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The total product of labor is given by the function, x = f(L;K). We can graph this as a cross-section of the production function.
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Total, Average, and Marginal Physical Products
Hold all but one of the inputs ¯xed (say, ¯x K = K). Perhaps we are in a short run situation, or perhaps we are just focusing on the e®ect of changing L.
The total product of labor is given by the function, x = f (L; K). We can graph this as a cross-section of the production function.
0
1
L
0
1
K
0
1
(K,L)
Cobb-Douglas Production Function
The average product of labor is de¯ned as
APL =
f(L; K) L
The marginal product of labor is de¯ned as
MPL =
@f (L; K) @L
Cobb-Douglas example: x = K ®^ L¯
Diminishing Marginal Returns
Diminishing marginal returns (to labor) occur when the marginal product (of labor) eventually falls as L increases. @MPL @L
That is, labor is less and less productive at the margin, as L increases. It can be shown that with CRS or DRS, we must have diminishing marginal returns to each input.
Cobb-Douglas example: x = K ®^ L¯
MPL =
Thus, we have diminishing marginal returns to labor when ¯ < 1. Constant returns to scale and diminish- ing marginal returns can easily coexist.
