Preface |
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vii | |
About the Author |
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xi | |
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xxi | |
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xxv | |
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1 Basic Notions of Production Functions |
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1 | (70) |
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1.1 Overview of the Production Function |
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1 | (30) |
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1.1.1 One Product, One-Variable Factor Relationship |
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4 | (4) |
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1.1.2 Elasticity of Production |
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8 | (2) |
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1.1.3 One Product, Two-Variable Factors |
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10 | (5) |
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1.1.3.1 Some typical multivariate production functions |
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15 | (2) |
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17 | (4) |
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1.1.4 Economic Consequences of the Production Function |
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21 | (10) |
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1.2 Definition of the Production Function |
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31 | (23) |
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1.2.1 Properties of the Production Function |
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32 | (3) |
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1.2.2 Law of Variable Proportions |
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35 | (2) |
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1.2.3 Elasticity of Scale |
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37 | (4) |
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1.2.4 Measures of Input Substitution |
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41 | (13) |
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1.3 Some Simple Production Mechanics |
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54 | (11) |
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1.3.1 Single Produce Primal Optimization |
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55 | (1) |
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1.3.1.1 Profit maximization |
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55 | (3) |
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1.3.1.2 Cost minimization |
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58 | (1) |
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1.3.2 Multiproduct Primal Functions |
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58 | (7) |
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65 | (1) |
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66 | (1) |
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66 | (5) |
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2 Estimation of the Primal |
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71 | (82) |
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2.1 Imputing the Parameters of a Production Function from Sample Means |
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72 | (3) |
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2.2 Estimation Using Ordinary Least Squares |
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75 | (6) |
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81 | (10) |
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2.3.1 Maximum Likelihood and Normality |
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83 | (2) |
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2.3.2 Estimating the Gamma Distribution |
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85 | (2) |
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2.3.3 Transformations to Normality |
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87 | (4) |
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91 | (11) |
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2.4.1 Indirect Least Squares |
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95 | (2) |
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2.4.2 Two-Stage Least Squares and Instrumental Variables |
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97 | (5) |
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2.5 Stochastic Production Functions |
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102 | (5) |
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2.6 Panel Data Estimation |
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107 | (15) |
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2.6.1 Analysis of Covariance |
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108 | (7) |
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2.6.1.1 Dummy variable formulation |
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115 | (1) |
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115 | (2) |
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2.6.2 Random Effects Models |
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117 | (5) |
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2.7 Other Considerations and Specifications |
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122 | (28) |
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2.7.1 Stochastic Error Functions |
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122 | (4) |
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2.7.1.1 Corrected ordinary least squares |
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126 | (1) |
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2.7.1.2 Modified ordinary least squares |
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127 | (3) |
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2.7.1.3 Maximum likelihood estimation |
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130 | (5) |
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2.7.2 Non-parametric Functions |
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135 | (1) |
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2.7.2.1 Fourier expansions |
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135 | (9) |
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2.7.2.2 Non-parametric regressions |
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144 | (6) |
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150 | (1) |
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151 | (1) |
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151 | (2) |
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3 Empirical Examples of the Primal |
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153 | (100) |
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3.1 The Problem with Data |
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155 | (53) |
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3.1.1 Aggregation Across Firms |
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156 | (16) |
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3.1.2 Aggregation of Inputs |
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172 | (18) |
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3.1.3 The Capital Question |
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190 | (6) |
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3.1.3.1 Multiple quasi-fixed assets |
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196 | (1) |
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3.1.3.2 Basic imputed value problem |
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197 | (2) |
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199 | (2) |
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201 | (1) |
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3.1.3.5 Estimates for continental United States |
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202 | (2) |
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3.1.3.6 Estimated shadow values based on Heartland |
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204 | (1) |
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3.1.3.7 Test for quasi-fixity |
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205 | (1) |
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206 | (2) |
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3.2 Production Functions in Agriculture |
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208 | (13) |
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3.3 Univariate Fitting of the Zellner Function --- Valuation of Precision Agriculture |
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221 | (28) |
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222 | (3) |
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3.3.2 Empirical application |
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225 | (3) |
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3.3.3 Application to precision agriculture |
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228 | (1) |
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3.3.3.1 Analysis based on the hyperbolic tangent production function |
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228 | (3) |
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3.3.3.2 Perfect separation |
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231 | (6) |
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3.3.3.3 Imperfect separation |
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237 | (4) |
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3.3.3.4 Using the Zellner and Cobb-Douglas specifications |
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241 | (8) |
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249 | (1) |
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249 | (1) |
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250 | (3) |
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4 Cost and Profit Functions |
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253 | (46) |
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4.1 Definition of the Cost Function |
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253 | (1) |
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4.2 Properties of the Cost Function |
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254 | (10) |
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4.2.1 Positive Cost of Production |
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256 | (1) |
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4.2.2 Higher Input Prices Imply Higher Cost |
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257 | (2) |
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4.2.3 Concavity of the Cost Function |
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259 | (2) |
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261 | (1) |
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261 | (3) |
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264 | (5) |
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4.4 The Duality Between Cost and Production Functions |
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269 | (22) |
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270 | (1) |
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4.4.1.1 Conditions on the Production Function |
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270 | (2) |
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4.4.1.2 Conditions on Production Possibility Sets L(y) |
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272 | (2) |
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4.4.1.3 Properties of the Cost Function |
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274 | (4) |
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278 | (1) |
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278 | (1) |
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279 | (5) |
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4.4.2.1 Shephard's Cost Function |
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284 | (7) |
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291 | (6) |
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4.5.1 Primal Approach to the Profit Function |
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291 | (1) |
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4.5.2 Starting with the Cost Function |
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292 | (1) |
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4.5.3 Properties of the Profit Function |
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292 | (1) |
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4.5.3.1 Properties of the Profit Function |
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292 | (1) |
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293 | (1) |
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294 | (2) |
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4.5.6 Le Chatelier--Samuelson Principle |
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296 | (1) |
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4.5.7 Dual Profit Function |
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296 | (1) |
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297 | (1) |
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298 | (1) |
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298 | (1) |
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5 Estimating Dual Relationships |
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299 | (80) |
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5.1 Flexible Functional Forms |
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299 | (6) |
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5.1.1 Generalized Second-Order Taylor Series Expansion |
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300 | (3) |
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303 | (2) |
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5.2 Estimation of Cost Systems |
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305 | (8) |
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5.2.1 Choice of Estimators |
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305 | (1) |
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5.2.2 Limits to Flexible Functional Forms |
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306 | (1) |
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306 | (2) |
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5.2.4 Imposing Restrictions |
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308 | (5) |
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5.3 Elasticities of Substitution |
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313 | (4) |
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5.4 Empirical Examples of Cost Specifications |
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317 | (59) |
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5.4.1 Quadratic Cost Function |
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317 | (22) |
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5.4.2 Normalized Quadratic Cost Function |
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339 | (4) |
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5.4.3 McFadden Cost Function |
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343 | (4) |
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5.4.4 Concepts of Subadditivity |
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347 | (2) |
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5.4.4.1 Measuring scope and scale economies in agricultural banking |
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349 | (2) |
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5.4.4.2 General formulation for the economies of scope and scale |
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351 | (1) |
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5.4.4.3 Quadratic example with pseudo-data |
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352 | (3) |
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5.4.4.4 Subadditivity and the translog |
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355 | (3) |
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5.4.4.5 Admissible region |
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358 | (1) |
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5.4.4.6 Application with agricultural productivity data |
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359 | (3) |
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5.4.4.7 Composite cost functions and subadditivity |
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362 | (2) |
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5.4.5 Estimating Revenue and Profit Functions |
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364 | (1) |
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5.4.5.1 Univariate revenue function |
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364 | (2) |
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5.4.5.2 Multioutput revenue function |
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366 | (1) |
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5.4.5.3 Empirical profit function |
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367 | (3) |
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5.4.6 Quasi-Fixed Inputs and Dual Cost Functions |
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370 | (1) |
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5.4.6.1 Empirical revenue function with quasi-fixed variable |
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370 | (3) |
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5.4.6.2 Quasi-fixed inputs and the profit function |
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373 | (3) |
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5.4.6.3 Quasi-fixed variables and the cost function |
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376 | (1) |
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376 | (1) |
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377 | (1) |
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377 | (2) |
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6 Technical Change and Efficiency |
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379 | (48) |
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6.1 The Economics of Technical Change |
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379 | (18) |
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6.1.1 Measuring Technical Change with Cost or Profit Functions |
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381 | (2) |
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6.1.2 Total Factor Productivity and Index Number Theory |
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383 | (6) |
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6.1.3 Valuing State-Level Research |
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389 | (1) |
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6.1.3.1 Cointegration estimator |
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390 | (2) |
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6.1.4 Technological Change and Factor Bias |
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392 | (5) |
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6.2 Measuring Economic Efficiency |
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397 | (26) |
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6.2.1 An Overview of Economic Efficiency |
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397 | (2) |
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6.2.1.1 Technical inefficiency |
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399 | (2) |
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6.2.1.2 Allocative inefficiency |
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401 | (2) |
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6.2.1.3 Total inefficiency |
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403 | (1) |
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6.2.2 Distance Function Formulations of Technical and Allocative Inefficiency |
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404 | (1) |
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6.2.2.1 Fare and Primont's approach to distance functions |
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405 | (3) |
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6.2.2.2 Properties of Debreu-Farrell measures of technical efficiency |
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408 | (3) |
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6.2.3 Parametric Estimation of Inefficiency --- Econometrics |
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411 | (12) |
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423 | (1) |
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424 | (1) |
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425 | (2) |
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7 Differential Models of Production |
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427 | (60) |
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7.1 Overview of the Differential Approach |
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428 | (12) |
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428 | (1) |
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7.1.2 Setting Up the Differential Formulation of Consumer Behavior |
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429 | (6) |
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7.1.3 Barten's Fundamental Matrix |
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435 | (5) |
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7.2 Differential Model of Production |
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440 | (30) |
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7.2.1 Derivation of the Single Product Input Demand Model |
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440 | (10) |
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7.2.2 Change in Marginal Cost of Production |
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450 | (5) |
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455 | (13) |
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7.2.4 Introduction of Quasi-Fixed Variables |
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468 | (2) |
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470 | (14) |
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7.3.1 Empirical Estimates Using Single Product Formulation |
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471 | (5) |
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7.3.2 Empirical Estimates Using Multiple Product Formulation |
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476 | (8) |
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484 | (1) |
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484 | (1) |
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485 | (2) |
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8 Topics and Applications |
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487 | (22) |
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8.1 An Economist's Lament --- A State-Space Approach to Production Functions |
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487 | (10) |
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8.1.1 Deriving the State-Space Production Function |
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488 | (5) |
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8.1.2 Beyond Economic Abstraction |
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493 | (1) |
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8.1.2.1 Variations in soil types |
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493 | (4) |
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8.2 Non-Normality and the Cost Function |
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497 | (3) |
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8.3 Derived Demand for Corn in the Production of Ethanol |
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500 | (6) |
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8.3.1 Data and Econometric Methods |
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503 | (1) |
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503 | (3) |
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506 | (3) |
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9 Conclusions and Suggestions for Further Research |
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509 | (8) |
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9.1 Reduction of the Production Decisions to Time |
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510 | (2) |
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9.2 Estimating the Production Function |
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512 | (2) |
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9.3 Misspecification of the Dual |
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514 | (2) |
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516 | (1) |
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Appendix A Closed-Form Solutions |
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517 | (4) |
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517 | (4) |
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Appendix B Numerical Approximations and Methods |
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521 | (6) |
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B.1 Approximating a Production Function with a Quadratic |
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521 | (2) |
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B.2 A Quick Primer on Numeric Optimization |
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523 | (4) |
Glossary |
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527 | (4) |
References |
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531 | (10) |
Index |
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541 | |