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Average and marginal production 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 P(L) = 200L + 10L2 − L3 gives the output of a system as a function of the number of laborers L The average product A(L) is the average output per laborer when L laborers are working; that is A(L) = P(L)/L. The marginal product M(L) is the approximate change in output when one additional laborer is added to L laborers; that is,
- a. For the given production function, compute and graph P, A, and M.
- b. Suppose the peak of the average product curve occurs at L = L0, so that A′ (L0) = 0. Show that for a general production function, M(L0) = A(L0).
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