Question

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

Short answer

The formula for the cross-price elasticity of demand is: \( ED = \cfrac {(Q1_f - Q1_i) \cdot(P2_f - P2_i)}{Q1_i\cdot P2_i} \)

Step-by-step solution

Understanding the Cross-Price Elasticity of Demand Formula Components

The cross-price elasticity of demand formula consists of three primary components: 1. The percentage change in the quantity demanded of Good 1 2. The percentage change in the price of Good 2 3. The cross-price elasticity of demand coefficient (ED)

Derive the Formula

To derive the formula for the cross-price elasticity of demand, divide the percentage change in the quantity demanded of Good 1 by the percentage change in the price of Good 2: \( ED = \frac {(\% \: Change \: in \: Quantity \: Demanded \: of \: Good\: 1)}{(\% \: Change\: in \: Price \: of\: Good\: 2)} \)

Calculate the Percentage Changes using Differences

Replace the percentage change in quantity demanded of Good 1 and the percentage change in the price of Good 2 with their respective differences: \(ED = \cfrac {(Q1_f - Q1_i) / Q1_i}{(P2_f - P2_i) / P2_i } \) Where: - \(Q1_i\) is the initial quantity demanded of Good 1 - \(Q1_f\) is the final quantity demanded of Good 1 - \(P2_i\) is the initial price of Good 2 - \(P2_f\) is the final price of Good 2

Cross Multiply

Cross multiply the equation to get rid of the division: \( ED(Q1_i)\cdot(P2_i) = (Q1_f - Q1_i) \cdot(P2_f - P2_i) \)

Solve for the Cross-Price Elasticity of Demand Coefficient (ED)

Finally, solve for the cross-price elasticity of demand coefficient (ED): \( ED = \cfrac {(Q1_f - Q1_i) \cdot(P2_f - P2_i)}{Q1_i\cdot P2_i} \) Now we have derived the formula for the cross-price elasticity of demand as follows: \( ED = \cfrac {(Q1_f - Q1_i) \cdot(P2_f - P2_i)}{Q1_i\cdot P2_i} \)