question_answer

When price of a commodity X falls by 10 percent, its demand rises from 150 units to 180 units. Calculate its price elasticity of demand. How much should be the percentage fall in its price so that its demand rises from 150 to 210 units?

Answer:

Percentage change in Price = \[(-)\,\,10%\]

Q = 150 units

\[{{Q}_{1}}\] = 180 units.

Ed =\[(-)\,\frac{%\Delta d}{%\Delta P}\]

Ed = \[\frac{20%}{10%}\]

Thus, price elasticity = \[{{Z}_{0}}\]

And, if Ed = 2,

Q = 150 units, \[{{Q}_{1}}\] = 210 units

% change in quantity demanded\[=\frac{210-150}{150}\,\,\times \,\,100\]

\[=\frac{60}{150}\,\,\times \,\,100\,\,=\,\,40%\]

\[Ed\,\,=\,\,(-)\,\,\frac{40}{x}\,\,%\]

\[2=(-)\,\,\frac{40}{x}%\]

\[2x\,\,=\,\,\left( - \right)\,\,40%\]

\[x\,\,=\,\,-\,\,20%\]

Therefore percentage fall in price will be 20%.