Over the past year,output grew 5%,capital grew 5%,and labor grew 1%.If the elasticities of output with respect to capital and labor are 0.5 and 0.5,respectively,how much did productivity grow?
A)0)5%
B)1)0%
C)1)5%
D)2)0%

Question

Quizplus · Accepted Answer

2.0%The growth rate of output (Y) can be represented by the equation: %ΔY = (%ΔCapital * Elasticity of Capital) + (%ΔLabor * Elasticity of Labor) + %ΔProductivity. Given that output grew by 5%, capital grew by 5%, labor grew by 1%, and both elasticities are 0.5, we can substitute these values into the equation: 5% = (5% * 0.5) + (1% * 0.5) + %ΔProductivity. This simplifies to 5% = 2.5% + 0.5% + %ΔProductivity, or 5% = 3% + %ΔProductivity. Solving for %ΔProductivity gives us 2%, indicating that productivity grew by 2%.

Over the Past Year,output Grew 5%,capital Grew 5%,and Labor Grew