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The Cross-Price Elasticity of Demand measures the rate of response of quantity demanded of one good, due to a cost change of another good. If two goods are substitutes, we should expect to see consumers purchase more of one good when the price of its substitute increases. Similarly if the two goods are complements, we should see a expense rise in one good cause the demand in spite of both goods to cataract. Your course may despise the more complicated Arc Cross-Price Elasticity of Demand formula. If so you’ll need to see the article on Arc Elasticity. The common formula for the Cross-Price Elasticity of Demand (CPEoD) is given by:

CPEoD = (% Change in Quantity Demand for Good X)/(% Change in Price for Good Y)

Calculating the Cross-Price Elasticity of Demand You’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 get QDemand(OLD)=150 and QDemand(NEW)=190. You should suffer with these four figures written down:

Price(OLD)=9
Price(NEW)=10
QDemand(OLD)=150
QDemand(NEW)=190

To calculate the cross-price elasticity, we need to calculate the percentage variety in quantity demanded and the percentage change in premium. We’ll gauge these one at a time. Calculating the Percentage Change in Quantity Demanded of Good X The formula used to add up the percentage modification 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 part terms this would be 26.67%). Calculating the Percentage Change in Price of Good Y The formula used to calculate the percentage change in price is:

[Price(NEW) - Price(OLD)] / Price(OLD)

We make full 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 contriving the cross-price elasticity of demand.

Final Step of Calculating the Cross-Price Elasticity of Demand We articulate 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 planned earlier.

CPEoD = (0.2667)/(0.1111) = 2.4005

We conclude that the cross-price elasticity of demand for X when the valuation 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 popular 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 penalty of one good goes up, the demand for the other good goes up as well. A negative tells us just the opposite, that an growing in the price of bromide good causes a let go in the demand for the other good. A mini value (either antipathetic 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 be to blame for 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 In the happening of our good, we calculated the cross-price elasticity of demand to be 2.4005, so our two goods are substitutes when the price of good Y is between $9 and $10.

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