Suppose q > 0 units of a commodity are produced at a total cost of C(q) dollars

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Suppose q > 0 units of a commodity are produced at a total cost of C(q) dollars and an average cost of


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In this section, we showed that q = qc satisfies A'(qc) = 0 if and only if C'(qc) = A(qc); that is, when marginal cost equals average cost. The purpose of this problem is to show that A(q) is minimized when q = qc.


a. Generally speaking, the cost of producing a commodity increases at an increasing rate as more and more goods are produced. Using this economic principle, what can be said about the sign of C"(q) as q increases?


b. Show that A"(qc) > 0 if and only if C"(qc) > 0. Then use part (a) to argue that average cost A(q) is minimized when q = qc.

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Calculus For Business, Economics And The Social And Life Sciences

ISBN: 9780073532387

11th Brief Edition

Authors: Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price

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