Measurement of Cross-Price Elasticity of Demand

Measurement of Cross-Price Elasticity of Demand

a) The Point Method:

vii. \(E_{AB} = \cfrac{\Delta Q_A}{\Delta P_B} \times \cfrac{Q_A}{P_B}\) (for a demand schedule)
viii. \(E_{AB} = \cfrac{\delta Q_A}{\delta P_B} \times \cfrac{Q_A}{P_B}\) (for a demand function with one independent variable)
ix. \(E_{AB} = \cfrac{\partial Q_A}{\partial P_B} \times \cfrac{Q_A}{P_B}\) (for a demand function with two or more independent variables)

b) The Arc Method:

\(E_{AB} = \cfrac{\Delta Q_A}{\Delta P_B} \times \cfrac{P_{B1} + P_{B2}}{Q_{A1} + Q_{A2}}\)

EXAMPLE:

Consider the following data on goods A and B.

Group A		Group B
Price (₦)	Quantity Demanded	Price (₦)	Quantity Demanded
20	300	50	100
30	200	60	80

You are required to:

1. Calculate cross-price elasticity of demand for commodity A with respect to the price of commodity B.

2. State the relationship between commodities A and B using your result (a) above.

SOLUTION:

1. Solution to (a):

\(E_{AB} = \cfrac{\Delta QA}{\Delta PB} \times \cfrac{PB}{QA}\)

\(= -\left[\cfrac{200 - 300}{60 - 50}\right] \times \left[\cfrac{50}{300}\right]\)

\(= \left[\cfrac{100}{10}\right] \times \left[\cfrac{50}{300}\right]\)

\(= \cfrac{-5,000}{3,000}\)

\(= \cfrac{-5}{3}\)

\(= -1.67\)

2. The E_AB being –1.67 (negative cross-price elasticity) implies that commodities A and B are complementary goods.