question_answer

A consumer spends Rs. 100 on a good priced at Rs. 4 per unit. When its price falls by 25 percent, the consumer spends Rs. 75 on the good. Calculate the price elasticity of demand by the Percentage method.

Answer:

Given:
Initial Total Expenditure\[T{{E}_{0}}\] = Rs. 100 Final Total Expenditure
\[T{{E}_{1}}\] = Rs. 75 Initial Price PO = Rs. 4 Percentage change in price = \[-25\]
Percentage change in price = \[\frac{{{P}_{1}}-{{P}_{0}}}{{{P}_{0}}}=100\]
\[25=\frac{{{P}_{1}}-4}{4}\,\,\times \,\,100\]
\[100\,\,=\,\,{{P}_{1}}-\,\,4\,\,\times \,\,100\]
\[\frac{100}{100}={{P}_{1}}-4\]
\[{{P}_{1}}=4-1=3\]
Price (P)	Total Expenditure TE = Price P \[\times \] Quantity Q	Quantity Q = TEP
\[{{P}_{0}}=Rs\,\,4\]	\[T{{E}_{0}}=\,\,Rs\,\,100\]	\[{{Q}_{0}}=\,\,25\]
\[{{P}_{1}}=\,\,Rs\,\,3\]	\[T{{E}_{1}}=\,\,Rs\,\,75\]	\[{{Q}_{ & 1}}=\,\,25\]
Now,
Ed = Percentage change in quantity demanded \[\div \] Percentage change in price
Percentage change in \[Q=\frac{{{Q}_{1}}-{{Q}_{0}}}{{{Q}_{0}}}\,\,\times \,\,100\]
\[=\frac{25-25}{25}\,\,\times \,\,100=0\]
\[Ed\,\,=\,\,\frac{0}{1}=0\]
Thus, the price elasticity of demand is 0.