PAM_2000_Spring_2009_Lecture_12

PAM_2000_Spring_2009_Lecture_12 - PAM 2000 Lecture 12...

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    PAM 2000 Lecture 12 Agenda: Input choice in the long run LRAC and SRAC Economies of Scope Competitive firms and markets
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    Input Choice in the Long-Run  Recall: Isoquants show the tradeoffs between K and L firm can make to produce the same constant amount of output Slope is the marginal technical rate of substitution Isocost show the combos of K and L that yield a constant input cost C = wQ L + rQ K
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    Input Choice in the Long-Run (con’t) Slope of isocost is –w/r Relative price of inputs Rate at which input prices allow the firm to trade inputs for each other
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    Input Choice in the Long-Run (con’t) Isocost differs from consumer’s budget line since the consumer only has one budget line, but the firm has many isocost lines Each corresponds to a different level of expenditure, different amounts of output Firm chooses the lowest cost way to produce a given level of output
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    Input Choice in the Long-Run (con’t) Firm will pick that bundle where the lowest isocost line is tangent to the relevant isoquant (so the isocost line moves down, not the isoquant ) This is the bundle where the isoquant and the isocost line are tangent
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    Cost Minimization
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    Input Choice in the Long-Run  (con’t) At the point of tangency, the slope of isoquant and isocost are equal, by definition Recall that slope of isoquant = MRTS = -MP L / MP K Slope of isocost is -w/r So at the tangency point, MP L /MP K = w/r
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    Input Choice in the Long-Run  (con’t) So firm picks a combination of K and L such that the rate at which the firm can substitute inputs in the production process is exactly the same as the rate at which it can trade K for L in the input market Can rewrite this as: MP L /w = MP K /r
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    Input Choice in the Long-Run (con’t) This is the “last dollar rule” (equi-marginal principle for consumer) Costs are minimized if inputs are chosen so that the last dollar spent on labor gives as much output as
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PAM_2000_Spring_2009_Lecture_12 - PAM 2000 Lecture 12...

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