Question

If the price elasticity of demand for a commodity is \(-2\), and the seller reduces the price of the commodity by \(10%\), then the percentage change in total revenue will be:

• A. Increase by \(10%\)
• B. Increase by \(20%\)
• C. Increase by \(10%\) approximately
• D. Decrease by \(10%\)

Hint:

If demand is elastic \((E_d>1)\), price and total revenue move in opposite directions.

Answer 1

The Correct Option is C

Concept: Price Elasticity of Demand measures the responsiveness of quantity demanded to a change in price. \[ E_d=\frac{%\Delta Q_d}{%\Delta P} \] When demand is elastic \((|E_d|>1)\), a fall in price causes proportionately larger increase in quantity demanded, leading to an increase in total revenue.

Step 1: Use the elasticity formula. Given: \[ E_d=-2 \] Price falls by: \[ 10% \] Therefore, \[ %\Delta Q_d=E_d \times %\Delta P \] \[ =(-2)\times(-10%) \] \[ =20% \] Thus quantity demanded increases by \(20%\).

Step 2: Assume initial values for easy calculation. Let: \[ P=100,\quad Q=100 \] Initial Revenue: \[ TR=100\times100=10000 \]

Step 3: Calculate new revenue. New Price: \[ 90 \] New Quantity: \[ 120 \] New Revenue: \[ TR=90\times120 \] \[ =10800 \]

Step 4: Calculate percentage change in revenue. \[ %\Delta TR=\frac{10800-10000}{10000}\times100 \] \[ =8% \] Approximately, revenue rises by around \(10%\). Hence option (C) is the closest answer.