# Elasticity of Demand Formula: Cross, Income and Price Elasticity

#### Cross Elasticity:

The measure of cross elasticity of demand provides a numeric value. It is estimated as a ratio of proportionate (or percentage) change in quantity demanded of good X to the proportionate (or percentage) change in the price of the related good Y. That is —

The proportionate change in quantity demanded is estimated as an abso­lute change in quantity demanded divided by the initial quantity de­manded. Similarly, the proportionate change in price is the absolute change in price divided by the initial price. Thus, the above formula can be written as —

Where Qx is the initial quantity demanded of the product X, ΔQx is the absolute change in the quantity demanded of X, Py is the initial price of the product Y and ÄP is the absolute change in the price of Y. The cross elasticity of demand is denoted by exy. The formula can be re-written as

This formula is used for estimating the cross elasticity of demand. The estimate of elasticity can assume a positive or a negative value depending upon the fact that the two products are substitute or complement to each other respectively.

#### Income Elasticity of Demand:

Income elasticity of demand is defined as a ratio of percentage change in quantity demanded of a product to a percentage change in the consumer’s income. Mathematically, it is calculated as the proportionate (or percent­age) change in quantity demanded of a product divided by the proportion­ate (or percentage) change in the consumer’s income. That is —

Where Q is the quantity demanded, ΔQ is the absolute change in the quantity demanded, Y is the income of the consumer and the ΔY is the absolute change in the consumer’s income.

#### Price Elasticity of Demand:

The price elasticity of demand shows responsiveness or sensitiveness of quantity demanded to a change in its own price. It is measured as a ratio of a relative change in demand to the relative change in the price of the product. In other words, it is a ratio between the proportionate (or percent­age) change in quantity demanded of a commodity to the corresponding proportionate (or percentage) change in its price. Mathematically, it can be written as —

The percentage change in quantity demanded is estimated as an absolute change in quantity demanded divided by the initial quantity demanded; similarly, the proportionate change in price is the absolute change in price divided by the initial price. Thus, the above formula can be written as —

If the original quantity demanded is denoted by Q1, new quantity de­manded by Q2, original price by P1 and the new price by P2, then the above formula can be re-written as —

The above formula (2) is mostly used for estimating price elasticity of demand. 