Question

Price elasticity of Good $X$ is one and a half times the price elasticity of Good $Y$. $S_X$ rises from $125$ units to $175$ units due to a $16$ percent rise in $P_X$. Calculate the percentage fall in $S_Y$ if $P_Y$ reduces from Rs. $10$ to Rs. $7$.

Answer 1

Percentage change in $S_X=\frac{175-125}{125}\times 100=\frac{50}{125}\times 100=40percent$
Percentage change in $P_X=16$ percent
Percentage change $P_Y=\frac{7-10}{10}\times 100=\frac{-3}{10}\times 100=(-)30percent$
Price elasticity of Good $X=1\frac{1}{2}$ (price elasticity of Good $Y$)
$\left(\frac{Percentagechangein{S}_X}{Percentagechangein{P}_X}\right)=1\frac{1}{2}\left(\frac{Percentagechangein{S}_Y}{Percentagechangein{P}_Y}\right)$
$\Rightarrow \frac{40}{16}=\frac{3}{2}\left(\frac{Percentagechangein{S}_Y}{(-)30}\right)$
$\Rightarrow$ Percentage change in $S_Y=\frac{40\times 2\times (-)30}{16\times 3}=(-)50$
Percentage fall in $S_Y=50$%