Consider the following production function $Y = A \times K ^ { a } \times L ^ { 1 - a }$ ?. If a = 0.5, over the past year output grew by 2 percent, total factor productivity grew 1 percent , and labor grew by 1 percent, capital grew by

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Given $a = 0.5$, the production function becomes $Y = A \times K^{0.5} \times L^{0.5}$. The growth rate of output (Y) is 2%, total factor productivity (A) is 1%, and labor (L) is 1%. To find the growth rate of capital (K), we use the formula for the growth rate of the production function: growth rate of Y = growth rate of A + a(growth rate of K) + (1-a)(growth rate of L). Substituting the given values: 2% = 1% + 0.5(growth rate of K) + 0.5(1%). Solving for the growth rate of K gives us 1%.

Consider the Following Production Function Y=A×Ka×L1−aY = A \times K ^ { a } \times L ^ { 1 - a }Y=A×Ka×L1−a

Consider the Following Production Function $Y = A \times K ^ { a } \times L ^ { 1 - a }$