Question

The demand function is given as \( \log Q = \log A + 0.5 \log P \), where \( Q \) is quantity, \( P \) is the unit price of the good and \( A \) is a positive real number. The own price elasticity of demand is:

• A. Perfectly elastic
• B. Perfectly inelastic
• C. Elastic
• D. Inelastic

Hint:

When the price elasticity of demand is less than 1, the demand is inelastic. This means that price changes have a smaller impact on the quantity demanded.

Answer 1

The Correct Option is D

Step 1: Differentiate the demand function.
The demand function is: \[ \log Q = \log A + 0.5 \log P \] Taking the derivative with respect to \( P \), we get: \[ \frac{dQ}{dP} = 0.5 \cdot \frac{1}{P} \] Now, calculate the price elasticity of demand using the formula: \[ \varepsilon = \frac{dQ}{dP} \cdot \frac{P}{Q} \] Substitute the values: \[ \varepsilon = 0.5 \cdot \frac{P}{Q} \] From the given demand function, we see that the elasticity is less than 1 (because of the 0.5 coefficient), meaning the demand is inelastic. 
Step 2: Analyze the result.
Since the price elasticity of demand is less than 1, it indicates inelastic demand, meaning the quantity demanded is not very responsive to changes in price.