question_answer

A consumer spends Rs. 1000 on a good price at Rs. 8 per unit. When price rises by 25 percent, the consumer continues to spend same amount on the good. Calculate price elasticity of demand by percentage method.*-

Answer:

Given:
Initial Total Expenditure (\[T{{E}_{0}}\]) = Rs. 1000
Final Total Expenditure (\[T{{E}_{1}}\]) = Rs. 1000
Initial Price (\[{{P}_{0}}\]) = Rs. 8
Percentage change in price = + 25%
Percentage change in price =\[\frac{{{P}_{1}}-{{P}_{0}}}{{{P}_{0}}}\,\,\times \,\,100\]
\[25=\frac{{{P}_{1}}-8}{8}\,\,\times \,\,100\]
\[\frac{200}{100}={{P}_{1}}-8\]
Price (P)	Total Expenditure (TE) = Price (P) \[\times \] Quantity (Q)	Quantity (Q) = \[\frac{TE}{P}\]
\[{{P}_{0}}=Rs\,\,8\]	\[T{{E}_{0}}=Rs\,\,1000\]	\[{{Q}_{0}}=125\]
\[{{P}_{1}}=Rs\,\,10\]	\[T{{E}_{1}}=Rs\,\,1000\]	\[{{Q}_{1}}=125\]
Now?
\[{{E}_{d}}\text{=}\,(-)\frac{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{quantity}\,\,\text{demanded}}{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{price}\,\,}\]
\[{{E}_{d}}=(-)\frac{\,\frac{{{Q}_{1}}-{{Q}_{0}}}{{{Q}_{0}}}\,\,\times \,\,100}{25}\,\,\]
\[{{E}_{d}}=(-)\frac{\frac{100-125}{125}\times \,\,1000}{25}\,\]
\[{{E}_{d}}=\frac{-20}{25}\]
\[\therefore \,\,\,\,\,\,\,\,\,\,\]
Thus, the price elasticity of demand is 0.8