ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

CROSS ELASTICITY OF DEMAND (CROSS PRICE ELASTICITY OF DEMAND) AND HOW IT IS CALCULATED

Updated on March 4, 2011

When there is a change essentially, in the own price of a commodity; prices of related commodities; and consumer income, quantity demanded responds to these changes. Elasticity of demand is concerned with the degree to which quantity demanded responds to changes in these three factors in particular mentioned above. By means, elasticity of demand has three sub-concepts. These are price elasticity of demand, cross elasticity of demand, and income elasticity of demand. Price elasticity of demand has been explained in my previous article.

By definition, cross price elasticity of demand is the relative responsiveness of quantity demanded of a commodity to changes in the price of a related commodity. Cross elasticity tells us the effect on the quantity demanded of a good, say good i when the price of a related good, say good j is changed, taking goods i and j to be two related goods. It is measured by dividing the percentage change in quantity demanded of good i by the corresponding percentage change in the price of good j.

Cross elasticity may be positive or negative. I t is positive if a rise in the price of good j increases the quantity demanded of good i. Suppose good i is tea and good j is coffee. An increase in the price of coffee may raise the demand for tea. In this case the cross elasticity of tea with respect to coffee is positive. Cross elasticity tends to be positive when two goods are substitutes and negative when two goods are complements or complementary goods.

Taking commodities i and j to be the related commodities, cross elasticity of demand of good i with respect to good j is percentage change in Qi divided by the percentage change in Pj where Pjis price of good j and Qi is quantity demanded of good i. Therefore elasticity of demand of good i with respect to good j is:

Eij = (∆Qi/∆Pj)×(Pj1/Qi1).

Using the idea of arc elasticity, Eij = (∆Qi/∆Pj)×(Pj1 + Pj2)/(Qi1 + Qi2)

where Pj2 and Qi2 are new price for commodity j and new quantity demanded for commodity i respectively.

Qi1 and Pj1 is initial quantity of good i and initial price of good j respectively. ∆Qi and ∆Pj are change in quantity of good i and change in price of good j respectively

An example would clarify how cross elasticity is calculated. Given that quantity demanded of tea is 100 boxes when the price of coffee is $25 per box. Price of tea increases to $30 per bag and quantity demanded of tea increases to 150 boxes. Calculate the elasticity of demand.

It is important to note that the word cross elasticity is note mentioned in the example. The reader ought to note that once two commodities are involved, cross elasticity formula is to be used. Let tea be i and coffee be j. Then using the arc elasticity concept,

Eij = (150 – 100)/(30 – 25)×(25 + 30)/(100 + 150)

= 2.2.

The result shows that tea and coffee are related as substitutes, since the answer is positive. This means increase in the price of coffee leads to increase in quantity demanded of tea and vice versa.

Again, given that price of torchlight is $2.5 and quantity demanded of batteries is 10. Price of torchlight increases to $3.0 and quantity demanded of battery is fall to 8 (we are holding the other uses of battery constant). Calculate the elasticity of demand.

Similarly, let battery be i and torchlight be j then

Eij = (8 – 10)/ (3.0 – 2.5)×(2.5+3.0)/(8+10)

= -1.22.

This result shows that torchlight and battery are related as complements, since the result is negative. Increase in price of torchlight, leads to decrease in quantity demanded of battery.

Comments

    0 of 8192 characters used
    Post Comment

    No comments yet.

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://hubpages.com/privacy-policy#gdpr

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)