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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 shortrun 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 firms shortrun 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 firms 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 firms 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. Firms short run supply function is the upward sloping portion of the SMC function starting at the point (4,14). (e) (5 points) Graph the shortrun 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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 Fall '10
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