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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.
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.
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.
- 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.