If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. The marginal cost is the rate of change of the cost with respect to the number of items produced, that is, the derivative C'(x). (a) Show that if the average cost is a minimum, then the marginal cost equals the average cost. (b) If C(x) = 16,000 + 200x + 4x³/², in dollars, find (i) the cost, average cost, and marginal cost at a produc- tion level of 1000 units; (ii) the production level that will minimize the average cost; and (iii) the minimum average cost.

If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. The marginal cost is the rate of change of the cost with respect to the number of items produced, that is, the derivative C'(x). (a) Show that if the average cost is a minimum, then the marginal cost equals the average cost. (b) If C(x) = 16,000 + 200x + 4x³/², in dollars, find (i) the cost, average cost, and marginal cost at a produc- tion level of 1000 units; (ii) the production level that will minimize the average cost; and (iii) the minimum average cost.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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