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ECS1010.04.post

# ECS1010.04.post - UNIT II Firms Markets 7/1 Theory of the...

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UNIT II: Firms & Markets 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)
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 ( Π 29 = 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
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
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
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.
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 = 18L + 36K = 9Q/(2) 1/2 + 9Q/(2) 1/2 = 18/(2) 1/2 (Q) = 12.73Q MC = 12.73 = AC We can solve for the firm’s long run total cost function for any level of output.

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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.
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ECS1010.04.post - UNIT II Firms Markets 7/1 Theory of the...

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