Complex Socio-Economic Systems in Regional Science

In this chapter, we will concentrate ourselves on the forms of complication and self-organization in linear spatial socio-economic systems. The description of the catastrophic effects of appearance of new information and new emerging properties in the states of the linear spatial socio-economic systems will be in a center of our considerations. An important predecessor in studies of linear economic structures was Goodwin (1983), who stated that “…economies are so impossibly complex as to defy any completely satisfactory analysis: rather the best can be hoped for a number of different approaches, each of which yields valuable but incomplete insights into the various aspects of the system. Thus ‘general equilibrium’ theory, whilst in principle admirable, always has seems to me be so ‘general’ as to be largely vacuous and even capable of diverting attention from important matters. By contrast Keynesian theory and cycle theory, for all their crudity, attracted me because of the usable practical results. Yet they lump together inhomogeneous elements into aggregates, which cannot be expected to yield empirically valid relationships. Making some sort of practical compromise by disaggregating, one is bound to be dealing with a complicated system with a large number of variables. A large system can yield little results unless it is linear. Therefore I was attracted to linear systems and in particular to the simplicities of Leontief’s input-output method which appeared to be capable of demonstrating some of the virtues as well as some of the faults of both the Keynesian and the Walrasian types of analysis& . The neoclassical economics made a tangible advance in the subtlety and realism of their analysis, but they tended to lose sight of the larger issues and sweep of the classical economists. Linear disaggregated systems seem to me to constitute a fruitful compromise between the virtues of these two divergent methodologies” (Goodwin, 1983, Preface, p. vi.). The second important source of the analysis of linear economic structure may be attributed to Gale (1960). In his book, he concentrated on linear programming, game theory, aspects of general linear algebra that were relevant to linear economic analysis, and linear models of production. In this chapter, we will’add some additional insights that build on the frame of Gale’s scheme, namely’sensitivity analysis of the classical linear programming problem in polyhedral’form; the economic interpretation of the theory of convex polyhedrons in the form’of the superposition principle of analysis of extreme tendencies, emerging in the’evolving linear economic systems.