## Price Elasticity, Income Elasticity and Cross Elasticity

The main objective in this reading is to understand how to calculate and interpret price elasticity, income elasticity, and cross elasticity. This section takes us through how percentage movements are calculated. In almost all the cases, average prices and quantities are used instead of the starting prices and quantities. The main aim is to ensure the percentage movements being calculated are the same. This is regardless of whether the prices and quantities are rising or falling.

Elasticity measures the sensitivity or responsiveness of one variable to another. Elasticity is measured in percentage changes in each of the variables. Thus we calculate elasticity using:

Where %ΔQxd equals the percentage change in quantity demanded and %ΔPx equals the percentage change in price.

%ΔQxd can also be written as ΔQxd / Qxdwhile %ΔPx can also be broken down to ΔPx / Px. Hence elasticity of price can be rewritten as:

## Example

Given the demand function Qxd = 40 – 5Px:

A unit change (an increase) in price will lead to a 5 unit decrease in demand. If, for instance, the price changes to \$1.5, the elasticity or percentage change can be calculated below.

Differentiating the demand function to get the elasticity of demand will give us:

-5. Multiplying the demand elasticity with the ratio of price to quantity will give us: Q = 40 – (5)(1.5) = 32.5.

Hence the elasticity of demand at a price of \$1.5 is:

Basically, the main determinant in the price elasticity is the change in price itself.

## Income Elasticity

The income elasticity is defined as the percentage change in quantity demanded divided by the percentage change in the income of the customers ceteris paribus.

Hence the income elasticity is given by:

The working (calculation) of the income elasticity is similar to price elasticity, however, “own” price elasticity is always negative whereas the income elasticity could either be negative, positive or zero.

When an increase in income leads to an increase in consumption/quantity demanded, there is positive income elasticity while negative elasticity means that a reduction in income leads to an increase in quantity demanded. Examples of goods possessing positive income elasticity are normal goods while negative income elasticity goods are inferior goods.

Holding every other factor constant, the main determinant of income elasticity is the income of the consumers.

## Cross-price Elasticity

Other than the price of a product and the income of the consumers, the price of other products can also affect the demand for a particular product. The cross-price elasticity is defined on this basis. Here we evaluate the effect of the percentage change in the price of other products on the quantity of demand for a particular product. This notion is represented mathematically as:

Where Py  represents the price of other products.

Cross-price elasticity is mostly found in goods with substitutes and complements.

When the price of a good with a close substitute, say detergent, increases, the demand for that particular detergent will likely shift to another brand of detergent. This relationship describes positive cross-price elasticity. Conversely, goods of complement, say cell phones and chargers, have negative cross-price elasticity. In other words, an increase in the price of phones may reduce the quantity demanded of phones; consequently, the quantity demanded of phone chargers will also decline.

calculate and interpret price, income, and cross-price elasticities of demand and describe factors that affect each measure

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