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Economists use production functions to describe how the output of a system varies with respect to another variable such as labor or capital. For example, the production function gives the output of a system as a function of the number of laborers . The average product is the average output per laborer when laborers are working; that is . The marginal product is the approximate change in output when one additional laborer is added to . laborers; that is, . (a). For the production function given here, compute and graph , and . (b). Suppose the peak of the average product curve occurs at , so that . Show that for a general production function,
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