The marginal product of labor function or MPL=[tex]9L^{2}-0.2L^{3}[/tex].
Step-by-step explanation:
The Average Production Function or APL is given as [tex]APL=3L^{2}-0.05L^{3}[/tex] where "L" represents the overall amount labor in the production process.
Therefore, the Total Production Function or TPL,in this case, would be [tex]TPL=(3L^{2}-0.05L^{3})\times L[/tex]=[tex]TPL=3L^{3}-0.05L^{4}[/tex]
Hence,the Marginal Product of Labor, which is abbreviated as MPL will be=[tex]\frac{dL}{dTPL}=(3\times 3L^{2})-(4\times 0.05L^{3})[/tex]=[tex]9L^{2}-0.2L^{3}[/tex]
Therefore,the marginal product of labor function or MPL=[tex]9L^{2}-0.2L^{3}[/tex]
