Respuesta :
Answer:
Following are the solution to the given question:
Explanation:
The decrease of a marginal input return implies that its input is increasing by one unit, thereby decreasing its marginal input product.
Function of production
[tex]F(K, L) = AK^{\frac{3}{4}} L^{\frac{3}{4}}[/tex]
Its capital products subject (MPK) is derived by differentiating the factor of production from K.
[tex]MPK = \frac{3}{4}\times AK^{\frac{3}{4}} - 1L^{\frac{3}{4}}\\\\MPK = \frac{3}{4}AK^{-\frac{1}{4}}L^{\frac{3}{4}}\\\\MPK = \frac{3}{4}\times A\times (\frac{L^{\frac{3}{4}}}{K^{\frac{1}{4}}})[/tex]
Note: When a value is changed from numerator to denominator, then the power symbol shifts between positive to negative.
Since k is in the denominator, K decreases [tex]\frac{3}{4}\times A\times (\frac{L^{\frac{3}{4}}}{K^{\frac{1}{4}}})[/tex], and therefore MPK is reduced.
There's hence a decreased effective return on capital again for production function.
Its marginal labor product (MPL) is determined by distinguishing the manufacturing function from L.
[tex]MPL = (\frac{3}{4})\times AK^{\frac{3}{4}}L^{\frac{3}{4}}-1\\\\MPL = (\frac{3}{4})AK^{\frac{3}{4}}L^{-\frac{1}{4}}\\\\MPL = (\frac{3}{4})\times A\times (\frac{K^{\frac{3}{4}}}{L^{\frac{3}{4}}})[/tex]
The denominator of L reduces L [tex](\frac{3}{4})\times A\times (\frac{K^{\frac{3}{4}}}{L^{\frac{3}{4}}})[/tex] and therefore reduces MPL.
So there is a decreasing marginal return to labor in the production function.
