ps5_s04 (ans)

# ps5_s04 (ans) - Econ 313 Spring 2004 PS#5-XtraQ ANSWERED 1...

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1. A competitive firm has the short-run cost function srtc(x) = x 3 – 2x 2 + 5x + 6 . Write down equations for: a. The firm's average variable cost function is : sravc = x 2 – 2x + 5. b. The firm's marginal cost function is: srmc = 3x 2 – 4x + 5. c. At what level of output is average variable cost minimized? So, sravc is minimized when sravc=srmc. Set x 2 – 2x + 5 = 3x 2 – 4x + 5 and solve for x and you get x = 1. d. Graph the short-run supply function for this firm, being careful to label the key points on the graph with the numbers specifying the exact prices and quantities at these points. The AVC curve is U-shaped with its “bottom” at x = 1, with sravc = \$4. The marginal cost curve is also U-shaped. It bottoms out at x = 2/3 and crosses the AVC curve from below at x = 1, so the short-run supply function for this firm starts at x = 1 with a price of \$4 and follows the srmc from there. 0 5 10 15 20 25 30 0 1 2 3 4 x \$ srmc sravc supply Econ 313 - Spring 2004 PS#5-XtraQ ANSWERED

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