Discussion
Let \(y = K^{\alpha}L^{\beta}\) be the Cobb-Douglas production function. Then, \(\alpha\) measures :
Answer: B
\(\alpha\) measures the elasticity of output with respect to capital.
For \(y = K^{\alpha}L^{\beta}\),
\[ \begin{aligned} \frac{\partial y}{\partial K} &= \alpha K^{\alpha - 1}L^{\beta} = \alpha\frac{y}{K} \\ \frac{\partial y}{\partial K}\cdot\frac{K}{y} &= \alpha \end{aligned} \]
So \(\alpha\) is the percentage change in output from a one per cent change in capital, and similarly \(\beta\) is the output elasticity of labour. The marginal product of capital is \(\alpha y/K\), which varies with the input mix, so it is not \(\alpha\) itself.
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