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
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