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# solmidIII10fa - Your name Econ 420K Midterm Exam III Fall...

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Unformatted text preview: Your name: Econ 420K Midterm Exam III Fall 2010 Svetlana Boyarchenko Solutions 1. (25 points) A competitive firm has the short-run cost function SC ( q ; ¯ k ) = q 3- 8 q 2 + 30 q/ ¯ k + 5 ¯ k, where ¯ k is a fixed quantity of capital. For ¯ k = 1, write down the equations for: (a) (3 points) The firm’s short-run average cost function. SAC ( q ;1) = SC ( q ;1) q = q 3- 8 q 2 + 30 q + 5 q = q 2- 8 q + 30 + 5 q . (b) (3 points) The firm’s average variable cost function. AV C ( q ;1) = V C ( q ;1) q = q 3- 8 q 2 + 30 q q = q 2- 8 q + 30 . (c) (3 points) The firm’s short run marginal cost function. SMC ( q ;1) = ∂SC ( q ;1) ∂q = 3 q 2- 16 q + 30 . (d) (4 points) At what level of output is average variable cost mini- mized? The average variable cost is minimized at a point where SMC ( q ;1) = AV C ( q ;1), equivalently, 3 q 2- 16 q + 30 = q 2- 8 q + 30 ⇔ 2 q 2- 8 q = 0 , whence we get two possible values of q : q = 0 and q = 4. Since AV C (0;1) =\$30, and AV C (4;1) = 16- 32+30 =\$14, q = 4 is the level of output that minimizes the AVC. 2 4 14 q AVC(q) SMC(q) Figure 1. Firm’s short run supply function is the upward sloping portion of the SMC function starting at the point (4,14). (e) (5 points) Graph the short-run supply function for this firm, be- ing careful to label the key points on the graph with the numbers specifying the exact prices and quantities at these points....
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solmidIII10fa - Your name Econ 420K Midterm Exam III Fall...

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