Answer:
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 Price\[\]Original 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
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