Price elasticity of supply of Good $Y$ is three-fourth the price elasticity of supply of Good- $X$ . The price of $X$ rises from Rs. $10$ to Rs. $11.50$ per unit and its quantity supplied increased by 18 percent. If price of $Y$ falls from Rs. $11$ to Rs. $9.90$ , find the percentage fall in its supply.

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Solution

Percentage change in price of $X = \frac{11.50 - 10}{10} \times 100 = \frac{1.5}{10} \times 100 = 15 p e r c e n t$
Percentage change in supply of $X = 18$ percent
Percentage change in price of $Y = \frac{9.90 - 11}{11} \times 100 = \frac{- 1.1}{11} \times 100 = (-) 10 p e r c e n t$
Percentage change in supply of $Y =$ ?

Given,
Price elasticity of supply of Good- $Y = \frac{3}{4} (P r i c e e l s t i c i t y o f s u p p l y o f G o o d - X)$
$\frac{P e r c e n t a g e c h a n g e i n s u p p l y o f Y}{P e r c e n t a g e c h a n g e i n p r i c e o f Y} = \frac{3}{4} (\frac{P e r c e n t a g e c h a n g e i n s u p p l y o f X}{P e r c e n t a g e c h a n g e i n p r i c e o f X})$
$\frac{P e r c e n t a g e c h a n g e i n s u p p l y o f Y}{(-) 10} = \frac{3}{4} (\frac{18}{15})$
Percentage change in supply of $Y = \frac{3 \times 18 \times (-) 10}{4 \times 15} = (-) 9 p e r c e n t$
Percentage fall in supply of $Y = 9 %$

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Price elasticity of supply of Good Y is three-fourth the price elasticity of supply of Good-X. The price of X rises from Rs. 10 to Rs.11.50 per unit and its quantity supplied increased by 18 percent. If price of Y falls from Rs. 11 to Rs. 9.90, find the percentage fall in its supply.