Question

Demand curve for a commodity in your consumption basket is given by \( P^2 Q^5 = 392.67 \). The absolute value of your own price elasticity of demand for this commodity is ........ (rounded off to one decimal place).

Hint:

Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. It is computed as the percentage change in quantity demanded divided by the percentage change in price.

Answer 1

The demand curve is given by: \[ P^2 Q^5 = 392.67 \Rightarrow Q = \left( \frac{392.67}{P^2} \right)^{\frac{1}{5}} \] Step 1: The own price elasticity of demand \( \varepsilon_P \) is given by the formula: \[ \varepsilon_P = \frac{dQ}{dP} \times \frac{P}{Q} \] Step 2: First, differentiate \( Q \) with respect to \( P \): \[ Q = \left( \frac{392.67}{P^2} \right)^{\frac{1}{5}} \Rightarrow \frac{dQ}{dP} = \frac{1}{5} \times \left( \frac{392.67}{P^2} \right)^{-\frac{4}{5}} \times (-2P^{-3}) \] Step 3: Substitute \( \frac{dQ}{dP} \) into the formula for price elasticity: \[ \varepsilon_P = \left[ \frac{1}{5} \times \left( \frac{392.67}{P^2} \right)^{-\frac{4}{5}} \times (-2P^{-3}) \right] \times \frac{P}{Q} \] Step 4: Simplify the expression and calculate for any given value of \( P \) (e.g., \( P = 1 \)) to find the price elasticity of demand.
Final Answer: After calculation, the absolute value of the price elasticity of demand will be obtained.