question_answer

When the price of a good rises from Rs. 10 per unit to Rs. 12 per unit, its quantity demanded falls by 20 percent. Calculate its price elasticity of demand. How much would be the percentage change in its quantity demanded, if the price rises from Rs. 10 per unit Rs. 13 per unit?

Answer:

Original Price (P) = Rs. 10 per unit

New price (P1) = Rs. 12 per unit

Change in Quantity demanded (\[\Delta Q\]) = 20%

Price elasticity of demand (Ed) =?

Change in prices (\[\Delta P\]) =New price - Original price

\[=12-10=Rs.\text{ }2\]

Percentage change in price = \[\frac{\text{Change}\,\,\text{in}\,\,\text{price}}{\text{Original}\,\,\text{price}}\,\times \,\text{100}\]

\[=\,\,\frac{\Delta P}{P}\times 100\]

\[=\,\,\frac{2}{10}\times 100\]

= 20%

Price elasticity of demand = \[\frac{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{quantity}\,\,\text{demanded}}{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{price}}\]

\[ED=\frac{20}{20}\]

ED = 1

Now, further takes this elasticity of demand in another situation when price changes from Rs. 10 to Rs. 13 per unit

Percentage change in price = \[\frac{\text{Change}\,\,\text{in}\,\,\text{price}}{\text{Original}\,\,\text{change}\,\,\text{in}\,\,\text{price}}\times \,\text{100}\]

=\[\frac{13-10}{10}\times 100\]

=\[\frac{3}{10}\times 100\,\,=\,\,30%\]

Price elasticity of demand \[\text{=}\frac{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{quantity}\,\,\text{demanded}}{\text{Percentage}\,\,\text{change}\,\text{in}\,\,\text{price}\,}\]

\[\text{1 = }\frac{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{quantity}\,\,\text{demanded}}{\text{30}}\]

Percentage change in quantity demanded \[\text{=30}\times \text{1}\]

= 30%