question_answer

A consumer spends Rs. 60 on a good priced at Rs. 5 per unit. When price falls by 20 percent, the consumer continues to spend Rs. 60 on the good. Calculate price elasticity of demand by percentage method.

Answer:

Given:
Initial Total Expenditure (\[T{{E}_{0}}\]) = Rs. 60
Final Total Expenditure (\[T{{E}_{1}}\]) = Rs. 60
Initial Price (\[{{P}_{0}}\]) = Rs. 5
Percentage change in price = \[-Rs.\text{ }20\]
Percentage change in price =\[\frac{{{P}_{1}}-{{P}_{0}}}{5}\times 100\]
\[-20=\frac{{{P}_{1}}-5}{5}\,\,\times \,\,100\]
\[\frac{-100}{100}={{P}_{1}}-5\]
\[{{P}_{1}}\] = 4
Price (P)	Total Expenditure (TE) = Price (P) \[\times \] Quantity (Q)	Quantity Q=\[\frac{TE}{P}\]
\[{{P}_{0}}=Rs\,\,5\]	\[T{{E}_{0}}=\,\,Rs\,\,60\]	\[{{Q}_{0}}=\,\,12\]
\[{{P}_{1}}=Rs\,\,4\]	\[T{{E}_{1}}=\,\,Rs\,\,60\]	\[{{Q}_{1}}=\,\,15\]
Now,
\[{{E}_{d}}=(-)\frac{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{quantity}\,\,\text{demanded}}{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{price}}\]
\[{{E}_{d}}=(-)\frac{\,\frac{{{Q}_{1}}-{{Q}_{0}}}{{{Q}_{0}}}\,\,\times \,\,100}{-20}\,\,\]
\[{{E}_{d}}=(-)\frac{\,\frac{15-12}{12}\,\,\times \,\,100}{-20}\,\,\]
\[{{E}_{d}}=(-)\frac{25}{-20}\]
\[{{E}_{d}}\]= 1.25
\[\therefore \]      \[\]
Thus, the price elasticity of demand is 1.25.