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A theorem on homogeneous functions and extended Cobb-Douglas forms.

A Charnes1, W W Cooper, A P Schinnar

  • 1Center for Cybernetic Studies, The University of Texas, Austin, Texas 78712.

Proceedings of the National Academy of Sciences of the United States of America
|October 1, 1976
PubMed
Summary

A new form of homogeneous functions extends Cobb-Douglas functions, offering novel interpretations for economic results. This generalization also connects economics with information theory and geometric programming.

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Area of Science:

  • Economics
  • Econometrics
  • Mathematical Economics

Background:

  • Homogeneous functions are fundamental in economic modeling, particularly in production and distribution.
  • Cobb-Douglas functions represent a well-established class of homogeneous functions with significant empirical and theoretical applications.
  • Existing models may not fully capture the nuances of economic phenomena requiring more flexible functional forms.

Purpose of the Study:

  • To introduce a generalized form of homogeneous functions.
  • To demonstrate the relationship between this new form and Cobb-Douglas functions.
  • To explore the implications of this extension for economic theory and empirical analysis.

Main Methods:

  • Mathematical derivation of a new functional form for homogeneous functions.

Related Experiment Videos

  • Comparative analysis of the proposed form with Cobb-Douglas functions.
  • Identification of shared properties and extensions.

    • Main Results:

    • The presented homogeneous function form is a simple extension of Cobb-Douglas functions.
    • This new form retains similar desirable properties relevant to production and distribution economics.
    • The generalization offers new avenues for interpreting existing economic results.

    Conclusions:

    • The proposed homogeneous function form provides a more flexible framework for economic modeling.
    • It facilitates novel interpretations of empirical and theoretical economic findings.
    • This work establishes interdisciplinary links with information theory and geometric programming.