Bài giảng Managerial Economics - Chapter 010: Production and Cost Estimation

Chapter 10: Production and Cost EstimationMcGraw-Hill/IrwinCopyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.Empirical Production FunctionAn empirical production function is the mathematical form of the production function to be estimatedEmpirical Production FunctionLong-run production functionA production function in which all inputs are variableShort-run production functionA production function in which at least one input is fixedEmpirical Production FunctionCubic empirical specification for a short-run production function is derived from a long-run cubic production functionCubic form of the long-run production function is expressed asProperties of a Short-Run Cubic Production FunctionHolding capital constant, short-run cubic production function is derived as follows:The average & marginal products of labor are, respectively:Properties of a Short-Run Cubic Production FunctionMarginal product of labor begins to diminish beyond Lm units of laborAverage product of labor begins to diminish beyond La units of laborProperties of a Short-Run Cubic Production FunctionMP & AP Curves for the Short-Run Cubic Production Function (Figure 10.1)Q = AL3 + BL2To have necessary properties of a production function, parameters must satisfy the following restrictions: A 0Properties of a Short-Run Cubic Production FunctionEstimation of a Short-Run Production FunctionTo use linear regression analysis, the cubic equation must be transformed into linear formQ = AX + BWWhere X = L3 and W = L2Estimated regression line must pass through the originSpecify in computer routineEstimate using data for which the level of usage of one or more inputs is fixedUsually time series data are usedEstimation of a Short-Run Production FunctionData collection may be complicated by the fact that accounting data do not include firm’s opportunity costsCapital costs should reflect not only acquisition cost but any foregone rental income, depreciation, & capital gains/lossesEstimation of a Short-Run Production FunctionNominal cost dataData that have not been corrected for the effects of inflationMust eliminate effects of inflationCorrect for the influence of inflation by dividing nominal cost data by an appropriate price index (or implicit price deflator)Estimation of a Short-Run Production FunctionAverage variable cost & marginal cost functions are, respectively:Properties of a Short-Run Cubic Cost FunctionAverage variable cost reaches its minimum value at:Properties of a Short-Run Cubic Cost FunctionTo conform to theoretical properties, parameters must satisfy the following restrictions: a > 0, b 0Properties of a Short-Run Cubic Cost FunctionCubic specification produces S-shaped TVC curve & U-shaped AVC & SMC curvesProperties of a Short-Run Cubic Cost FunctionAll three cost curves employ the same parametersOnly necessary to estimate one of these functions to obtain estimates of all threeIn the short-run cubic specification, input prices are assumed constantNot explicitly included in cost equationProperties of a Short-Run Cubic Cost FunctionSummary of Short-Run Empirical Production FunctionsShort-run cubic production equationsTotal productAverage product of laborMarginal product of laborDiminishing marginal returnsRestrictions on parameters A 0Summary of Short-Run Empirical Cost FunctionsShort-run cubic cost equationsTotal variable costAverage variable costMarginal costAverage variable cost reaches minimum atRestrictions on parametersa > 0, b 0