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Suppose a firm’s short-run production function is given by 𝑄𝑄 = 16𝐿𝐿0.8. What is the marginal product ofthe fourth worker?a) 36b) 10c) 49d) 1.85

Question

Suppose a firm’s short-run production function is given by 𝑄𝑄 = 16𝐿𝐿0.8. What is the marginal product ofthe fourth worker?a) 36b) 10c) 49d) 1.85

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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 = 12.8 / (4^0.2) ≈ 8.06.

So, the marginal product of the fourth worker is approximately 8.06, which is not listed in the provided options. Please check the question or the options again.

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