question_answer

A consumer spends Rs. 1,000 on a good priced at 10 per unit. When its price falls by 20 percent, the consumer spends Rs. 800 on the good. Calculate the price elasticity of demand by the Percentage method.

Answer:

Given:
Initial Total Expenditure (\[T{{E}_{o}}\]) = Rs. 1000
Final Total Expenditure (\[T{{E}_{1}}\]) = Rs. 800
Initial Price (\[{{P}_{0}}\]) = Rs. 10
Percentage change in price \[=20\]
Percentage change in price \[=\frac{{{P}_{1}}-{{P}_{o}}}{{{P}_{o}}}\times 100\]
\[-\,20=\frac{{{P}_{1}}-10}{10}\times 100\]
\[\frac{-200}{100}={{P}_{1}}-10\]
\[{{P}_{1}}=8\]
Price (P)	Total Expenditure (TE) = Price (P)x	Quantity (Q) \[=\frac{TE}{P}\]
\[{{P}_{o}}=Rs\,\,10\]	\[T{{E}_{o}}=\,\,Rs\,\,1000\]	\[{{Q}_{o}}=100\]
\[{{P}_{1}}=\,\,Rs\,\,8\]	\[T{{E}_{1}}=\,\,Rs\,\,800\]	\[{{Q}_{1}}=100\]
Now,
\[{{E}_{d}}=(-)\frac{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{quantity}\,\,\text{demanded}}{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{price}}\]
\[{{E}_{d}}=(-)\frac{\frac{{{Q}_{1}}-{{Q}_{0}}}{{{Q}_{0}}}\times 100}{-20}\]
\[{{E}_{d}}=(-)\frac{\frac{100-100}{100}\times 100}{-20}\]
\[{{E}_{d}}=0\]
Thus, the price elasticity of demand is 0.