APL (Average Product of Labor) is calculated by dividing total product (Q) by the quantity of labor (L). In this case, since the capital is fixed, we can consider K as a constant and focus on the relationship between output and labor.
APL = Q/L
To find MPL (Marginal Product of Labor), we need to calculate the derivative of the production function with respect to labor (L) while holding capital (K) constant:
MPL = ∂Q/∂L
Differentiating the production function with respect to L:
MPL = 4L^3K^4
Thus, APL = Q/L = L^4K/ L = L^3K
And MPL = 4L^3K^4
1. Suppose the production function is given by Q(L,K) = L
4
3
K
4
1
. Assuming capital is fixed,
find APL and MPL
.
1 answer