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301lec12 - Microeconomics 301 Professor Severinov...

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Microeconomics 301 Professor Severinov Department of Economics UBC Winter 2010 Lecture 12- Production Shut-Down Decision. Cost curve shifts Example of production and shut-down decision. TC ( q ) = C ( q ) = q 3 3 - 2 q 2 + 5 q + 10 . 33. FC = 10 . 33 ATC = q 2 3 - 2 q + 5 + 10 . 33 q AV C = q 2 3 - 2 q + 5 MC ( q ) = q 2 - 4 q + 5 is U shaped. 1
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MC 0 ( q ) = 2 q - 4 which is negative for q 2 and positive for q > 2. Increasing part of the MC ( q ) curve is q 2.
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Shut-down points: Long-run: min q = ATC ( q ) = q 2 3 - 2 q + 5 + 10 . 33 q First-order condition: 2 q 3 - 2 - 10 . 33 q 2 = 0 . or 2 q 3 3 - 2 q 2 = 10 . 33 Solve to get: q minatc = 4 p sL = ATC ( q minatc ) = ATC (4) = 5. Note MC (4) = AV C (4). Short run: min q = AV C ( q ) = q 2 3 - 2 q + 5 First-order condition: 2 q 3 - 2 = 0 2
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i.e. q minavc = 3, p sS = AV C ( q minavc ) = AV C (3) = 2. Note that MC (3) = AV C (3).
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Supply curve: MC ( q ) = p or q 2 - 4 q + 2 = p . Solve the quadratic equation: q 2 - 4 q + 2 - p = 0 Choose its larger root. Call it firm’s supply: q * = S ( p ) provides that p > 3 (short- run) and p > 4 (in the long-run).
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