1. Suppose the production function is given by Q(L,K) = L

Question

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
.

Answer 1

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