Consider the following graph of a production function when capital is constant. (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; three levels of labor are shown as reference; there are L1, L2, and L3; they are related as follows L1<L2<L3; the graph is convex from 0 to L1, that is, its slope is increasing; the graph is concave from L1 on, that is, its slope is decreasing; the line that is tangent to the curve at L2, passes through the origin of the graph.)
Denote by APL(L,K)=f(L,K)/L the so-called average product of labor (here f is the production function of the firm). From the graph we know that for the corresponding K:
APL(L1,K)=MPL(L1,K)
APL(L2,K)>MPL(L2,K)
APL(L1,K)<MPL(L1,K)
APL(L1,K)>MPL(L1,K)
APL(L2,K)<MPL(L2,K)
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