ECE1010.05.post

ECE1010.05.post - UNIT II: FIRMS & MARKETS 10/15 Theory of...

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UNIT II: Theory of the Firm Profit Maximization Perfect Competition Review 11/5 MIDTERM 10/15
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Profit Maximization Last Time The Long-Run and the Short-Run Firm and Market Supply Perfect Competition (Part 1)
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We saw last time that we can solve the firm’s cost minimization problem analogously to the consumer’s utility maximization problem. Cost minimization requires that the firm produce using a combination of inputs for which the ratios of the marginal products, or the marginal rate of technical substitution, equals the ratio of the input prices: MRTS = w/r Last Time 2 Provisos: Only in the Long-Run Only part of the firm’s problem
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How much will it cost this firm to produce 10 units of output in the long-run? Q = 4K 1/2 L 1/2 w = 18; r = 36 MRTS = MP L /MP K MP L = 2K 1/2 L -1/2 MP K = 2K -1/2 L 1/2 MRTS = K/L. = w/r = 18/36 = L = 2K . Cost Minimization in the Long-Run The firm’s optimal factor proportion (given technology and factor prices). Condition MRTS = w/r
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How much will it cost this firm to produce 10 units of output in the long-run? Q = 4K 1/2 L 1/2 L = 2K => Q = 4K 1/2 (2K) 1/2 = 4(2) 1/2 K Q = 4(2) 1/2 K => K = Q/[4(2) 1/2 ] Q = 5.66K => K = Q/5.66 For Q =10 => K = 1.77; L = 3.54 TC = wL + rK TC(Q=10) = 36(1.77)+18(3.54) = $127.28 Cost Minimization in the Long-Run To produce 10 units of output, we solve for K and L in terms of Q and substitute in the total cost function. Producing 10 units costs $127.28 . At this point, the firm is using 1.77 units of capital and 3.54 units of labor .
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How much will it cost this firm to produce Q units of output in the long-run? TC = 18L + 36K = 9Q/(2)1/2 + 9Q/(2)1/2 = 18/(2)1/2(Q) = 12.73Q MC = 12.73 = AC Cost Minimization in the Long-Run We can also solve for the firm’s long run total cost function for any level of output. Q = 4(2) 1/2 K K = Q/4(2) 1/2 L = Q/2(2) 1/2
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How much will it cost this firm to produce Q units of output in the long-run? TC = 18L + 36K = 9Q/(2) 1/2 + 9Q/(2) 1/2 = 18/(2) 1/2 (Q) TC = 12.73Q MC = 12.73 = AC Cost Minimization in the Long-Run We can also solve for the firm’s long run total cost function for any level of output. …with constant marginal and average cost .
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Cost Minimization Graphically: Q = 4K 1/2 L 1/2 w = 18; r = 36 Q $ In the SR, K = 16 TC sr = 576 + 18(Q/16) 2 Fixed Costs = rK = $576 TC lr = 12.73Q MC = 12.73 At this point, 16 units of capital is optimal. TC sr = minimum cost to produce various levels of Q; optimal labor utilization for a fixed K. TC lr = minimum cost to produce various levels of Q; all factors variable; optimal factor proportion
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Profit Maximization Graphically: Q = 4K 1/2 L 1/2 w = 18; r = 36 Q $ In the SR, K = 16 TC sr = 576 + 18(Q/16) 2 TC lr = 12.73Q MC = 12.73 How can the firm maximize its profits?
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Q $ TC lr MC TR = PQ To maximize profits, the firms finds Q where distance between TC and TR is greatest. the same slope.
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This note was uploaded on 12/09/2009 for the course ECON 1010 taught by Professor Neugeboren during the Fall '09 term at Harvard.

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ECE1010.05.post - UNIT II: FIRMS & MARKETS 10/15 Theory of...

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