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)
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
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
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
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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