To determine the product of labour (APL) function, divide the total output (Q) by the labor input (L):
APL = Q / L = (8 + 4LK - 5L^2 + 0.8K^2) / L
To find the level of labor where the total output reaches its maximum, we need to take the derivative of the production function with respect to labor (L) and set it equal to zero:
∂Q/∂L = 4K - 10L + 0.8K^2 = 0
Simplifying the equation:
10L = 4K + 0.8K^2
Substituting the value of K=10:
10L = 4(10) + 0.8(10)^2
10L = 40 + 80
10L = 120
L = 12
Therefore, the level of labor where the total output reaches its maximum is 12.
To find the maximum production of good A, substitute the value of L=12 into the production function:
Q = 8 + 4(12)(10) - 5(12)^2 + 0.8(10)^2
Q = 8 + 480 - 5(144) + 80
Q = 8 + 480 - 720 + 80
Q = -152
Therefore, the maximum production of good A is -152 units.
Suppose the short-run production function of good A is given by Q = 8+4LK-5L^2+0.8K^2, where Q is quantity of good A produced, L is labour input and K is fixed capital input (k = 10).
A)Determine the product of labour (APL) function?
B)At what level of labour does the total output of good A reach maximum?
C)What will be the maximum production of good A?
1 answer