The price elasticity of supply of good X is half the price elasticity of supply of 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.

Explanation

(i) `P.e_(S)" of good "Y:Q=400,Q_(1)=520,DeltaQ=120`
`%DeltaQ=(DeltaQ)/(Q)xx100=(120)/(400)xx100=30%`
`P.e_(S)" of "Y=(%DeltaQ_(y))/(%P_(y))=(30%)/(10%)=3`
`P.e_(S)" of "X=(1)/(2)"of P".e_(S)Y`
`=(1)/(2)"of 3"=1.5`
(ii) Let's find out `%DeltaQ_(x)`
`P=10," "P_(1)=8," "DeltaP=(-)2`
`%DeltaP=((-)2)/(10)xx100=(-)20%`
`P.e_(S)" of X"=(%DeltaQ_(x))/(%DeltaP_(x))`
`1.5=(%DeltaQ_(x))/(-20%)`
`%DeltaQ_(x)=(-)30%`
Percentage fall in supply of `X=30%`.