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.
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ISBN-13
978-94-011-0651-1 (9789401106511)
DOI
10.1007/978-94-011-0651-1
Schweitzer Klassifikation
1 Theories of the Firm Through Duality.- 1.1 The Different Behavioral Assumptions.- 1.2 Using Duality Theory to Overcome Data Problems.- 1.3 The Completion of Ronald W. Shephard's Duality.- 1.4 Remarks on the Literature.- 2 Distance Functions.- 2.1 Input and Output Distance Functions.- 2.2 Efficiency Measurement.- 2.3 Quantity Index Applications.- 2.4 Modelling Returns to Scale.- 2.5 Remarks on the Literature.- 3 Cost and Revenue Functions.- 3.1 Duality Theorems.- 3.2 Derivative Properties of Cost and Revenue Functions.- 3.3 Shadow Pricing of Inputs and Outputs.- 3.4 Overall Efficiency Measurement.- 3.5 Price Indexes.- 3.6 Inverse Homotheticity.- 3.7 Remarks on the Literature.- 3.A Appendix.- 4 Indirect Distance Functions.- 4.1 Cost and Revenue Constrained Firms.- 4.2 Dualities.- 4.3 Derivative Properties of the Indirect Distance Functions.- 4.4 Nonparametric Testing.- 4.5 Remarks on the Literature.- 4.A Appendix.- 5 Indirect Cost and Revenue Functions.- 5.1 Duality Theorems.- 5.2 Derivative Properties.- 5.3 Cost Benefit Analysis.- 5.4 Remarks on the Literature.- 5.A Appendix.- 6 The Profit Function.- 6.1 Duality Theorems.- 6.2 The Profit, Cost, and Revenue Functions.- 6.3 The Profit, Indirect Input Distance and Indirect Output Distance Functions.- 6.4 The Profit, Indirect Cost and Indirect Revenue Functions.- 6.5 Remarks on the Literature.- 7 Towards Empirical Applications.- 7.1 An Overview.- 7.2 Monotonicity, Homogeneity and Convexity.- 7.3 Homogeneous and Inversely Homothetic Technologies.- 7.4 Functional Forms.- 7.5 Remarks on the Literature.- References.- Author Index.
