ECS1010.04.post

ECS1010.04.post - UNIT II: Firms & Markets 7/1 Theory...

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UNIT II: Theory of the Firm Profit Maximization Perfect Competition/Review 7/15 MIDTERM 7/1
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Profit Maximization Last Time The Short-Run and the Long-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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Profit Maximization The firm wants to maximize this difference: Profit ( Π29 = Total Revenue(TR) – Total Cost(TC) TR(Q) = PQ TC(Q) = rK + wL P Price L Labor Q Quantity K Capital w Wage Rate r Rate on Capital Q = f(K,L) Revenue Cost
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Last time: we considered a firm that produces output according to the following production function. Q = 4K ½ L ½ and w = $18 and r = $36. How much will it cost this firm to produce 10 units of output in the long-run? Q units? Profit Maximization
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Last time: we considered a firm that produces output according to the following production function. Q = 4K ½ L ½ and w = $18 and r = $36. How much will it cost this firm to produce 10 units of output in the long-run? Q units? The long-run total cost curve (TC(Q)) represents the minimum cost to produce Q units of output. Profit Maximization
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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).
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Cost Minimization in the Long-Run L* L K K* Q = 10 How much will it cost this firm to produce 10 units of output in the long-run? L = 2K Tangency between the isoquant and an isocost curve shows the economically efficient combination K*, L*. Hence, the condition for optimal factor proportion is: MRTS = w/r
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Cost Minimization in the Long-Run L* L K K* Q = 10 How much will it cost this firm to produce 10 units of output in the long-run? L = 2K The condition for optimal factor proportion is: MRTS = w/r . This is LR condition! Why? Because some factors (K) are fixed in the SR .
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Cost Minimization in the Long-Run L* L K K* Q = 10 How much will it cost this firm to produce 10 units of output in the long-run? L = 2K Another way to think about this: TC is a projection of the firm’s long-run output expansion path : the locus of optimal factor bundles (K,L) for different levels of Q.
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Cost Minimization in the Long-Run K K* Q = 10 How much will it cost this firm to produce 10 units of output in the long-run? TC
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This note was uploaded on 06/29/2010 for the course ECON ECON 1010 taught by Professor Robert during the Summer '10 term at Harvard.

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ECS1010.04.post - UNIT II: Firms & Markets 7/1 Theory...

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