Deriving the Labor Demand Curve
Deriving the Labor Demand Curve
This Demonstration illustrates the origin of the labor demand curve. A firm facing a fixed amount of capital has a logarithmic production function in which output is a function of the number of workers . The marginal product of labor (MPN) is the amount of additional output generated by each additional worker. In other words, MPN is the derivative of the production function with respect to number of workers, .
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The tangent lines at certain points of the production function show that the MPN for any value of is simply the slope of a line tangent to the production function for that value of . The firm's profit-maximizing condition is when wage equals MPN (explained below), such that for any number of workers, the wage the firm is willing to pay is equal to the MPN associated with that value of . For this reason, the labor demand curve is simply the MPN. As productivity increases or decreases, MPN and therefore the labor demand curve respond by shifting to the right for a productivity increase and the left for a productivity decrease.
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