Answer:
The marginal product of capital (MPK) is [tex]0.25(\frac{L}{K})^{0.75}[/tex]
Step-by-step explanation:
Data provided in the question:
The firm's Cobb-Douglas production function is given as
⇒ Q = [tex]L^{0.75}K^{0.25}[/tex]
Now,
To find the marginal product of capital (MPK) computing the partial derivation of the Cobb-Douglas production function
i.e
[tex]\frac{\partial Q}{\partial K} =\frac{\partial (L^{0.75}K^{0.25})}{\partial K}[/tex]
here, term L will be constant as it is a partial derivation with respect to K
thus,
[tex]\frac{\partial Q}{\partial K} =0.25L^{0.75}K^{0.25-1}[/tex]
or
[tex]\frac{\partial Q}{\partial K} =0.25L^{0.75}K^{-0.75}[/tex]
or
[tex]\frac{\partial Q}{\partial K} =0.25(\frac{L}{K})^{0.75}[/tex]
Hence,
the marginal product of capital (MPK) is [tex]0.25(\frac{L}{K})^{0.75}[/tex]
