Political scientists have observed that annual budget changes follow long-tail distributions, detailed analyses suggest power-law distributions. We have overviewed the possible macroscopic and microscopic mechanisms, which may generate exact or approximate power-law distributions and suggest a generic macroscopic model and modelling framework.

In this talk, I describe a model of consumer choice based on localized increasing returns. Consumers choose products by first limiting their choice to a subset of options, in order to reduce the information costs of their decision or to satisfy product attribute requirements, and then selecting from this feasible set based on a combination of individual preferences and increasing returns to sales. The market level consequences of the model are examined through simulation, and two key findings are explored. First, the critical factor in determining the shape of the market share distribution is the distribution of feasible set sizes. Second, in most cases, the resulting distribution of shares follows a power law. This second finding is supported by recent empirical research and explains why in many markets a ?Long Tail? of niche products is observed despite the winner take-all-prediction of previous increasing returns research. I demonstrate that consumer preference data can be employed to predict market success with both global and local increasing returns, but that consumer choices more accurately reflect individual consumer preferences when increasing returns are localized.

Characteristic features of the autocatalytic reactions. Survey of the phenomena connected to autocatalytic reactions. Frontreactions; coupling of reaction and diffusion. Gravity induced anisotropy of the velocity of front reaction. Role of convection. Chemical contraction and dilatation. The effect of magnetic fields. Clock reactions. Oxidation of thisulfate by chlorite ion. Individually irreproducible clock reaction with reproducible cummulative probability distribution. Extreme sensitivity to the reaction volume and stirring rate. Interpretation. An algorithm for the design of propagating acidity fronts.