To determine the average product of labour (APL) function, we need to divide the total product (Q) by the amount of labor input (L).
APL = Q / L
Given the production function Q = 4KL - 0.6K^2 - 0.1L^2, we substitute K=5 for the fixed capital input:
Q = 4(5)L - 0.6(5)^2 - 0.1L^2
Q = 20L - 15 - 0.1L^2
Now we can calculate APL:
APL = (20L - 15 - 0.1L^2) / L
APL = 20 - (15/L) - 0.1L
To find the level of labor at which the total output of cut-flower reaches the maximum, we need to find the maximum point of the production function. We can do this by taking the derivative of Q with respect to L and setting it equal to zero.
dQ/dL = 20 - (15/L) - 0.1L
0 = -15/L - 0.1
0.1 = -15/L
1/L = 0.1/15
L = 15/0.1
L = 150
When L = 150, the total output of cut-flower reaches its maximum.
To find the maximum achievable amount of cut-flower production, we substitute L = 150 into the production function:
Q = 4(5)(150) - 0.6(5)^2 - 0.1(150)^2
Q = 3000 - 15 - 2250
Q = 735
The maximum achievable amount of cut-flower production is 735.
Example: Suppose that the short-run production function of certain cut-flower firm is given by:
𝑸=𝟒𝑲𝑳−𝟎.𝟔𝑲^𝟐-0.1𝑳^𝟐 :where Q is quantity of cut-flower produced, L is labour input and K is fixed capital input (K=5).
Determine the average product of labour (APL) function.
At what level of labour does the total output of cut-flower reach the maximum?
What will be the maximum achievable amount of cut-flower production?
1 answer