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Cross Price Elasticity MICROECONOMICS HERRINGTON

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Cross Price Elasticity Measures how sensitive DEMAND for a commodity is to changes in the price of a substitute or compliment commodity.

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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 price rise in one good cause the demand for both goods to fall.

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

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Calculating the Cross-Price Elasticity of Demand "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."

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

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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.

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Calculating the Percentage Change in Quantity Demanded of Good X The 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%).

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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 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.

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

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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.

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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 case 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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