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 %age change in quantity supplied of good X when its price falls from Rs 10 to Rs 8 per unit.

Let initial quantity supplied (Q1) be 400 units
Final quantity supplied (Q2) be 520 units

Change in quantity supplied Q = Q2-Q1=520-400=80 units

Percentage change in quantity supplied of good Y =Change in quantity suppliedInitial quantity supplied×100=80400×100=30%

Percentage change in price of good Y =10% givenPercentage change in price of good X=P2-P1P1×100=8-1010×100=-20%

According to the question,

Price elasticity of supply of good X12נ​Price elasticity of supply of good Y

% change in quantity supplied of good X% change in price of good X=12×% change in quantity supplied of good Y% change in price of good Xor, % change in quantity supplied of good X-20=12×3010 % change in quantity supplied of good X=-30

The negative sign denotes the percentage fall in the supply of good X.

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