Measurement of Price Elasticity of Demand

Measurement of Price Elasticity of Demand

a) The Point Method:

1. \(E_d = -\cfrac{\Delta Q}{\Delta P} \times \cfrac{P}{Q}\) (for a demand schedule)

2. \(E_d = -\cfrac{\delta Q}{\delta P} \times \cfrac{P}{Q}\) (for a demand function with one independent variable)

3. \(E_d = -\cfrac{\partial Q}{\partial P} \times \cfrac{P}{Q}\) (for a demand function with two or more independent variables)

b) The Arc Method:

\(E_d = -\cfrac{\Delta Q}{\Delta P} \times \cfrac{P_1 + P_2}{Q_1 + Q_2}\)

Example:

Given the demand function of a commodity estimated as:

\(Q = 100 – 3P\)

Where unit price \((P) = ₦20\).

Compute the price elasticity of demand and interpret your result.

Solution:

Using the point method for a demand function with one independent variable, we have:

\(E_d = \cfrac{-\delta Q}{\delta P} \times \cfrac{P}{Q}\)

From \(Q = 100 – 3P\), we have

\(\cfrac{\delta Q}{\delta P} = -3\)

Substituting into \(E_d = \cfrac{-\delta Q}{\delta P} \times \cfrac{P}{Q}\), we have

\(E_d = -(-3)\cfrac{P}{Q}\)

When \(P = 20\)

\(Q = 100 – 3(20)\)

\(= 100 – 60\)

\(= 40\)

\(\therefore E_d = -(-3) \times \cfrac{20}{40}\)

\(= \cfrac{60}{40}\)

\(= 1.5\)

Since \(1 < E_d = 1.5 < \infty\), this means that demand is price elastic.