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

The Organization of ProductionInputsLabor, Capital, LandFixed InputsVariable InputsShort RunAt least one input is fixedLong RunAll inputs are variable

Q = f(L, K)Production Function With Two Inputs

Production Function With Two InputsDiscrete Production Surface

Continuous Production SurfaceProduction Function With Two Inputs

Production FunctionWith One Variable InputTotal ProductMarginal ProductAverage ProductProduction or Output ElasticityTP = Q = f(L)

Production FunctionWith One Variable InputTotal, Marginal, and Average Product of Labor, and Output Elasticity

Production Function With One Variable Input

Production Function With One Variable Input

Optimal Use of the Variable InputMarginal Revenue Product of LaborMRPL = (MPL)(MR)Marginal Resource Cost of LaborMRCL = w =Optimal Use of LaborMRPL = MRCL

Use of Labor is Optimal When L = 3.50Optimal Use of the Variable Input

Optimal Use of the Variable Input

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

Production With Two Variable InputsIsoquants show combinations of two inputs that can produce the same level of output.

Unitsof K402010 6 4Unitsof L 512203050Point ondiagramabcdeaUnits of capital (K)Units of labour (L)An isoquant

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:

Marginal Rate of Technical SubstitutionMRTS = -K/L = MPL/MPKProduction With Two Variable InputsHome work: Show this using Production function

Production With Two Variable InputsMRTS = -(-2.5/1) = 2.5

IsoquantsProduction With Two Variable Inputs

Economic Region of ProductionProduction With Two Variable Inputs

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.

Perfect SubstitutesPerfect Complements: Fixed Coefficient TechnologyProduction With Two Variable Inputs

Optimal Combination of InputsIsocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.

Units of labour (L)Units of capital (K)Assumptions

r = Rs.20 000 w = Rs10 000TC = Rs 300000TC = Rs300000aAn isocost

Optimal Combination of InputsIsocost LinesABC = 100, w = r = 10ABC = 140, w = r = 10ABC = 80, w = r = 10AB*C = 100, w = 5, r = 10

Optimal Combination of InputsMRTS = w/r

Optimal Combination of InputsEffect of a Change in Input Prices

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.

Returns to ScaleConstant Returns to Scale (CRS)Increasing Returns to Scale (IRS)Decreasing Returns to Scale (DRS)

Empirical Production FunctionsCobb-Douglas Production FunctionQ = AKaLbEstimated using Natural Logarithmsln Q = ln A + a ln K + b ln L

d(K/L)/(K/L)s = --------------------------- d(MRTS)/MRTSElasticity of Substitution (s)

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

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.

Innovations and Global CompetitivenessProduct InnovationProcess InnovationProduct Cycle ModelJust-In-Time Production SystemCompetitive BenchmarkingComputer-Aided Design (CAD)Computer-Aided Manufacturing (CAM)

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