Cross elasticity of demand

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In economics, the cross elasticity of demand or cross price elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in the price of another good.

It is measured as the percentage change in demand 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 quantity of new cars that are fuel inefficient demanded decreased by 20%, the cross elasticity of demand would be -20%/10% = -2.

In the example above, the two goods, fuel and cars, are complements - that is, one is used with the other. In these cases the cross elasticity of demand will be negative. In the case of perfect complements, the cross elasticity of demand is 'negative' infinity.

Where the two goods are substitutes the cross elasticity of demand will be positive, so that as the price of one goes up the quantity demanded of the other will increase. For example, in response to an increase in the price of fuel, the demand for new cars that are fuel efficient hybrids for example will also rise. In the case of perfect substitutes, the cross elasticity of demand is 'positive' infinity.

Where the two goods are independent, the cross elasticity demand will be zero: as the price of one good changes, there will be no change in quantity demanded of the other good. In case of perfect independence, the cross elasticity of demand is zero.

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 (Bordley, 1986)

Bordley,R (1986). "Relating Cross-Elasticities to First Choice/Second Choice Data." Journal of Business and Economic Statistics. , measuring how much of the demand diverting from project 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.' (Bordley,1986)

Bordley, R. (1986) Relating Cross-Elasticities to First/Second Choice Data." Journal of Business and Economic Statistics.