question_answer

The Price Elasticity of Supply of good X is half of the Price Elasticity of Supply good Y. A 10% rise in the price of good Y results in a rise in its supply from 400 units to 520 units. Calculate the percentage change in quantity supplied of good X when its price falls from Rs.10 to Rs.8 per unit.                                                

Answer:

Given, for good Y,                                                                          Initial Quantity (Q) = 400 units; New Quantity\[({{Q}_{1}})\] = 520 units                                       Change in Quantity\[(\Delta Q)={{Q}_{1}}Q=520-400\]=120 units                                        Percentage Change in Quantity Supplied of\[Y\,\,\,\,\,\,\,\frac{\Delta Q}{Q}\times 100=\frac{120}{400}\times 100=30%\] Percentage Change in Price of Y =10% (given)                                                              \[\Rightarrow \]Elasticity of supply\[({{E}_{s}})\]of Good Y =\[\frac{Percentage\,Change\,in\,Quantity\,Supplied\,of\,Y}{Percentage\,Change\,in\,\Pr ice\,of\,Y}=\frac{30}{10}\]=30% Since\[{{E}_{S}}\]of X, is half of the \[{{E}_{S}}\] of Y, therefore \[{{E}_{S}}\] of\[X=3\times \frac{1}{2}=1.5\] For good X, Initial Price (P) = Rs.10, New Price\[({{P}_{1}})\]= Rs.28 Change in Price\[(\Delta P)={{P}_{1}}-P=8-10=-2\] Percentage change in price of\[X=\frac{\Delta P}{P}\times 100=\frac{-2}{10}\times 100=-20%\]             Percentage change in quantity supplied of X=?             \[\Rightarrow \,\,\,\,\,\,\,\]Elasticity of Supply\[({{E}_{s}})\]of Good X\[=\frac{Percentage\,Change\,in\,Quantity\,Supplied\,of\,X}{Percentage\,Change\,in\,\Pr ice\,of\,X}\]                                                             \[1.5=\frac{Percentage\,Change\,in\,Quantity\,Supplied\,of\,X}{-20}\]             Percentage change in quantity supplied of\[X=1.5\times -20=-30\] Therefore, supply of X falls by 30%.