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# Definition and formula of cross elasticity of demand

## What is cross elasticity of demand?

Cross elasticity of demand is an economic concept that measures the responsiveness of the quantity demanded of one good when the price of another good changes. Also called cross-price elasticity of demand, this measure is calculated by taking the percentage change in the quantity demanded of one good and dividing it by the percentage change in the price of the other good.

Key points to remember

• Cross elasticity of demand is an economic concept that measures the responsiveness of the quantity demanded of one good when the price of another good changes.
• The cross elasticity of demand for substitute goods is always positive because the demand for a good increases when the price of the substitute good increases.
• Alternatively, the cross elasticity of demand for complementary goods is negative.

Cross elasticity of demand

### Cross elasticity demand formula



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begin {aligned} & E_ {xy} = frac { text {Percentage change in quantity of X}} { text {Percent change in price of Y}} & phantom {E_ {xy}} = frac { frac { displaystyle Delta Q_x} { displaystyle Q_x}} { frac { displaystyle Delta P_y} { displaystyle P_y}} & phantom {E_ {xy}} = frac { Delta Q_x} {Q_x} times frac {P_y} { Delta P_y} & phantom {E_ {xy}} = frac { Delta Q_x} { Delta P_y} times frac {P_y} {Q_x} & textbf {where:} & Q_x = text {Quantity of good X} & P_y = text {Price of good Y} & Delta = text {Change} end {aligned}

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## Understanding the cross elasticity of demand

In economics, cross elasticity of demand refers to the sensitivity of demand for one product to changes in the price of another product.

### Substitute products

The cross elasticity of demand for substitute goods is always positive because the demand for a good increases when the price of the substitute good increases. For example, if the price of coffee increases, the quantity demanded for tea (a substitute drink) increases as consumers switch to a cheaper but substitutable alternative. This is reflected in the cross elasticity of the demand formula, as the numerator (percentage change in demand for tea) and denominator (the price of coffee) show positive increases.

Articles with a coefficient of 0 are unrelated articles and are independent goods of each other. Items can be weak substitutes, in which the two products have positive but low cross elasticity of demand. This is often the case for different product substitutes, like tea versus coffee. Items that are strong substitutes have a higher cross elasticity of demand. Consider different brands of tea; an increase in the price of one company’s green tea has a greater impact on another company’s demand for green tea.

Toothpaste is an example of a substitute; if the price of a brand of toothpaste increases, then demand for a competitor’s brand of toothpaste increases.

### Complementary

Alternatively, the cross elasticity of demand for complementary goods is negative. As the price of an item increases, an item that is closely associated with that item and needed for its consumption decreases because the demand for the primary good has also decreased.

For example, if the price of coffee increases, the quantity demanded for coffee sticks drops because consumers drink less coffee and have to buy fewer sticks. In the formula, the numerator (requested quantity of sticks) is negative and the denominator (the price of coffee) is positive. This results in negative cross elasticity.

## Usefulness of cross elasticity of demand

Firms use the cross elasticity of demand to establish the selling prices of their products. Products without substitutes have the ability to be sold at higher prices because there is no cross elasticity of demand to take into account. However, incremental price changes of goods with substitutes are analyzed to determine the appropriate level of desired demand and the associated price of the good.

In addition, complementary products are strategically priced according to the cross elasticity of demand. For example, printers can be sold at a loss, with the understanding that the demand for future complementary products, such as printer ink, is expected to increase.

## What does the cross elasticity of demand measure?

Cross elasticity of demand assesses the relationship between two products when the price of one of them changes. It shows the relative change in demand for one product as the price of the other rises or falls.

## What does a positive cross elasticity of demand indicate?

A positive cross elasticity of demand means that the demand for good A will increase as the price of good B increases. This means that goods A and B are good substitutes. so that if B becomes more expensive, people are happy to switch to A. An example would be the price of milk. If the price of whole milk increases, people can switch to 2% milk. Likewise, if the price of 2% milk increases instead, whole milk becomes more in demand.

## What does negative cross elasticity of demand indicate?

A negative cross elasticity of demand indicates that the demand for good A will decrease as the price of B increases. This suggests that A and B are complementary products, such as printer and printer toner. If the price of the printer goes up, demand goes down. Due to the decrease in the number of printers sold, less toner will also be sold.

## How does cross elasticity of demand differ from elasticity of demand?

Cross elasticity examines the proportional changes in demand between two goods. Elasticity of demand (or price elasticity of demand) itself examines how the demand for a single item changes as its price changes.

## How does cross elasticity of demand differ from cross elasticity of supply?

Contrary to the evolution of the demand for of them goods in response to prices, cross elasticity of supply measures the proportional change in the quantity supplied or produced with respect to changes in the price of a good.

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