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Unformatted text preview: d illustrate on this graph the concept of average cost and marginal cost. (c) Explain in detail, with the aid of the graph, why marginal cost must intersect average cost at its minimum. (d) Prove that marginal cost must intersect average cost at its minimum. Solution: (a) Marginal cost is c (q). Average cost is AC(q) = c(q)q. f (x) = 0 (b) The figure is: 5 c(q) q (c) Since the average cost is geometrically represented by the slopes of the rays from the origin, and that the flattest ray is also tangent to the total cost curve, this implies that the marginal cost must necessarily be equal to the average cost where average cost reaches a minimum. c (q )q  c(q ) c(q ) = 0 c (q )q  c(q ) = 0 c (q ) = q 2 q (d) If AC(q) reaches a minimum at q then: AC (q ) = 4. Consider the set X = (2, 3). (b) Is the set X closed? Why or why not? (a) For every x X, show explicitly some > 0 so that B (x) X. (c) Is the set X compact? Why or why not? Solution: (a) Take any x (2, 3). Then if...
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This document was uploaded on 03/20/2014 for the course ECON 2p30 at Brock University.
 Fall '12
 laster
 Economics

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