Answer:
1.25
Explanation:
The production function is correctly sated as follows:
[tex]q = K^{0.8}L^{0.2}[/tex]
[tex]MP_{K} = 0.8K^{-0.2}L^{0.2}[/tex]
[tex]MP_{L} = 0.2K^{0.8}L^{-0.8}[/tex]
Where, [tex]MP_{K}[/tex] represents marginal product of capital, and [tex]MP_{L}[/tex] represents marginal product of labor.
At the optimal level, we have:
[tex]\frac{MP_{K}}{MP_{L}} = \frac{P_{K}}{P_{L}}[/tex]
Where, [tex]P_{K}[/tex] represents price of capital, and [tex]P_{L}[/tex] price of labor.
[tex]\frac{0.8K^{-0.2}L^{0.2}}{0.2K^{0.8}L^{-0.8}} = \frac{24}{12}[/tex]
[tex]0.4\frac{L}{K} = 2[/tex]
[tex]\frac{L}{K} = 0.8[/tex]
[tex]\frac{K}{L} =\frac{1}{0.8} = 1.25[/tex]
Therefore, the optimal capital/labor ratio is 1.25.
