitive the demand for a good is to a price change of another good. A high positive cross-price elasticity tells us that if the price of one good goes up, the demand for the other good goes up as well. A negative tells us just the opposite, that an increase in the price of one good causes a drop in the demand for the other good. A small value (either negative or positive) tells us that there is little relation between the two goods.
Often an assignment or a test will ask you a follow up question such as "Are the two goods complements or substitutes?". To answer that question, you use the following rule of thumb:
- If CPEoD > 0 then the two goods are substitutes
- If CPEoD =0 then the two goods are independent (no relationship between the two goods
- If CPEoD < 0 then the two goods are complements
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