question_answer

A consumer buys 18 units of a good at a price of Rs. 9 per unit. The price elasticity of demand for the good is (-)1. How many units the consumer will buy a price of Rs. 10 per unit? Calculate.

Answer:

Given, \[{{Q}_{1}}=18,\,{{Q}_{2}}=?,\] \[{{P}_{1}}\] = Rs. 9 and \[{{P}_{2}}\]= Rs. 10

Therefore,          \[\Delta Q={{Q}_{2}}-{{Q}_{1}}\]

\[\Delta P={{P}_{2}}-{{P}_{1}}=Rs\,\,1\]

\[{{E}_{d}}\frac{\Delta Q}{Q}\times \frac{P}{\Delta P}\]

\[-1=\frac{{{Q}_{2}}-{{Q}_{1}}}{{{Q}_{1}}}\,\,\times \,\,\frac{P}{{{P}_{2}}-{{P}_{1}}}\]

\[-1=\frac{{{Q}_{2}}-18}{18}\,\,\times \,\,\frac{9}{10-9}\]

\[-1=\frac{{{Q}_{2}}-18}{18}\,\,\times \,\,\frac{9}{1}\,\,\]

\[-2={{Q}_{2}}-18\]

\[-2+18={{Q}_{2}}\]

\[{{Q}_{2}}=16\]

Therefore, the consumer will buy 16 units of the good at a price of Rs. 10.