question_answer

A consumer spends Rs. 100 on a good priced at Rs. 4 per unit. When price falls by 50 percent, the consumer continues to spend Rs. 100 on the good. Calculate price elasticity of demand by percentage method.

Answer:

Given:
Initial Total Expenditure (\[T{{E}_{0}}\]) = Rs. 100
Final Total Expenditure (\[T{{E}_{1}}\]) = Rs. 100
Initial Price (\[{{P}_{0}}\]) = Rs. 4
Percentage change in price = \[\text{ }50\]
Percentage change in price \[=\frac{{{P}_{1}}-{{P}_{0}}}{{{P}_{0}}}\,\,\times \,\,100\]
\[-\,50\,\,=\frac{{{P}_{1}}-4}{4}\,\,\times \,\,100\]
\[\frac{-200}{100}={{P}_{1}}-4\]
\[{{P}_{1}}\]=2
Price (P)	Total Expenditure (TE) = Price (P) x Quantity (Q)	Quantity Q=\[\frac{TE}{P}\]
\[{{P}_{0}}=Rs\,\,4\]	\[T{{E}_{0}}=Rs\,\,100\]	\[{{Q}_{0}}=25\]
\[{{P}_{1}}=Rs\,\,2\]	\[T{{E}_{1}}=Rs\,\,100\]	\[{{Q}_{0}}=50\]
Now,
\[{{E}_{d}}=(-)\frac{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{quantity}\,\,\text{demanded}}{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{price}}\]
\[{{E}_{d}}=(-)\frac{\,\frac{{{Q}_{1}}-{{Q}_{0}}}{{{Q}_{0}}}\,\,\times \,\,100}{-50}\,\,\]
\[{{E}_{d}}=(-)\frac{\,\frac{50-25}{25}\,\,\times \,\,100}{-50}\,\,\]
\[{{E}_{d}}=(-)\frac{100}{-50}\]
\[{{E}_{d}}\] = 2
\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\]
Thus, the price elasticity of demand is 2.