question_answer

A consumer buys 30 units of a good at a price of Rs. 10 per unit. Price elasticity of demand for the good is (-1). How many units the consumer will buy at a price of Rs. 9 per unit? Calculate.

Answer:

Given,

\[{{Q}_{1}}=30,{{Q}_{2}}=?,{{P}_{1}}=Rs\,\,10,\,\,{{P}_{2}}=\,Rs\,\,9\] and \[{{E}_{d}}=-1\]

Therefore,          \[\Delta Q={{Q}_{2}}-{{Q}_{1}}\] and \[\Delta P={{P}_{2}}-{{P}_{1}}=\,\,Rs\,\,(-1)\]

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

\[-1=\frac{({{Q}_{2}}-{{Q}_{1)}}}{30}\,\,\times \,\,\frac{{{P}_{1}}}{\Delta P}\]

\[-1=\frac{({{Q}_{2}}-30)}{30}\,\,\times \,\,\frac{10}{(-1)}\]

\[3={{Q}_{2}}-30\]

\[{{Q}_{2}}=33\,\,units\]

Therefore, the consumer will buy 33 units of the good at a price of Rs. 9.