MIT1_201JF08_lec10

MIT1_201JF08_lec10 - Transportation Costs Moshe Ben-Akiva...

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Transportation Costs Moshe Ben-Akiva 1.201 / 11.545 / ESD.210 Transportation Systems Analysis: Demand & Economics Fall 2008
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Review: Theory of the Firm Basic Concepts Production functions – Isoquants – Rate of technical substitution Maximizing production and minimizing costs – Dual views to the same problem Average and marginal costs 2
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Outline Long-Run vs. Short-Run Costs Economies of Scale, Scope and Density Methods for estimating costs 3
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Long-Run Cost All inputs can vary to get the optimal cost Because of time delays and high costs of changing transportation infrastructure, this may be a rather idealized concept in many systems 4
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Short-Run Cost Some inputs ( Z ) are fixed (machinery, infrastructure) and some ( X ) are variable (labor, material) C ( q ) = W Z Z + W X X ( W , q , Z ) W X ( W , q , Z ) W Z Z X MC ( q ) = = 0 q q 5
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Long-Run Cost vs. Short-Run Cost Long-run cost function is identical to the lower envelope of short- run cost functions AC AC 1 LAC AC 4 AC 3 AC 2 q 6
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Outline Long-Run vs. Short-Run Costs Economies of Scale, Scope and Density Methods for estimating costs 7
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Economies of Scale C(q+ Δ q) < C(q) + C( Δ q) cost MC < AC AC MC q Economies of scale are not constant. A firm may have economies of scale when it is small, but diseconomies of scale when it is large. 8
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Example: Cobb-Douglas Production Function Are there economies of scale in the production? Production function approach: – K – capital – L – labor q = α K a L b F c – F – fuel Economies of scale: a+b+c > 1 Constant return to scale: a+b+c = 1 Diseconomies of scale: a+b+c < 1 9
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Example (cont) Long-run cost function approach – The firm minimizes expenses at any level of production – Production expense: E = W K K + W L L + W F F W K - unit price of capital (e.g. rent) W L - wages rate W F - unit price of fuel – Production cost: C ( q ) = min E s . t . α K a L b F c = q 10
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Example (cont) Finding the optimal solution: – Lagrangean function: W K K + W L L + W F F + λ ( q α K a L b F c ) – Solution: ( a + b + c ) ( a + b + c ) W ( a + b + c ) W ( a + b + c ) C = β q 1 W K a L b F c 11
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Example (cont) The logarithmic transformation of the cost function: ln C = d 0 + d 1 ln q + d 2 ln W K + d 3 ln W L + d 4 ln W F d 1 = 1/(a+b+c) d 2 = a/(a+b+c) d 3 = b/(a+b+c) d 4 = c/(a+b+c) Properties: – Can be estimated using linear regression (linear in the parameters) d 1 represents the elasticity of cost w.r.t output – Economies of scale if d 1 < 1 (i.e. a+b+c > 1) – Cost function is linearly homogenous in input prices Intuition: If all input prices double, the cost of producing at a constant level should also double ( d 2 + d 3 + d 4 = 1) 12
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Economies of Scope Cost advantage in producing several different products as opposed to a single one C(q1,q2) < C(q1,0) + C(0,q2) – The cost function needs to be defined at zero 13
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MIT1_201JF08_lec10 - Transportation Costs Moshe Ben-Akiva...

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