Cross Elasticity of Demand Definition

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Cross Elasticity of Demand Definition

Cross elasticity of demand refers to an economic concept that usually measures the responsiveness in the demanded quantity of one good when the price of another product changes. Also referred to as the cross-price elasticity of demand, the measurement is calculated by taking the percentage difference in the demanded quantity of one good and then diving it by the percentage difference in the price of another product.

A Little More on What is Cross Elasticity of Demand

Cross elasticity on demand also measures the sensitivity of the demand for a product or service to the variation of the price of a different good or service. As such, the subject seeks to determine how much the consumption of product changes when the value and cost of a different product also changes. For instance, how much increase in the price of vehicles there is when the price of gasoline declines. Or better yet, how much the decrease in the purchase of printers there will be if the price of the printer tub goes up. The cross elasticity of demand can be calculated with any products or services. Below, you’ll learn more about how the relationship between the products impacts whether they are substitutes, complementariness, or independent.

Calculation of cross elasticity

To calculate the cross elasticity, it was evaluated in the following way:

X, Y = Percentage Variation of the quantity demand of X/Percentage variation of the price of product Y.

In arithmetic terms, the following formula will be used:


Qx = amount of x

Qy = amount of y

Px = price of x

Py = price of y

▲ = variation

Substitute Goods

When the cross-elasticity of demand is positive, the product, Y, is substituted for X. In this case, before experiencing an increase in price Y, the quantity demand of X will increase. The above illustration implies that consumers can be a great substitute such that when the price of product Y increases, they reduce the purchasing power of Y to replace them to a more significant purchase amount of X.


Let us look at this example closely: butter can substitute margarine. This is at least for many people. In this instance, if the price of butter goes up, the amount of margarine demanded is expected to increase as well.

Complementary Goods

When the cross-elasticity is negative, the products, as well as services, are complementary. This implies that they are consumed together- for instance, bread and butter.  Because most individuals like to consume the products, they will reduce the purchase of these items thereby reducing the purchase of bread.

Independent goods

When the cross elasticity is zero, the goods, as well as services, are interconnected and independent. That implies that buyers don’t consider these goods as substitutes or complements. Therefore, their demands are independent. Check out this example.

Shoes and milk are goods that satisfy entirely different needs. There’s no expected reaction in the industry of shoes prior to a variation in the milk industry.

References for Cross Elasticity of Demand

Academic Research for Cross Elasticity of Demand

  • Factoring the elasticity of demand in electricity prices, Kirschen, D. S., Strbac, G., Cumperayot, P., & de Paiva Mendes, D. (2000). IEEE Transactions on Power Systems, 15(2), 612-617. This paper analyzes the enormous effects that the market structure of a product can have on the elasticity of the demand for electricity. As such, it was noted that electricity markers are often liberalized. Therefore, consumers are exposed to volatile electricity prices. They may decide to modify the profile of their demand to reduce their elasticity costs. The paper describes how consumer behavior can be manipulated using a matrix of self-and-cross elasticities. That’s how the illustrated elasticities can be taken into consideration especially when scheduling generation as well as setting the price of electricity in a pool based electricity industry. A 26-generator system is used to illustrate these processes.
  • The balance of payments constraint as an explanation of the international growth rate differences, Thirlwall, A. P. (1979). PSL Quarterly Review, 32(128). This paper analyzes the neo-classical approach to why growth rates differ between countries. It also concentrates on the supply side of the economy by utilizing the production function concept. Although this approach is advantageous and fruitful, it barely explains why the growth of factors supplies, as well as productivity, differs between countries. The research paper indicates how closely the growth experience of various countries approximates to the growth rate of exports divided by the income elasticity of demand for imports. Based on certain assumptions, this research can be regarded as a measure of what the author refers to as the balance of payments equilibrium rate.
  • A theory of demand for products distinguished by place of production, Armington, P. S. (1969). Staff Papers, 16(1), 159-178. This study offers theoretical support for some form of research practices that often suggest that the main variation of a certain trade flow between countries is considered as the result of two main elements: would produce if the given supplier country was to retain its share of a market and the gap between actual sales and those that would take place if the market share remained constant. Such practices would include the exchange of forecasting method which in turn would forecast the expansion of various markets.
  • The crosselasticity of demand for national newspaper advertising, Busterna, J. C. (1987). Journalism Quarterly, 64(2-3), 346-351. This paper analyses the fact that several contributors to the trade of scholarly literature have often lamented about the high and developing concentration in the newspaper industry. Yet, there’s still no general agreement about the boundaries of the market in which newspapers operate. Without settling on consistent definition if the existing boundaries, it would not be possible to measure newspaper concentration. This dispute concerns of whether the advertising media and the other co-located newspapers compete with a given newspaper.
  • A complete scheme for computing all direct and cross demand elasticities in a model with many sectors, Frisch, R. (1959). Econometrica: Journal of the Econometric Society, 177-196.  In this paper, researchers establish the fact that it’s easier to obtain estimates for various budget proportions as well as Engel elasticities than for elasticities with respect to the price of products. By making particular wants independence assumptions, the elasticies can be reduced with respect to price. In this chapter of connection, it was discovered that the concept of flexibility of the marginal utility of money is crucial. A system formula that describes these relations is provided. Certain fundamental properties of the relations between marginal as well proper choice fields are also discussed.
  • Estimating the short-run income elasticity of demand for electricity by using cross-sectional categorized data, Hsiao, C., & Mountain, D. (1985). Journal of the American Statistical Association, 80(390), 259-265. This research paper publishes contents of a study that uses the 1980 energy application survey that was conducted by Ontario Hydro to estimate a short-run or demand for electricity model. The two-step inference procedures are created to take account of the unique nature of data in which the income variable is recorded in a categorical form. As such, comparisons of short-run income elasticities with other studies by utilizing the complete information of income variable are made as well.
  • Short-run, long-run and cross elasticities of gasoline demand in Brazil, Alves, D. C., & da Silveira Bueno, R. D. L. (2003). Energy economics, 25(2), 191-199. This paper highlights the basic facts about gasoline market prices and oil-derivative products. Its value if closely related to its function in the value of significant of many countries. And in most cases, it is one of the critical determinants of their balance of payment deficit and fiscal deficit as well as economic growth. Unlike most nations, Brazil has been manufacturing gasoline substitute since 1985. Many studies have tried to approximate the income as well as the price elasticities of the demand for gasoline in various countries.
  • Monopolistic competition and optimum product diversity, Dixit, A. K., & Stiglitz, J. E. (1977). The American Economic Review, 67(3), 297-308. This article capitalizes on the impact of the scale of economies and on whether a market solution will yield the socially optimum kinds as well as quantities of commodities in welfare economics. It also emphasizes on the development of some models to study critical aspects of the relationship between market as well as optimal resource allocations in the presence of some of the markets that have nonconvexities. As such, it was concluded that monopoly power, which is a vital ingredient of nonconvexities markets.
  • The demand for housing: A review of cross-section evidence, De Leeuw, F. (1971). The Review of Economics Statistic, 1-10. This article highlights that past studies of the demand for housing leave a wide margin of uncertainty in regards to the response of housing expenditures to a change of income. Some estimates of the income elasticity of the demand for housing usually range between 0.4 and 2.1. The range is too wide that it complicates the process of drawing quantitative conclusions regarding many housing developments as well as policies.
  • A summary of demand response in electricity markets, Albadi, M. H., & El-Saadany, E. F. (2008). Electric power systems research, 78(11), 1989-1996. In this research paper, a careful analysis of the Demand Response in deregulated electricity markets is presented. The definition, as well as classification of demand response and its potential benefits alongside cost components, are also presented. Besides, common indices used for demand response measurement as well as evaluation are highlighted. Some utility experiences with demand response programs are also given insight.
  • A review of new demand elasticities with special reference to short and long-run effects of price changes, Goodwin, P. B. (1992). Journal of transport economics and policy, 155-169. This literature paper is the second one that gives an in-depth comparison of price elasticities. The review suggests that increases in fuel prices would lead to a short run reduction in traffic as well as consumption because of careful driving practice and differential responses for different journeys. Also, in the long run, the impacts would be increased. It additionally suggested that non-dynamic estimation methods are biased. Therefore, transport prices have broader significant effects and are a more vital lever of transport policy.

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