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Multi-Output Production and Duality : Theory and Applications - Rolf Fare

Multi-Output Production and Duality

Theory and Applications


Published: 31st December 1994
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Our original reason for writing this book was the desire to write down in one place a complete summary of the major results in du­ ality theory pioneered by Ronald W. Shephard in three of his books, Cost and Production Functions (1953), Theory of Cost and Produc­ tion Functions (1970), and Indirect Production Functions (1974). In this way, newcomers to the field would have easy access to these important ideas. In adg,ition, we report a few new results of our own. In particular, we show the duality relationship between the profit function and the eight equivalent representations of technol­ ogy that were elucidated by Shephard. However, in planning the book and discussing it with colleagues it became evident that such a book would be more useful if it also provided a number of applications of Shephard's duality theory to economic problems. Thus, we have also attempted to present exam­ ples of the use of duality theory in areas such as efficiency measure­ ment, index number theory, shadow pricing, cost-benefit analysis, and econometric estimation. Much of our thinking about duality theory and its uses has been influenced by our present and former collaborators. They include Charles Blackorby, Shawna Grosskopf, Knox Lovell, Robert Russell, and, not surprisingly, Ronald W. Shephard. We have also benefit­ ted over the years from many discussions with W. Erwin Diewert.

List of Figures
Theories of the Firm through Dualityp. 1
The Different Behavioral Assumptionsp. 2
Using Duality Theory to Overcome Data Problemsp. 3
The Completion of Ronald W. Shephard's Dualityp. 4
Distance Functionsp. 7
Input and Output Distance Functionsp. 7
Efficiency Measurementp. 28
Quantity Index Applicationsp. 36
Modelling Returns to Scalep. 38
Cost and Revenue Functionsp. 43
Duality Theoremsp. 43
Derivative Properties of Cost and Revenue Functionsp. 51
Shadow Pricing of Inputs and Outputsp. 54
Overall Efficiency Measurementp. 59
Price Indexesp. 66
Inverse Homotheticityp. 69
Indirect Distance Functionsp. 79
Cost and Revenue Constrained Firmsp. 79
Dualitiesp. 87
Derivative Properties of the Indirect Distance Functionsp. 91
Nonparametric Testingp. 94
Indirect Cost and Revenue Functionsp. 99
Duality Theoremsp. 99
Derivative Propertiesp. 113
Cost Benefit Analysisp. 117
The Profit Functionp. 123
Duality Theoremsp. 123
The Profit, Cost, and Revenue Functionsp. 135
The Profit, Indirect Input Distance and Indirect Output Distance Functionsp. 140
The Profit, Indirect Cost and Indirect Revenue Functionsp. 142
Towards Empirical Applicationsp. 147
Monotonicity, Homogeneity and Convexityp. 151
Homogeneous and Inversely Homothetic Technologiesp. 152
Functional Formsp. 155
Referencesp. 161
Subject Indexp. 169
Author Indexp. 171
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792395188
ISBN-10: 0792395182
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 172
Published: 31st December 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.13 x 16.51  x 1.27
Weight (kg): 0.43