nlecture10 - cost

nlecture10 - cost - Topic 5: Production (2) Cost...

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opic 5: Production (2) Topic 5: Production (2) Cost minimization USC Marshall
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Cost minimization • Having described the production technology, we can now consider the costs of production • The cost of producing Q units is simply the amount of capital and labor needed times their price: C rK wL – We call this the isocost line, analogous to budget constraint – Of course, a firm is not tied to a given cost level. But it still wants to produce any quantity at the west cost possible USC Marshall lowest cost possible
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Cost minimization • Sometimes undertaking any production requires a fixed capital outlay, even in the long-run. We call this outlay an avoidable fixed cost, FC. It simply shifts the total cost curve upwards by a fixed amount. – An avoidable fixed cost is any cost incurred by the rm that is dependent of the scale of firm that is independent of the scale of production but has to be paid to undertake any production. • Minimum size of a factory , phone line, computer,… USC Marshall C rK wL F
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Cost minimization Short run: the firm has a fixed level of capital but can adjust its level of labor – Ability to optimize production is limited Long run: the firm can adjust both capital and labor levels – Want the minimum-cost combination of labor and capital to produce Q* units of output USC Marshall
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Cost minimization Short run: – The level of capital is fixed. The compensation for capital is thus a fixed cost – Sunk or avoidable? • If they payment has already been made and it cannot be resold (approximately the definition of short n) then it is a sunk cost a short-run), then it is a sunk cost USC Marshall
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Cost minimization Short-run (total) cost of production: – The firm is stuck at a given level of capital. • The capital is a (sunk) fixed cost – But the firm is free to alter the amount of labor it hires • Labor is a variable cost Q F K , L L Q – The amount of L needed to produce Q units of output is given by L(Q) – The short-run total cost of production is then: C r K wL Q USC Marshall fixed variable
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Cost minimization • Measures of short-run costs: – Instead of using the costs on the previous slide, more useful to look at three different measures: Short-run marginal cost: • Short-run average total cost: SMC Q dSTC Q dQ • Short-run average variable cost: SATC Q STC Q Q Defined for any given level of capital SAVC Q STVC Q Q USC Marshall
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Cost minimization Example: Suppose your production function is given by , so that the marginal Q 5 K 1/2 L productivities are MP L 5 K and K 5 L •S u ppose that the wage rate is w and the rental L K rate of capital is r . Derive the short-run total cost and marginal cost functions USC Marshall
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Cost minimization STC(K) _ $ $ STFC Q Q USC Marshall
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Cost minimization STC(K) _ $ $ $ 1 STFC Q Q Q 1 USC Marshall
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Cost minimization STC(K) _ $ $ SATC 1 = $ 1 /Q 1 $ 1 STFC Q Q Q 1 USC Marshall
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Cost minimization STC(K) _ $ $ SAVC 1 = ($ 1 -STFC)/Q 1 $ 1 STFC Q Q Q 1 USC Marshall
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Cost minimization STC(K) _ $ $ SMC 1 =dSTC/dQ $ 1 STFC Q Q Q 1 USC Marshall
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Cost minimization STC(K) _ $ $ $ 1 STFC Q Q Q 2 USC Marshall
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Cost minimization STC(K) _ $ $ $ 2 SATC 2 STFC Q Q Q 2 USC Marshall
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Cost minimization STC(K) _ $ $ $ 2 SAVC 2 STFC Q Q Q 2 USC Marshall
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Cost minimization STC(K) _ $ $ $ 2 SMC STFC Q Q Q 2 USC Marshall
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Cost minimization STC(K) _ $ $ $ 3 STFC Q Q Q 3 USC Marshall
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Cost minimization STC(K) _ $ $ $ 3 SATC STFC Q Q Q 3 USC Marshall
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Cost minimization STC(K) _ $ $ $ 3 SAVC STFC Q Q Q 3 USC Marshall
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Cost minimization STC(K) _ $ $ $ 3 SMC STFC Q Q Q 3 USC Marshall
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Cost minimization STC(K) _ $ $ $ 4 STFC Q Q Q 4 USC Marshall
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Cost minimization STC(K) _ $ $ $ 4 STFC Q Q Q 4 USC Marshall
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Cost minimization STC(K) _ $ $ $ 4 STFC Q Q Q 4 USC Marshall
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Cost minimization STC(K) _ $ $ $ 4 STFC Q Q Q 4 USC Marshall
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Cost minimization STC(K) _ $ $ SMC $ 4 SATC STFC SAVC Q Q Q 4 USC Marshall
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This note was uploaded on 03/09/2009 for the course BUAD 351 taught by Professor Eastin during the Spring '07 term at USC.

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nlecture10 - cost - Topic 5: Production (2) Cost...

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