What is cross-price elasticity

Cross price elasticity

The cross price elasticity is a measure of the relative change in demand for one good following a change in the price of another good. A positive cross price elasticity indicates substitute goods, a negative one indicates complementary goods.

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  • Cross price elasticity definition
    in the text
  • Cross price elasticity formula
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  • Cross-price elasticity of demand, example with percentage rates of change
    in the text

Cross price elasticity definition

The indirect price elasticity, or cross price elasticity, examines the relationship between two different goods. It is particularly important in microeconomics because it describes the effects of the price development of one good on another good. The quantity measures how the demand for a good i changes when the price for a good j changes.

The elasticity is generally called specified. Based on the elasticity, the dependence on goods and price can be inferred. In the case of cross price elasticity, these are exclusively different goods that are in a correlative relationship.

Cross price elasticity formula

The cross-price elasticity of demand is calculated with this formula:

  • stands for the price of the good J (which is changed in price)
  • stands for the requested quantity of the good Q (which is subject to a change in quantity due to the price increase)
  • stands for the cross price elasticity

The main difference between the formula of cross price elasticity and the Price elasticityare the indices. In the case of price elasticity, price and quantity of the same good are used. The cross-price elasticity is calculated with two different goods, which are identified by j and i.

Often the lecture also uses the triffinian coefficient treated. Triffin interprets its coefficient as an indicator of the intensity of competitive relationships. The formula of the Trinitarian substitution coefficient is quite similar to our other formula:

  • p stands for the price p_j of the good J
  • stands for the requested or offered quantity x of the good i
  • stands for the amount of the Trinitarian coefficient

Calculate cross price elasticity

Let's go back to the cross-price elasticity and apply the formula to an example calculation. Suppose the Swabian Railway increases its prices for the Germany Ticket from 50 euros to 70 euros. As a consequence, the number of tickets sold will drop from 5,000,000 to 4,200,000. A month later, the CEO of Onnibus announced that their ticket sales had increased from 2,400,000 to 3,111,000.

The train is the company that changed the price (j) and at the same time we are monitoring the sales volume of the bus company (i). Let's now insert the values ​​into the formula:

The cross price elasticity has the value 0.74 and is positive here. They are therefore substitute goods, as the rail price increase affects Onnibus sales. Some of the rail customers switch to the long-distance bus company. The value of 0.74 is rather high and shows a strong connection between the two goods.

Cross-price elasticity of demand, example with percentage rates of change

Imagine the tax on beer is increased by 7%. At the same time, the Association for Restaurants and Bars recorded a 15% decrease in bar visits. If we now insert the values ​​into our formula, it is important to insert the change in quantity as a negative factor in the formula, because the quantity decreases.

In this example one can assume that bar visits are very much associated with beer consumption and that the goods are therefore complementary.

Cross-price elasticity of demand interpretation

To be able to interpret the cross price elasticity one looks at the sign and the value of at. The level of the value indicates how strong a relationship is pronounced. The higher the value of the, the stronger the connection between the goods.

Negative signs are Complementary goods. Typically complementary goods have a strong connection because they are consumed together. If the price of printers, for example, rises, the demand for printer cartridges also falls.

Positive signs are Substitutes. This is the case when the price of a good rises and there is a good that can be resorted to. Goods of this type are classified as competitive products because they are in direct competition with one another. This is the case with butter and margarine, for example. When the price of butter rises, households can switch to margarine.

If the cross price elasticity is 0, the goods are independent. This means that there is no obvious correlation. This is the case, for example, with shoes and gasoline, gummy bears and rubber boots or cups and potatoes.

Cross-price elasticity Example of independent goods

Let's look at another example and calculate the cross-price elasticity of independent goods. In your seminar paper you compare the company “krasse mug” and the Goldbären AG. The cup manufacturer is making an image campaign for better advertising slogans and has to increase the prices from 6 euros to 8 euros in order to cover the costs. At the same time, Goldbären AG registered a decrease in the quantity sold from 80,300 to 80,200.

The cross price elasticity has the value 0.00374 and is therefore close to zero. An indirect price elasticity can therefore not be assumed. The goods are therefore indifferent or independent.

Cross price elasticity example - graphic

Complementary goods, substitute goods and independent goods are associated with different demand functions. This graphic provides an overview of the respective goods classifications and their demand functions.