# Economic Dynamics, Linearities, and the Classical Mechanistic Worldview

## Abstract

Economics in its modern form was introduced as a serious and distinguished science during the second half of the 18th century. Unlike earlier attempts to understand economic phenomena (usually in the context of political economy like, *e.g*., mercantilism) the writings of Adam Smith or David Ricardo constitute the first successful approaches toward an abstract explanation of human economic behavior. One reason why economics emerged as a science in that particular period surely has to do with the expansion of capitalism in the advanced societies of that day and the increasing complexity of trade. It is not surprising that economics as a modern science originated in Great Britain, which not only is considered as the homeland of capitalistic production but which also had been the dominant factor in international trade for more than 150 years. Much of the early economists’ interest was therefore devoted to the major economic subjects of the day like the effects of international trade on the prosperity of the domestic economy.^{1}

## Keywords

Dynamical Phenomenon Linear Dynamical System Mainstream Economic Complex Conjugate Eigenvalue General Equilibrium Framework## Preview

Unable to display preview. Download preview PDF.

## References

- 1.In many cases, inquiries into international trade represent the renowned work of classical writers; for example, most economists will probably remember David Ricardo mainly for his investigations of comparative cost advantages rather than for his labor value theory.Google Scholar
- 2.Quoted from Crutchfield et al. (1986).Google Scholar
- 3.Cf. West (1985), p. 70.Google Scholar
- 4.West (1985), p. 70.Google Scholar
- 6.The standard reference for questions concerning the relation between physics and economics is, of course, Georgescu-Roegen (1971).Google Scholar
- 7.V. Pareto had a doctoral degree in railroad engineering and, like his predecessor
**L**. Walras in Lausanne, had not published much on economic theory when he got his first academic appointment. However, Debreu’s (1986) statement that Walras and Pareto had published only novels and other belletristic literature before their first appointments is misleading.Google Scholar - 8.Walras’ German translator, L.v. Winterfeld, compared Walras with the astronomer J. Kepler: “chrw(133) Walras appears to me as the Kepler of economics, who incontestably and for all time proves the laws which once were suspected and expressed by (the) German scholarchrw(133) H.H. Gossen in the style of a Kopernikus.” Own translation from the German preface to Walras (1876) ( H.-W.L. )Google Scholar
- 9.Walras (1874), p. 7. Own translation (H.-W. L.) from Walras (1876).Google Scholar
- 10.Cf. Fisher (1961), p. 25. Fisher himself attempted to develop a consistent value theory analogous to the theory of equilibrating water cisterns. He even constructed mechanical devices to illustrate his ideas.Google Scholar
- 11.Mill (1973), pp. 847f., emphases in original. For the purpose of this little excursion into the history of science, Mill’s Logic can be considered as the gap filling contribution between enlightenment philosophy, the methodology of the subsequent development of classical mechanics, and the methodology of economics and other social sciences.Google Scholar
- 12.Compare, e.g., Blaug (1978), p. 311, for the resistance to the emerging mathematical methods among well-reputed economists.Google Scholar
- 13.Marshall (1938), p.772.Google Scholar
- 14.Marshall’s remark on the actual analogy between economics and biology is most vividly incorporated in the so-called evolution economics which surely can be considered a discipline not in the mainstream of modern economics.Google Scholar
- 15.Indeed, to an outsider it may be surprising that economics still elaborates on auxiliary constructions like Walras’ auctioneer, though the recent analytical techniques are of course much more sophisticated than at Walras’ times.Google Scholar
- 16.Poincaré (1908), p. 68. English translation from Poincaré (1952), p. 76. I am grateful to D. Farmer for providing this reference to me.Google Scholar
- 17.Of course, this does not mean that in the course of the century there was no mathematical progress in the theory of nonlinear dynamical systems. Indeed, relaxation oscillations, for example, were intensively discussed in the 1920s. The work of Cartwright, Levinson, and Littlewood in the late 1940s actually laid the foundations for the recent analysis of chaotic dynamical systems.Google Scholar
- 18.Cf. Harcourt (1984) or Velupillai/Ricci (1988) for honory lectures on Goodwin’s work.Google Scholar
- 19.The few economic models which make use of differential equations with fixed delays, i.e., mixed difference-differential equations, will be ignored in the sequel.Google Scholar
- 20.Extensive treatments of linear dynamical systems with many economic examples can be found, e.g., in Allen (1963), Chapters 5 and 6, Takayama (1974), or Gandolfo (1983). See also Hirsch/Smale (1974), Chapters 3 and 4. As most of the following subjects can be found in all of these standard references, detailed sources are rarely provided in this section.Google Scholar
- 21.If the eigenvalues are identical, (1.2.9) must be replaced by x
_{1}(t) = (m_{1}+tm2)eatGoogle Scholar - 23.If both eigenvalues are identical the solution (1.2.20) must be replaced by xi = (m
_{i}+ tm2)At•Google Scholar - 24.Cf. West (1985), pp. 3–10.Google Scholar
- 25.In fact, in some mathematical disciplines like game theory, optimal control, or fixed point problems, economists definitely belong to the pioneers in developing the appropriate mathematical apparatus which may be useful in other disciplines as well.Google Scholar
- 26.Usually, this simplification goes hand in hand with the prospect of future research on the topic which should investigate the influence of nonlinearities. Compare also Baumol (1987), p. 105, for a discussion of this procedure.Google Scholar
- 27.Lucas/Sargent (1978), p. 314.Google Scholar
- 28.The observation that the influence of additive random terms in linear business cycle models indeed implies theoretically generated time series which closely resemble actual series dates back to Frisch (1933), Slutzky (1937), and Kalecki (1954). Cf. also Gabisch/Lorenz (1989), pp. 87ff.Google Scholar
- 29.Compare also Brock (1988b) for a discussion of Blatt’s results.
^{39}Cf. Gabisch/Lorenz (1989), pp. 49ff.Google Scholar