The purpose of this problem is to provide a numerical example of the following phenomenon: If an additional unit of a good is more expensive to produce than the cost of production on average, then the relatively high cost of this marginal unit will pull up the average cost. Similarly, if the marginal unit is cheaper to produce than the cost of production on average, then the relatively low cost of this marginal unit will bring down the average cost. Consider a firm whose total costs of production as a function of its output x are given as TC(x) = 3x 2 + 7x + 12 for x > 0.
(e) Show that the average-cost function is rising: AC0 (x) > 0 whenever x > 2.
(f) Show the marginal cost is less than the average cost: MC(x) < AC(x) whenever 0 < x < 2.
(g) Show that the average-cost function is falling: AC0 (x) < 0 whenever 0 < x < 2.
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The purpose of this problem is to provide a numerical example of the f.docx
1. The purpose of this problem is to provide a numerical example of the following phenomenon: If
an additional unit of a good is more expensive to produce than the cost of production on average,
then the relatively high cost of this marginal unit will pull up the average cost. Similarly, if the
marginal unit is cheaper to produce than the cost of production on average, then the relatively
low cost of this marginal unit will bring down the average cost. Consider a firm whose total costs
of production as a function of its output x are given as TC(x) = 3x 2 + 7x + 12 for x > 0.
(e) Show that the average-cost function is rising: AC0 (x) > 0 whenever x > 2.
(f) Show the marginal cost is less than the average cost: MC(x) < AC(x) whenever 0 < x < 2.
(g) Show that the average-cost function is falling: AC0 (x) < 0 whenever 0 < x < 2.
