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A competitive firm has the shortrun 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 shortrun 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 Ushaped with its “bottom” at x = 1, with sravc =
$4. The marginal
cost curve is also Ushaped. It bottoms out at x = 2/3 and crosses the AVC curve from
below at x = 1, so the shortrun supply function for this firm starts at x
= 1 with a price
of $4 and follows the srmc from there.
0
5
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 Fall '06
 MASSON
 Microeconomics

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