1. Suppose the production function is given by Q(L,K) = L
4
3
K
4
1
. Assuming capital is fixed,
find APL and MP
To find the average product of labor (APL) and marginal product (MP) of labor, we need to differentiate the production function with respect to labor (L).
The production function is Q(L, K) = L^4 * K^1.
To find APL, we divide the total output (Q) by the amount of labor (L):
APL = Q / L = (L^4 * K^1) / L.
Simplifying the equation, we can cancel out one L, resulting in:
APL = L^3 * K^1.
To find MP, we differentiate the production function with respect to labor (L):
MP = dQ / dL = 4 * L^3 * K^1.
Therefore, the average product of labor (APL) is L^3 * K^1 and the marginal product of labor (MP) is 4 * L^3 * K^1.