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In economics, the cross elasticity of demand or cross-price elasticity of demand measures the percentage change of the quantity demanded for a good to the percentage change in the price of another good, ceteris paribus^[1]. In real life, the quantity demanded of good is dependent on not only its own price but also the price of other "related" products. $Cross-price\,Elasticity\,Of\,Demand={\frac {\%change\ in\,Quantity\,Demand\,of\,good\,A}{\%change\ in\,Price\,of\,good\,B}}$ The concept is used to identify whether good B are complements or substitutes of good A, so it helps businesses group products that are likely to support or compete with them. The magnitude of the elasticity indicates the degree to which the good B is substitutable or complementary to good A.

A negative cross elasticity denotes two products that are complements, while a positive cross elasticity denotes two substitute products. If products A and B are complements, an increase in the price of B leads to a decrease in the quantity demanded for A, as A is used in conjunction with B^[2]. Equivalently, if the price of product B decreases, the demand curve for product A shifts to the right reflecting an increase in A's demand, resulting in a negative value for the cross elasticity of demand. If A and B are substitutes, an inclination in the price of B will increase the market demand for A, as customers would easily replacing B with A^[3], like McDonald's and Domino's Pizza.

For example, in response to a 10% increase in the price of printer's ink, the demand for printer would decreased by 20%, so the cross elasticity of demand would be: ${\frac {-20\%}{10\%}}=-2$ , which means an increase in the price of ink will decrease the demand for printer, so printer and ink are complements.

Results for main types of goods

In the example above, the two goods, ink and printers (consists of fuel consumption), are complements; that is, one is used with the other. In these cases the cross elasticity of demand will be negative, as shown by the decrease in demand for cars when the price for fuel will rise. In the case of perfect substitutes, the cross elasticity of demand is equal to positive infinity (at the point when both goods can be consumed). Where the two goods are independent, or, as described in consumer theory, if a good is independent in demand then the demand of that good is independent of the quantity consumed of all other goods available to the consumer, the cross elasticity of demand will be zero i.e. if the price of one good changes, there will be no change in demand for the other good.

When goods are substitutable, the diversion ratio, which quantifies how much of the displaced demand for product j switches to product i, is measured by the ratio of the cross-elasticity to the own-elasticity multiplied by the ratio of product i's demand to product j's demand. In the discrete case, the diversion ratio is naturally interpreted as the fraction of product j demand which treats product i as a second choice,^[4]^[5] measuring how much of the demand diverting from product j because of a price increase is diverted to product i can be written as the product of the ratio of the cross-elasticity to the own-elasticity and the ratio of the demand for product i to the demand for product j. In some cases, it has a natural interpretation as the proportion of people buying product j who would consider product i their "second choice".

Approximate estimates of the cross price elasticities of preference-independent bundles of goods (e.g. food and education, healthcare and clothing, etc.) can be calculated from the income elasticities of demand and market shares of individual bundles, using established models of demand based on a differential approach.^[6]

Selected cross price elasticities of demand

Below are some examples of the cross-price elasticity of demand (XED) for various goods:^[7]

Good	Good with Price Change	XED
Butter	Margarine	+0.81
Beef	Pork	+0.28
Entertainment	Food	-0.72

Notes

^ "OECD Glossary of Statistical Terms - Cross price elasticity of demand Definition". stats.oecd.org. Retrieved 2021-04-17.
^ Hemmati, M.; Fatemi Ghomi, S.M.T.; Sajadieh, Mohsen S. (2017-09-04). "Inventory of complementary products with stock dependent demand under vendor managed inventory with consignment policy". Scientia Iranica. 0 (0): 0–0. doi:10.24200/sci.2017.4457. ISSN 2345-3605.
^ Das, R. L.; Jana, R. K. (2019-09-01), "Some Studies on EPQ Model of Substitutable Products Under Imprecise Environment", Asset Analytics, Singapore: Springer Singapore, pp. 331–360, ISBN 978-981-13-9697-7, retrieved 2021-04-17
^ Bordley, R., "Relating Elasticities to Changes in Demand", Journal of Business and Economic Statistics, Vol.3, No. 2, p.156-158 (1985), https://www.jstor.org/stable/1391869
^ Capps, O. and Dharmasena, S., "Enhancing the Teaching of Product Substitutes/Complements: A Pedagogical Note on Diversion Ratios",Applied Economics Teaching Resources, Vol. 1, Issue 1, p.32-45, (2019), https://www.aaea.org/UserFiles/file/AETR_2019_001ProofFinal_v1.pdf
^ Sabatelli L (2016) Relationship between the Uncompensated Price Elasticity and the Income Elasticity of Demand under Conditions of Additive Preferences. PLoS ONE11(3): e0151390. https://doi.org/10.1371/journal.pone.0151390
^ Frank (2008) p.186.

References

Frank, Robert (2008). Microeconomics and Behavior (7th ed.). McGraw-Hill. ISBN 978-0-07-126349-8.

External links

Database for Commodity Elasticity at Food and Agricultural Policy Research Institute, University of Iowa

[1] "OECD Glossary of Statistical Terms - Cross price elasticity of demand Definition". stats.oecd.org. Retrieved 2021-04-17.

[2] Hemmati, M.; Fatemi Ghomi, S.M.T.; Sajadieh, Mohsen S. (2017-09-04). "Inventory of complementary products with stock dependent demand under vendor managed inventory with consignment policy". Scientia Iranica. 0 (0): 0–0. doi:10.24200/sci.2017.4457. ISSN 2345-3605.

[3] Das, R. L.; Jana, R. K. (2019-09-01), "Some Studies on EPQ Model of Substitutable Products Under Imprecise Environment", Asset Analytics, Singapore: Springer Singapore, pp. 331–360, ISBN 978-981-13-9697-7, retrieved 2021-04-17

[4] Bordley, R., "Relating Elasticities to Changes in Demand", Journal of Business and Economic Statistics, Vol.3, No. 2, p.156-158 (1985), https://www.jstor.org/stable/1391869

[5] Capps, O. and Dharmasena, S., "Enhancing the Teaching of Product Substitutes/Complements: A Pedagogical Note on Diversion Ratios",Applied Economics Teaching Resources, Vol. 1, Issue 1, p.32-45, (2019), https://www.aaea.org/UserFiles/file/AETR_2019_001ProofFinal_v1.pdf

[6] Sabatelli L (2016) Relationship between the Uncompensated Price Elasticity and the Income Elasticity of Demand under Conditions of Additive Preferences. PLoS ONE11(3): e0151390. https://doi.org/10.1371/journal.pone.0151390

[7] Frank (2008) p.186.

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 {{Economics sidebar}}
-In [[economics]], the '''cross elasticity of demand''' or '''cross-price elasticity of demand''' measures the responsiveness of the quantity demanded for a [[Good (economics)|good]] to a change in the [[price]] of another good, [[ceteris paribus]]. It is measured as the [[percentage change]] in quantity demanded for the first good that occurs in response to a percentage change in price of the second good.  For example, if, in response to a 10% increase in the price of fuel, the demand for new cars that are fuel inefficient decreased by 20%, the cross elasticity of demand would be: <math>\frac{-20 \%}{10 \%}=-2</math>. An increase in the price of fuel will decrease demand for cars that are not fuel efficient.
+In [[economics]], the '''cross elasticity of demand''' or '''cross-price elasticity of demand''' measures the percentage change of the quantity demanded for a [[Good (economics)|good]] to the percentage change in the [[price]] of another good, [[ceteris paribus]]<ref>{{Cite web|title=OECD Glossary of Statistical Terms - Cross price elasticity of demand Definition|url=https://stats.oecd.org/glossary/detail.asp?ID=3185|access-date=2021-04-17|website=stats.oecd.org}}</ref>. In real life, the quantity demanded of good  is dependent on not only its own price but also the price of other "related" products. <math display="block">Cross-price\, Elasticity\, Of\, Demand
+=
+\frac{% change\ in\,  Quantity\, Demand\, of\, good\,A}{% change\ in\,  Price\, of\, good\,B}</math>The concept is used to identify whether good B are [[Complementary good|complement]]<nowiki/>s or [[Substitute good|substitute]]<nowiki/>s of good A, so it helps businesses group products that are likely to support or compete with them. The magnitude of the elasticity indicates the degree to which the good B is substitutable or complementary to good A.
-A negative cross elasticity denotes two products that are [[complementary good|complements]], while a positive cross elasticity denotes two [[substitute good|substitute]] products. For example, if products A and B are ''complements'', an increase in the price of B leads to a decrease in the quantity demanded for A. Equivalently, if the price of product B decreases, the demand curve for product A shifts to the right reflecting an increase in A's demand, resulting in a ''negative'' value for the cross elasticity of demand. The exact opposite reasoning holds for substitutes.
+A negative cross elasticity denotes two products that are complements, while a positive cross elasticity denotes two substitute products. If products A and B are ''complements,'' an increase in the price of B leads to a decrease in the quantity demanded for A, as A is used in conjunction with B<ref>{{Cite journal|last=Hemmati|first=M.|last2=Fatemi Ghomi|first2=S.M.T.|last3=Sajadieh|first3=Mohsen S.|date=2017-09-04|title=Inventory of complementary products with stock dependent demand under vendor managed inventory with consignment policy|url=http://dx.doi.org/10.24200/sci.2017.4457|journal=Scientia Iranica|volume=0|issue=0|pages=0–0|doi=10.24200/sci.2017.4457|issn=2345-3605}}</ref>. Equivalently, if the price of product B decreases, the demand curve for product A shifts to the right reflecting an increase in A's demand, resulting in a ''negative'' value for the cross elasticity of demand. If A and B are substitutes, an inclination in the price of B will increase the market demand for A, as customers would easily replacing B with A<ref>{{Citation|last=Das|first=R. L.|title=Some Studies on EPQ Model of Substitutable Products Under Imprecise Environment|date=2019-09-01|url=http://dx.doi.org/10.1007/978-981-13-9698-4_18|work=Asset Analytics|pages=331–360|place=Singapore|publisher=Springer Singapore|isbn=978-981-13-9697-7|access-date=2021-04-17|last2=Jana|first2=R. K.}}</ref>, like McDonald's and Domino's Pizza.
+For example, in response to a 10% increase in the price of printer's ink, the demand for printer would decreased by 20%, so the cross elasticity of demand would be: <math>\frac{-20 \%}{10 \%}=-2</math>, which means an increase in the price of ink will decrease the demand for printer, so printer and ink are complements.
 ==Results for main types of goods==
-In the example above, the two goods, fuel and cars (consists of fuel consumption), are ''[[complement good|complements]]''; that is, one is used with the other. In these cases the cross elasticity of demand will be ''negative'', as shown by the decrease in demand for cars when the price for fuel will rise. In the case of perfect substitutes, the cross elasticity of demand is equal to positive infinity (at the point when both goods can be consumed). Where the two goods are ''[[Independent goods|independent]]'', or, as described in [[consumer theory]], if a good is independent in demand then the demand of that good is independent of the quantity consumed of all other goods available to the consumer, the cross elasticity of demand will be ''zero'' i.e. if the price of one good changes, there will be no change in demand for the other good.
+In the example above, the two goods, ink and printers (consists of fuel consumption), are ''[[complement good|complements]]''; that is, one is used with the other. In these cases the cross elasticity of demand will be ''negative'', as shown by the decrease in demand for cars when the price for fuel will rise. In the case of perfect substitutes, the cross elasticity of demand is equal to positive infinity (at the point when both goods can be consumed). Where the two goods are ''[[Independent goods|independent]]'', or, as described in [[consumer theory]], if a good is independent in demand then the demand of that good is independent of the quantity consumed of all other goods available to the consumer, the cross elasticity of demand will be ''zero'' i.e. if the price of one good changes, there will be no change in demand for the other good.
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