4.4: Cross-price elasticities - cable or satellite

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The price elasticity of demand tells us about consumer responses to price changes in different regions of the demand curve, holding constant all other influences. One of those influences is the price of other goods and services. A cross-price elasticity indicates how demand is influenced by changes in the prices of other products.

The cross-price elasticity of demand is the percentage change in the quantity demanded of a product divided by the percentage change in the price of another.

We write the cross price elasticity of the demand for x due to a change in the price of y as

For example, if the price of cable-supply internet services declines, by how much will the demand for satellite-supply services change? The cross-price elasticity may be positive or negative. These particular goods are clearly substitutable, and this is reflected in a positive value of this cross-price elasticity: The percentage change in satellite subscribers will be negative in response to a decline in the price of cable; a negative divided by a negative is positive. In contrast, a change in the price of tablets or electronic readers should induce an opposing change in the quantity of e-books purchased: Lower tablet prices will induce greater e-book purchases. In this case the price and quantity movements are in opposite directions and the elasticity is therefore negative – the goods are complements.

Application Box 4.1 Cross-price elasticity of demand between legal and illegal marijuana

In November 2016 Canada's Parliamentary Budget Office produced a research paper on the challenges associated with pricing legalized marijuana. They proposed that taxes should be low rather than high on this product, surprising many health advocates. Specifically they argued that the legal price of marijuana should be just fractionally higher than the price in the illegal market. Otherwise marijuana users would avail of the illegal market supply, which is widely available and of high quality. Effectively their research pointed to a very high cross-price elasticity of demand. This recommendation may mean that tax revenue from marijuana sales will be small, but the size of the illegal market will decline substantially, thereby attaining a prime objective of legalization.