Question

What is the formula for the cross-price elasticity of demand?

Short answer

The formula for the cross-price elasticity of demand (CPED) is given by \(E_{AB} = \frac{\Delta Q_A}{\Delta P_B} \cdot \frac{P_B}{Q_A}\), where \(E_{AB}\) represents the cross-price elasticity between Good A and Good B, \(\Delta Q_A\) is the change in quantity demanded of Good A, \(Q_A\) is the initial quantity demanded of Good A, \(\Delta P_B\) is the change in price of Good B, and \(P_B\) is the initial price of Good B.

Step-by-step solution

Definition of Cross-Price Elasticity of Demand

The cross-price elasticity of demand (CPED) is a measure that calculates the percentage change in the quantity demanded of one good (Good A) in response to a percentage change in the price of another good (Good B). It is represented by the symbol: \(E_{AB}\)

Formula for Cross-Price Elasticity of Demand

The formula for Cross-Price Elasticity of Demand is as follows: \[E_{AB} = \frac{\% \text{ change in quantity demanded of Good A}}{\% \text{ change in price of Good B}}\]

Representation in terms of quantity and price

To express the formula entirely in terms of quantity and price, we can use the following formula: \[E_{AB} = \frac{(\Delta Q_A / Q_A)}{(\Delta P_B / P_B)}\] Where: - \(E_{AB}\) is the cross-price elasticity of demand between Good A and Good B. - \(\Delta Q_A\) is the change in quantity demanded of Good A. - \(Q_A\) is the initial quantity demanded of Good A. - \(\Delta P_B\) is the change in price of Good B. - \(P_B\) is the initial price of Good B.

Simplifying the formula

To simplify the formula, multiply both the numerator and the denominator by \(Q_A\) and \(P_B\). This gives us: \[E_{AB} = \frac{\Delta Q_A}{\Delta P_B} \cdot \frac{P_B}{Q_A}\] Now, we have the formula for the cross-price elasticity of demand expressed in terms of the changes in quantity and price of both goods.