Question

A consumer buys 2,000 units of a good at a price of Rs. 10/- per unit. When the price falls he buys 2,500 units. If price elasticity of demand is -2, what is the new price?

Answer 1

Given:

• A consumer buys 2,000 units of a good at Rs 10 per unit.
• A consumer buys 2,500 units of a good at a lesser price.
• The elasticity of demand is -2.

To find: The new price.

Answer:

The formula to calculate the elasticity of demand is as follows:

$\sf E_d\ =\ -\ \dfrac{\Delta\ Q}{\Delta\ P}\ \times\ \dfrac{P}{Q}$

where,

$\bullet\ \sf E_d\ =\ Elasticity\\\\\bullet\ \sf \Delta\ Q\ =\ Change\ in\ quantity\ demanded\\\\\bullet\ \sf \Delta\ P\ =\ Change\ in\ price\\\\\bullet\ \sf Q\ =\ Original\ quantity\ demanded\\\\\bullet\ \sf P\ =\ Original\ price$

As per the question, we have:

$\bullet\ \sf E_d\ =\ -2\\\\\bullet\ \sf \Delta\ Q\ =\ 2,000\ -\ 2,500\ =\ -500\\\\\bullet\ \sf \Delta\ P\ =\ Change\ in\ price\\\\\bullet\ \sf Q\ =\ 2,000\\\\\bullet\ \sf P\ =\ 10$

Substituting them in the formula,

$\sf -2\ =\ \dfrac{-500}{\Delta\ P}\ \times\ \dfrac{10}{2,000}\\\\\\-2\ =\ \dfrac{-500}{\Delta\ P}\ \times\ \dfrac{1}{200}\\\\\\-2\ =\ \dfrac{-5}{\Delta\ P}\ \times\ \dfrac{1}{2}\\\\\\\Delta\ P\ =\ \dfrac{-5}{-2}\ \times\ \dfrac{1}{2}\\\\\\\Delta\ P\ =\ \dfrac{5}{4}$

We have the change in price.

We know that ΔP = New price - Original price.

$\sf \dfrac{5}{4}\ =\ New\ price\ -\ 10\\\\\\\dfrac{5}{4}\ +\ 10\ =\ New\ price\\\\\\11.25\ =\ New\ price$

Therefore, the new price is Rs 11.25.