question_answer

A consumer spends Rs. 400 on a good priced at Rs. 8 per unit. When its price rises by 25 percent, the consumer spends Rs. 500 on the good. Calculate the price elasticity of demand by the Percentage method.

Answer:

Given
Initial Total Expenditure\[T{{E}_{0}}\] = Rs. 400
Final Total Expenditure\[T{{E}_{1}}\] = Rs. 500
Initial Price \[{{P}_{0}}\] = Rs. 8
Percentage change in price = + 25
Percentage change in price = \[\frac{{{P}_{1}}-{{P}_{0}}}{{{P}_{0}}}\,\,\times \,\,100\]
\[25=\frac{{{P}_{1}}-8}{8}\,\,\times \,\,100\]
\[\frac{200}{100}={{P}_{1}}-8\]
\[{{P}_{1}}=10\]
Price (P)	Total Expenditure Te = Price P \[\times \] Quantity Q	Quantity Q = TEP
\[{{P}_{o}}=Rs\,\,8\]	\[T{{E}_{0}}=\,\,Rs\,\,400\]	\[{{Q}_{0}}=50\]
\[{{P}_{1}}=\,\,Rs\,\,10\]	\[T{{E}_{1}}=\,\,Rs\,\,500\]	\[{{Q}_{1}}=50\]
Now
\[\text{Ed = }\frac{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{quantity}\,\,\text{demanded}}{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{price}}\]
Percentage change in Quantity =  \[\frac{{{Q}_{1}}-{{Q}_{0}}}{{{Q}_{0}}}\,\times \,\,100\]
\[=\frac{50-50}{50}\,\,\times \,\,100\]
\[\text{Ed = }\frac{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{quantity}\,\,\text{demanded}}{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{price}}\]
\[=\frac{0}{25}\]
Ed = 0
Thus, the price elasticity of demand is 0.