Econometrica: Nov, 1977, Volume 45, Issue 8

Integrability and Mathematical Programming Models: A Survey and a Parametric Approach

https://doi.org/0012-9682(197711)45:8<1957:IAMPMA>2.0.CO;2-X
p. 1957-1976

Malachy Carey

A convenient technique used for solving several types of economic problems is to cast them as optimization problems having the line integral of the (inverse) demand and/or supply functions in the objective. But if these functions are non-integrable (having a nonsymmetric Jacobian matrix) then alternative techniques must be used. This paper surveys these and proposes an additional solution technique, based on making the given functions integrable by making a small number of substitutions and iteratively adjusting a parameter associated with each substitution until a solution is found. The technique is particularly applicable when certain neoclassical assumptions are satisfied.