Transforms and Approximations in Cost and Production Function Relations.

Abstract

Process analysis and related approaches to the study of energy economics have made extensive use of Shephard's lemma as well as other aspects of the Shephard-Samuelson transformation theories. A major problem is shown to be present in the use of these transforms to go from cost functions to production possibility sets in that the latter will always be unbounded above. Capacity conditions, which are especially important in energy policy studies, are therefore not adequately addressed. Troubles also occur in the use of translog approximations because of the functional forms which can result when the Shephard-Samuelson transformations are employed. Nondiffferentiability is not the primary difficulty with the translog approximations as is shown with an infinitely differentiable function. Relations between other parts of mathematical transform theory, e.g. as exhibited in Laplace transforms, are also indicated along with possible extensions that might be made in the Shephard-Samuelson 'duality' theories. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1979
Accession Number
ADA068993

Entities

People

  • A. P. Schinnar
  • Abraham Charnes
  • William W. Cooper

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Business Administration
  • Convex Sets
  • Differential Equations
  • Economics
  • Elastic Properties
  • Electric Power
  • Engineering
  • Equations
  • Integer Programming
  • Linear Programming
  • Mathematics
  • Operations Research
  • Power
  • Production
  • United States
  • United States Government
  • Universities

Readers

  • Calculus or Mathematical Analysis
  • Industrial Economics