Cross elasticity of demand (XED)

XED measures the effect of a change in the price of one good (good X) on consumer demand for another good (good Y). XED can be calculated by using the following formula:

Examples

The following table is a demand schedule showing how demand for good Y responds to different prices of good X.

If we apply the formula to a specific price change 10 to 12. We can calculate the XED result (co-efficient).

In this case, there is a negative relationship, which signifies that two goods are complementary goods.

The fact that XED is less than 1 (at 0.5) means that they are closely related to each other. The higher the co-efficient the more complementary the products are. In the real world there will be many example of complementary products, including breakfast cereal and milk, air flights and hotels, and smartphones and apps.

Alternatively, goods may be related in terms of being substitutes for each other. Again, there will be many examples of this in the real world. Consumer the following schedule for substitute goods.

In the case of substitutes the cross elasticity will be positive - as the price of one substitute rise, demand for the other also rises. Over the price range 10 to 12 for good X, demand for Y rises from 15 units to 20 units. The XED value is:

In this case, the positive sign indicates the goods are substitutes, and the value of 1.67 is greater than one, suggesting that they are fairly close substitutes.

As an example, we can consider research on smokers from New Zealand who looked to establish how closely demand for e-cigarettes was affected by the price of tobacco cigarettes. Researchers estimated that the cross-price elasticity for e-cigarettes was (+) 0.16, indicating that e-cigarettes were only partially substitutable for regular cigarettes.

The significance of cross elasticity of demand

Given that most firms sell goods and services which have both complements and substitutes it is unsurprising that firms conduct research into various cross elasticities.

The ultimate aim of this research is to gather data that will enable them to make rational decisions about their prices, and other policies that they may adopt to either increase revenue and profits, or to make strategic discussions.

For example, data on cross elasticities indicates the relative 'strength' or closeness of substitutes as well as the significance of complements. Firms are ultimately vulnerable to the policies of other firms, especially when they operate in oligopolistic markets.

For example, airlines are vulnerable both to an increase in the price of aviation fuel, and to reductions in the ticket prices of a rival airline. This can inform other decisions, such as stockpiling fuel reserves and merging or forming an alliance with rival airlines.

Hence, if a firm can map out the cross elasticities of firms in its market it can reduce information failure and take steps to minimise risks associated with the decisions of other firms, including decisions on pricing.

Questions

Read the questions and complete an answer before revealing if you are correct:

Q1. The price of an Audi A3 in the UK increases from £35,000 to £36,750, and during the next 6 months the demand for Mercedes 'A' class cars rises from 55,000 to 56,000. What is the cross elasticity of demand between the two cars, assuming no other information? Q2. The annual motor insurance premium (price) for a Mercedes A Class increases from £1200 a year to £1,320. Within six month, demand for the Mercedes had fallen from 56,000 to 55,720. What is the cross elasticity of demand for Mercedes with respect to motor insurance, assuming no other information? Q3. Audi decides to reduce the price of its Q5 in the UK by £2,200, from its original price of £55,000. 3 months later Range Rover noticed that its sales had fallen from 44,000 to 42,560. What is the best estimate of cross elasticity, assuming no other information?

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