Question

What is the formula for calculating elasticity?

Short answer

The formula for calculating elasticity (E) is: \( E = \dfrac{\Delta Y / Y}{\Delta X / X} \), where \(Y\) is the dependent variable, \(X\) is the independent variable, \(\Delta Y\) represents the change in the dependent variable, and \(\Delta X\) represents the change in the independent variable. This general formula can be adapted for specific types of elasticity such as price elasticity of demand, price elasticity of supply, income elasticity of demand, and cross-price elasticity of demand.

Step-by-step solution

Definition of Elasticity

Elasticity is a measure of how much one variable (typically a dependent variable) changes in response to a change in another variable (typically an independent variable). In economics, it is often used to measure how sensitive the quantity demanded or supplied of a good is to changes in price, income, or the price of other goods.

General Formula for Elasticity

The general formula for calculating elasticity (E) can be expressed as: \( E = \dfrac{\% \text{ change in dependent variable}}{\% \text{ change in independent variable}} \) Or, equivalently: \( E = \dfrac{\text{change in dependent variable} / \text{original dependent variable}}{\text{change in independent variable} / \text{original independent variable}} \) Or, more concisely: \( E = \dfrac{\Delta Y / Y}{\Delta X / X} \) Where: - \(E\) is the elasticity - \(Y\) is the dependent variable (e.g., quantity demanded or supplied) - \(X\) is the independent variable (e.g., price, income, or the price of other goods) - \(\Delta Y\) represents the change in the dependent variable - \(\Delta X\) represents the change in the independent variable

Applying the Formula for Specific Types of Elasticity

The general formula can be adapted for specific types of elasticity: 1. Price elasticity of demand: \(E_d = \dfrac{\Delta Q_d / Q_d}{\Delta P / P}\) 2. Price elasticity of supply: \(E_s = \dfrac{\Delta Q_s / Q_s}{\Delta P / P }\) 3. Income elasticity of demand: \(E_i = \dfrac{\Delta Q_d / Q_d}{\Delta I / I }\) 4. Cross-price elasticity of demand: \(E_{xy} = \dfrac{\Delta Q_x / Q_x}{\Delta P_y / P_y }\) Where: - \(E_d\) is the price elasticity of demand - \(E_s\) is the price elasticity of supply - \(E_i\) is the income elasticity of demand - \(E_{xy}\) is the cross-price elasticity of demand - \(Q_d\) is the quantity demanded - \(Q_s\) is the quantity supplied - \(P\) is the price level - \(I\) is the income - \(Q_x\) is the quantity demanded of good X - \(P_y\) is the price of another good Y