Suppose a firm’s short-run production function is given by 𝑄𝑄 = 16𝐿𝐿0.8. What is the marginal product ofthe fourth worker?
Question
Suppose a firm’s short-run production function is given by . What is the marginal product of the fourth worker?
Solution
The marginal product of labor (MPL) is the additional output that is produced when one more unit of labor is added, holding all other inputs constant. It is calculated by taking the derivative of the production function with respect to labor (L).
The production function given is Q = 16L^0.8.
To find the MPL, we take the derivative of Q with respect to L:
MPL = dQ/dL = 0.8 * 16L^(0.8-1) = 12.8L^-0.2.
To find the marginal product of the fourth worker, we substitute L = 4 into the MPL equation:
MPL = 12.8 * 4^-0.2 = 7.2 units.
So, the marginal product of the fourth worker is 7.2 units.
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