I need help finding the marginal product of one additional worker. The production function provided to me is Q = 25KL, where Q is magazines sold per day, K is the number of telephones and L is the number of workers. Worker wages are $50/day, telephones rent for $100/day and magazines sell for $1 each. And my answer should be expressed in terms of units of capital, K.

In terms of capital, K, the marginal product of labor, or MPL, is:

MPL = 25K

This is constant because the function is linear.

Expert Answers

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The marginal product of one additional worker is known as the "marginal product of labor" (MPL). This is the additional amount of output that will be generated when another worker is added. It is marginal in the sense that it varies with the quantity. Therefore, we are looking for a rate of change.

MPL = change in L/change in quantity

As it describes production, it is found in the production function and will vary according to the other variables in the function. In this production function:

Y = 25KL

Y = output (product), K = capital (number of telephones), and L = labor (number of workers)

Intuitively, it makes sense that the amount of output depends on the levels of capital (telephones the workers have to work with) and the number of workers.

Since MPL is a rate of change, it is found by deriving the function with respect to L. So taking the partial derivative yields:

dL/dY = 25K = MPL

This is a linear relationship, as the marginal product of any additional worker at any production level will always be the amount of telephones K multiplied by 25. Thus, to state the answer in terms of K:

MPL = 25K

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