• # question_answer A consumer buys 200 units of a good at a price of Rs. 20 per unit. Price elasticity of demand is$(-)\,2$. At what price will he be willing to purchase 300 units? Calculate.

 Original Price (P) = Rs. 20 per Unit Original Quantity ($\theta$) = 200 Units Elasticity of demand (${{E}_{d}}$) = $(-)\,2$ New Qty. (${{\theta }_{1}}$) = 300 Units New Price (${{P}_{1}}$) =? Change in Qty = New Qty.  Original Qty ($\Delta \theta$) $=300200$ = 100 Units New Price (${{P}_{1}}$) = $\Delta PP$(Change in PriceOriginal Price) Utilizing the formula: ${{E}_{d}}=\,\,\frac{\Delta \theta }{\Delta P}\,\,X\,\,\frac{P}{Q}$ Where, ${{E}_{d}}$ = Price elasticity of demand $\Delta \theta$= Change in Qty. $\Delta P$= Change in Price P = Original Price Q = Original Qty. Change in Qty ($\theta$) = New Qty.Original Qty. $=300200$ = 100 Units $(-)\,2$ =$\frac{100}{\Delta P}\,\,\times \,\,\frac{20}{200}$ $(-2)\,\Delta P=10$ $\therefore$     $(-2)\,\Delta P=\frac{10}{2}=5$ $(-)$ sign is ignored since it tells only the inverse relationship between Price and Qty. demanded. New Price (${{P}_{1}}$)$=P-\Delta P$ $=Rs.\text{ }20Rs.\text{ }5=Rs.\text{ }15$ Hence New Price (${{P}_{1}}$) will be Rs. 15 at New Qty. of 300 units.                                       Ans. Rs. 15