Computer testing of a non-parametric partial equilibrium model prototype

On the basis of non-parametric formulations of the production program problem (previously known) and the consumer choice problem (new), a computable partial equilibrium model with a non-parametric representation of both supply and demand is proposed. In this model the problems of the producer and the consumer are represented by simultaneous inequalities of the dual problems pair. This converts the problem of finding an equilibrium to minimizing the differences between objective functions in each pair, summarized over producers and consumers. Such a problem, however, may have multiple local optima. Computer tests on artificial data sets confirmed that inserting such “technical” constraints into a computable model, that are always valid in an equilibrium, can effectively direct the search for a solution using the CONOPT4 procedure to the global optimum (to which the sought equilibrium corresponds). In all 36 tests carried out, equilibrium solutions were found on the first try. The result obtained is of significant importance for the creation of tools used at the sectoral level in managing the unstable economic dynamics that are characteristic of periods of change in systems of dominant technologies. Such tools will make better use of the information in the original empirical data.

partial equilibrium, computable model, nonparametric production frontier, nonparametric consumption frontier, first duality theorem, computer-aided testing.