# Duality and Geometric Programming

Rekliatis G, Salas V, & Whinston AB (1975). Duality and Geometric Programming. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-75-145

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## Abstract

Two main problems arise from the use of the Transcendental Logarithmic form:

1. For practical and estimation purposes, the authors take the approximating function as the true function and include any possible source of error in the error term of the regression equation. This implies that there is no way of telling whether the results are affected by stochastic or approximation error.

2. The Cobb-Douglas and the CES production function have the property of "self duality", i.e., both the production and the cost forms are members of the same family of functional forms. This makes irrelevant the choice of representation of the technology by the production or cost functions. The Transcendental Logarithmic Form when taken as, the true form for the primal (dual) problem and then taken again as the true form of the dual (primal), makes one of the selections arbitrary since the form is not self-dual. This point is treated by Burgess [9] who shows with empirical results the consequences of choosing the cost or the production Transcendental Logarithmic form as a representation of the underlying technology.

This paper is addressed to the possible solution of these two problems while still being able to work with more general production functions. We propose for the consideration of the economists interested in the Theory of Production, the Geometric Programming (GP) method of solving cost minimization problems which is extensively used in engineering. The similarities observed in both fields also indicate the possible benefits of closer communication among them. In the coming sections, we give an introduction to GP and illustrate with examples using the Cobb-Douglas, CES, and a more general explicit production function.

Item Type: Monograph (IIASA Working Paper) System and Decision Sciences - Core (SDS) IIASA Import 15 Jan 2016 01:41 27 Oct 2016 05:33 http://pure.iiasa.ac.at/283