This monograph is intended as a contribution to applied work in production theory by treating: a) The measurement problems involved whenever several outputs are jointly produced, and b) The (possible) econometric framework for estimating production function parameters whenever (relative) prices vary sufficiently over the observations. Thus, the "pure" theory of production, and the theory of non-linear regression is not treated in sufficient detail: for these topics we refer to the available literature~ for a comprehensive list of references we refer to Uebe (1975). Some years ago, papers by L. J. Lau and W. E. Diewert initiated my interest in duality within production theory, and then I started to appreciate R. W. Shephard's fundamental contribution to this topic. This monograph is a (minor) revision of a Ph. D. dissertation submitted to the Department of Economics, The University of Wisconsin, Madison, in August 1973. The Graduate School and the Social Systems Research Institute provided funds for the reported computer work, Lawrence R. Klein and Laurits R. Christensen provided data, and as a Graduate Student I received financial support in form of an University Fellowship~ all this is very much appreciated. With some nostalgia I think back to the enjoyable period of learning during the preparation of my diFosertation~ I appreciate the spirit within the department, and the guidance of my committee Arthur S. Goldberger, Dennis J. Aigner, and Laurits R. Christensen.

Inhalt

One Introduction.- Two Multiple-Output Production Functions.- A. Introduction.- B. Basic Theory of Production.- 1. Notation.- 2. Long-run profit function.- 3. Short-run profit function.- a) Cost Function.- b) Revenue Function.- 4. Interpretation of ?*.- C. Almost-Homogeneity and Separability.- 1. Notation.- 2. Almost homogeneity.- 3. Separability.- 4. Implications.- D. The Treatment of Raw Materials in Production Theory - or Subaggregation of Inputs.- 1. Weakly separable forms of the input function.- 2. Partial Leontief input function.- 3. General comment.- E. Subaggregation of Outputs.- 1. Weakly separable form of the output function.- 2. Partial Leontief output function.- F. Conclusions.- Three Functional Forms for Multiple-Output Technologies.- A. Introduction.- B. Input Functions.- 1. Cobb-Douglas input function.- a) Notation.- b) The derived (long-run) cost function.- c) The derived (short-run) cost function.- d) The derived profit function.- 2. Constant-Elasticity-of-Substitution input function.- a) Notation.- b) The derived (long-run) cost function.- c) The derived (short-run) cost function.- d) The derived profit function.- C. Output Functions.- 1. Constant-Elasticity-of-Transformation output function.- a) Notation.- b) The derived (long-run) revenue function.- c) The derived profit function.- 2. Quadratic output function.- a) Notation.- b) The derived revenue and profit function.- 3. Generalized output function.- D. Separable Multiple-Output Production Functions.- 1. Models with a CD input function.- a) Model 1: CET output - CD input.- b) Model 2: DQ output - CD input.- c) Model 3: GO output - CD input.- 2. Models with a CES input function.- a) Model 4: CET output - CES input.- b) Model 5: DQ output - CES input.- c) Model 6: GQ output - CES input.- E. Nonseparable Multiple-Output Production Functions.- 1. Log-Quadratic (or translog).- a) Production function.- b) Profit function.- c) Cost function.- 2. Diewert.- a) Production function.- b) Profit function.- c) Cost function.- Appendix: Algebraic Derivation of Aggregate Variables.- 1. Aggregate price variable for the CD input function.- a) Long-run cost function.- b) Short-run cost function.- 2. Aggregate price variable for the CES input function and CET output function.- a) The cost function for the CES function.- b) The revenue function for the CET output function.- 3. Aggregate price variable for the DQ output function.- Four Stochastic Specification.- A. Introduction.- B. The Stochastic System of output Supply and Input Demand.- 1. Basic framework.- 2. Interpretation of the stochastic specification.- C. Stochastic Profit and Cost Functions.- 1. General remarks.- 2. Stochastic profit.- 3. Stochastic cost.- D. Estimation.- 1. Notation.- 2. Properties of estimator.- 3. Computational aspects.- Five Empirical results.- A. Introduction.- B. Cross-Section Data for U.S. Railroads.- 1. Characteristics of the data.- 2. Formulation of empirical work.- 3. Results of empirical work with the (logarithmic) input demand system.- 4. Interpretation of estimation results using the input demand system.- 5. Result of empirical work with the cost function.- 6. Comparison with Klein's result.- C. Time Series Data for U.S. Economy.- 1. Characteristics of the data.- 2. Formulation of empirical work.- 3. Result of empirical work with the input demand system.- 4. Interpretation of estimation results using the input demand system.- 5. Result of empirical work with the cost function.- 6. Comparison with results in Christensen et.al..