Production Analysis
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Transcript of Production Analysis
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Topic 3.1
Production Function Theory and Estimation
(Pl. read the prescribed chapter & cases given in it before coming for the class)
Ref: Chapter 6
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The Organization of ProductionInputsLabor, Capital, LandFixed InputsVariable InputsShort RunAt least one input is fixedLong RunAll inputs are variable
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Q = f(L, K)Production Function With Two Inputs
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Production Function With Two InputsDiscrete Production Surface
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Continuous Production SurfaceProduction Function With Two Inputs
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Production FunctionWith One Variable InputTotal ProductMarginal ProductAverage ProductProduction or Output ElasticityTP = Q = f(L)
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Production FunctionWith One Variable InputTotal, Marginal, and Average Product of Labor, and Output Elasticity
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Production Function With One Variable Input
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Production Function With One Variable Input
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Optimal Use of the Variable InputMarginal Revenue Product of LaborMRPL = (MPL)(MR)Marginal Resource Cost of LaborMRCL = w =Optimal Use of LaborMRPL = MRCL
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Use of Labor is Optimal When L = 3.50Optimal Use of the Variable Input
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Optimal Use of the Variable Input
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Empirical Evidence
Labour Productivity and Total compensation in the U.S. and other G7 CountriesProdtvty Wage USG7
1981-19959.29.01.22.2
1996-20002.31.4
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Production With Two Variable InputsIsoquants show combinations of two inputs that can produce the same level of output.
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Unitsof K402010 6 4Unitsof L 512203050Point ondiagramabcdeaUnits of capital (K)Units of labour (L)An isoquant
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Diminishing marginal rate of factor substitution: (or marginal rate of technical substitution)Units of capital (K)Units of labour (L)ghjkDK = 2DL = 1DK = 1DL = 1isoquantMRTS = 2MRTS = 1MRTS = DK / DL
Sheet:
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Marginal Rate of Technical SubstitutionMRTS = -K/L = MPL/MPKProduction With Two Variable InputsHome work: Show this using Production function
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Production With Two Variable InputsMRTS = -(-2.5/1) = 2.5
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IsoquantsProduction With Two Variable Inputs
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Economic Region of ProductionProduction With Two Variable Inputs
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Firms will only use combinations of two inputs that are in the economic region of production, which is defined by the portion of each isoquant that is negatively sloped.
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Perfect SubstitutesPerfect Complements: Fixed Coefficient TechnologyProduction With Two Variable Inputs
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Optimal Combination of InputsIsocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.
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Units of labour (L)Units of capital (K)Assumptions
r = Rs.20 000 w = Rs10 000TC = Rs 300000TC = Rs300000aAn isocost
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Optimal Combination of InputsIsocost LinesABC = 100, w = r = 10ABC = 140, w = r = 10ABC = 80, w = r = 10AB*C = 100, w = 5, r = 10
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Optimal Combination of InputsMRTS = w/r
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Optimal Combination of InputsEffect of a Change in Input Prices
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Returns to ScaleProduction Function Q = f(L, K)Q = f(hL, hK)If = h, then f has constant returns to scale.If > h, then f has increasing returns to scale.If < h, the f has decreasing returns to scale.
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Returns to ScaleConstant Returns to Scale (CRS)Increasing Returns to Scale (IRS)Decreasing Returns to Scale (DRS)
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Empirical Production FunctionsCobb-Douglas Production FunctionQ = AKaLbEstimated using Natural Logarithmsln Q = ln A + a ln K + b ln L
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d(K/L)/(K/L)s = --------------------------- d(MRTS)/MRTSElasticity of Substitution (s)
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Production Function Q = f(L, K)Let Q = d LaKbMP for L and K: a (APL), b (APK)MRTSElasticity of Substitution = s d(K/L)/(K/L)s = --------------------------- d(MRTS)/MRTS
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Returns to Scale - Example Production Function Q = 10L0.4K0.9Compute Production elasticity w.r.t. L Compute Production elasticity w.r.t. K What can we say about the RTS?Find Elasticity of Substitution.
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Innovations and Global CompetitivenessProduct InnovationProcess InnovationProduct Cycle ModelJust-In-Time Production SystemCompetitive BenchmarkingComputer-Aided Design (CAD)Computer-Aided Manufacturing (CAM)
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