e100_winter2010_lecture10_topost

e100_winter2010_lecture10_topost - Economies of Scale: Why?...

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Economies of Scale: Why? • Larger scale means workers can specialize at most productive activities • Larger scale may provide more flexibility, allow for different combinations of inputs • Larger scale may provide for some inputs to be purchased at lower cost (quantity discounts)
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Diseconomies of Scale: Why? • Shortage of factory space, fixed equipment (lower labor productivity) • Managing a larger firm may be complex, and inefficiencies develop • At some point, supplies of inputs may be limited (after volume discounts), costs rise
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Measure of Economies of Scale • Want to summarize relationship between expanding scale and cost of production • Consider elasticity of production costs with respect to quantity produced AC MC q C q C q q C C / / / /
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• MC/AC is a measure of economies of scale – If MC/AC = 1 have no economies (or diseconomies of scale) : costs increase proportionately with output – IF MC/AC < 1 have economies of scale: average costs are declining as q increases – IF MC/AC > 1 have diseconomies of scale: average costs are rising as q increases
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One more example: Production Function to Cost Function • Cobb-Douglas form of production function is very flexible, commonly used form • F(K,L) = AK α L β • Note that parameters of production function tell us something about nature of technology α,β< 1 guarantees decreasing marginal product
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• α + β < 1: decreasing returns to scale • α + β = 1: constant returns to scale • α + β > 1: increasing returns to scale • A gives measure of how much is produced • Find amount of capital & labor that minimizes cost of producing output q
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• Form Lagrangian: Φ = wL + rK – λ(AK α L β -q 0 ) take derivatives with respect to L,K and λ (16) (17) (18) 0 0 ) ( 0 ) ( 0 1 1 q L AK L AK r K L AK w L
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• Solve (16) for λ and substitute into (17) to get (20) or (21) L AK w L AK r 1 1 K w r L
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e100_winter2010_lecture10_topost - Economies of Scale: Why?...

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