Optimality Versus Stability: Pattern Formation in Spatial Economics

Abstract

Whenever economists try to explain any observed pattern of facts, a favorite candidate is the optimality of this particular pattern over alternatives. So, Christaller’s observation of predominantly hexagonal market areas in Southern Germany led Lösch to point at this as the most economic solution in terms of minimum total transportation cost, given one had to deal with a close packing of market areas in the twodimensional plane. And so has it remained. Economists have little interest in formulating dynamical models, or even in dealing with the dynamic issues implicit in considering at least the stability of al1ternative patterns. It is taken for granted that systems seek the optima, minimizing expenditure or maximizing utility, without regard of the frictions (=costs) inherent in transforming an existent pattern to another optimal one. They are always satisfied just by designing a state which is best in some sense, and never even calculate how much better this is than an existent alternative. This imagery was, of course, helped by the fact that most economic models are linear, which among other things implies that optima are unique. There is hence no multi stability, i.e. no existent optima, and no need for considerations about whether any dynamic process is likely to take the system from one local optimum to a global optimum which might be slightly better. This is, in my opinion, the worst consequence of the preoccupation with linear systems in economics. (See the QWERTY issue raised by Arthur (1990) to appreciate the importance in a general, non spatial context.)