Foreword by Kenneth J. Arrow to Arthur's book,

Increasing Returns and Path Dependence in the Economy, 1994, U.Mich Press, Ann Arbor

The concept of increasing returns has had a long but uneasy presence in economic analysis. The opening chapters of Adam Smith's Wealth of Nations put great emphasis on increasing returns to explain both specialization and economic growth. Yet the object of study moves quickly to a competitive system and a cost-of-production theory of value, which cannot be made rigorous except by assuming constant returns. The English school (David Ricardo, John Stuart Mill) followed the competitive assumptions and quietly dropped Smith's boldly-stated proposition that, "the division of labor is limited by the extent of the market," division of labor having been shown to lead to increased productivity.

Other analysts in different traditions, especially the French mathematician and economist, A. A. Cournot (1838), saw clearly enough the incompatibility of increasing returns and perfect competition and developed theories of monopoly and oligopoly to explain the economic system implied by increasing returns. But this tradition acts like an underground river, springing to the surface only every few decades. Alfred Marshall expanded broadly, if vaguely, on the implications of increasing returns, including those for economic growth, irreversible supply curves, and the like, as well as the novel and far-reaching concept of externalities, where some, at least, of the increasing returns are captured, not by the producer but by others.

The implications of increasing returns for imperfect competition were developed, though far from completely, by Edward Chamberlin and Joan Robinson in the 1930s. There was sporadic emphasis on the role of increasing returns in economic growth byAllyn Young (1928) (but only in very general terms) and then by Nicholas Kaldor in the1950s. Many developmental theorists, particularly in the 1950s, advocated radical planning policies based on vague notions of increasing returns.

It is in this context that Brian Arthur's precise and fully-modeled papers caused us all to understand clearly and specifically what kinds of models have what kinds of implications. One outstanding characteristic of Arthur's viewpoint is its emphatically dynamic nature. Learning by using or doing plays an essential role, as opposed to static examples of returns to scale (e.g., those based on volume-area relations). The object of study is a history.

Another distinctive feature of most of the work is its stochastic character. This permits emphasis on the importance of random deviations for long-term tendencies. In particular, nonlinear Polya processes, studied by Arthur and his probabilistic colleagues, have very interesting properties. Among them are several essential implications of Arthur's viewpoint, in particn particn particn particn partic