Kinh tế học - Chapter 10: Production & cost estimation

Chapter 10Production & Cost EstimationEmpirical 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 as2Properties of a Short-Run Cubic Production FunctionHolding capital constant, short-run cubic production function is derived as follows:3Properties of a Short-Run Cubic Production FunctionThe average & marginal products of labor are, respectively:4Properties of a Short-Run Cubic Production FunctionMarginal product of labor begins to diminish beyond Lm units of labor•5MP & AP Curves for the Short-Run Cubic Production Function (Figure 10.1)Q = AL3 + BL26Properties of a Short-Run Cubic Production FunctionTo have necessary properties of a production function, parameters must satisfy the following restrictions:7Estimation 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 routine8Estimation of a Short-Run Cost FunctionEstimate using data for which the level of usage of one or more inputs is fixedUsually time series data are usedData 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/lossesMust eliminate effects of inflationDivide by appropriate price index9Properties of a Short-Run Cubic Cost FunctionAverage variable cost & marginal cost functions are, respectively:10Properties of a Short-Run Cubic Cost FunctionAverage variable cost reaches its minimum value at:To conform to theoretical properties, parameters must satisfy the following restrictions:11Properties of a Short-Run Cost FunctionCubic specification produces S-shaped TVC curve & U-shaped AVC & SMC curvesAll 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 equation12Summary of Short-Run Empirical Production FunctionsShort-run cubic production equationsTotal productAverage product of laborMarginal product of laborDiminishing marginal returnsRestrictions on parameters13Summary of Short-Run Empirical Cost FunctionsShort-run cubic cost equationsTotal variable costAverage variable costMarginal costAverage variable cost reaches minimum atRestrictions on parameters14