ProductionBook-08-24 - Production Economics An Empirical...

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Production Economics: An Empirical Approach Quantifying Production Relationships v0.10 Charles B. Moss
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Contents List of illustrations page vi List of tables vii PART ONE THE PRIMAL APPROACH 1 1 Basic Notions of Production Functions 3 1.1 Overview of the Production Function 4 1.1.1 One Product, One-Variable Factor Rela- tionship 6 1.1.2 Elasticity of Production 9 1.1.3 One Product, Two Variable Factors 12 1.1.4 Economic Consequences of the Production Function 17 1.2 Production Function Defined 19 1.2.1 Properties of the Production Function 19 1.2.2 Law of Variable Proportions 22 1.2.3 Elasticity of Scale 23 1.2.4 Measures of Input Substitution 27 1.3 Some Simple Production Mechanics 35 1.3.1 Single Produce Primal Optimization 35 1.3.2 Multiproduct Primal Functions 37 2 Estimation of the Primal 39 2.1 Estimation Using Ordinary Least Squares 39 2.2 Simultaneity 41 2.2.1 Indirect Least Squares 44 2.2.2 Two-Stage Least Squares and Instrumental Variables 46 iii
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iv Contents 2.2.3 Maximum Likelihood Estimators 51 2.3 Stochastic Production Functions 51 2.4 Panel Data Estimation 54 2.4.1 Analysis of Covariance 55 2.4.2 Random Effects Models 63 2.5 Other Considerations and Specifications 67 2.5.1 Stochastic Error Functions 67 2.5.2 Nonparametric Functions 73 3 Empirical Examples of the Primal 75 3.1 Multiple Quasi-Fixed Assets 75 3.1.1 Basic Imputed Value Problem 76 3.1.2 Empirical Model 78 3.1.3 Data 80 3.1.4 Results 81 3.1.5 Implications 84 3.2 Euler Theorem and Land Values 85 3.3 Univariate Fitting of the Zellner Function 86 3.3.1 Estimation 88 3.3.2 Empirical Application 90 3.3.3 Implications 91 PART TWO THE DUAL APPROACH 93 4 Cost and Profit Functions 95 4.1 The Cost Function Defined 95 4.2 Properties of the Cost Function 96 4.2.1 Discussion of Properties 97 4.2.2 Comparative Statics 103 4.3 The Duality Between Cost and Production Functions 108 4.3.1 Diewert’s Proof 108 4.3.2 Shephard’s Proof 115 5 Estimating Dual Relationships 123 5.1 Flexible Functional Forms 123 PART THREE TECHNICAL EFFICIENCY AND DIFFERENTIAL MODELS 127 6 Technical Change and Efficiency 129
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Contents v 7 Differential Models of Production 130 8 A Review of Empirical Studies 131 PART FOUR LAST THOUGHTS 133 9 Conclusions and Suggestions for Further Research 135 Appendix A Closed Form Solutions 137 Appendix B Numerical Approximations and Methods 138 Notes 141 References 142 Author index 143 Subject index 144
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Illustrations 1.1 Three Production Functions 7 1.2 Production Function for Average Yield 8 1.3 Average and Marginal Physical Product Graphs 9 1.4 Stages of Production on Total Physical Product Graph 10 1.5 Factor Elasticity for the Zellner Function 11 1.6 Factor Elasticity for a Quadratic Production Function 11 1.7 Production of a Single Output with Two Inputs 12 1.8 Isoquants Between Two Inputs 15 1.9 Isoquants, Isoclines, and Ridge Lines 16 1.10 Concavity 20 1.11 Level Sets 22 1.12 Elasticity of Scale 24 1.13 Elasticity of Scale 26 4.1 Minimizing Cost with a Level Set 98 4.2 Dual Frontier 99 4.3 Relationship Between Average and Marginal Cost 107 4.4 Definition of the Distance Function 118 4.5 Cost Minimization subject to the Distance Function 119 4.6 Relationship between Level Set and Cost Function 120 B.1 Transcendental Production Function with Two Inputs 139 vi
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