Question 4. Integral Diffrentiation
A firm uses one input labour(L) to produce output (Q). The marginal product function for the input is MP (L) = 10L^1/2. Find the production function, Q(L).
To find the production function Q(L), we need to integrate the marginal product function MP(L) with respect to L.
Given that MP(L) = 10L^1/2, we can integrate this function to find Q(L) as follows:
∫MP(L)dL = ∫10L^1/2 dL
Q(L) = 10 ∫L^1/2 dL
Q(L) = 10 * [(2/3)L^(3/2)]
Therefore, the production function Q(L) is:
Q(L) = (20/3)L^(3/2)
This is the production function that represents the relationship between the input labor (L) and the output (Q) produced by the firm.