On Market Economies: How Controllable Constructs Become Complex

Since Lėon Walras neoclassical economists hold an inalterable belief in a unique and stable equilibrium for the economic system which however remains to this day unobservable. Yet that belief is the corner stone of other theories such as the ‘Effi-cient Market Hypothesis’ as well as the philosophy of neo-liberalism, whose out-comes are also shown to be flawed by recent events. A modern market economy is obviously an input/output nonlinear controllable construct. However, this paper examines four such models of increasing complexity, including the affine nonlinear feedback H∞-control, to show that the ‘data requirement’ precludes all attempts at the empirical verification of the existence of a stable equilibrium. If equilibria of complex nonlinear deterministic systems are most likely unstable, multiple or deterministically chaotic depending on their parameter values and uncertainties, then society should impose limits on the state space and focus on endurable patterns thrown-off by such systems.
JEL Classification C61, C62, C68, C68, D57, D58
Full Article
  1. Aliyu, M. S., 2011. Nonlinear H¥-Control, Hamiltonian Systems, and Hamilton-Jacobi Equations. New York: CRC Press.
  2. Anderson, B. D. O. et al., 1998.Robust stabilization of nonlinear systems via normalized coprime factor representation. Automata, 34, pp. 1559-1593.
  3. Ball, J. A., and Walker, M.L., 1993.H¥-control for nonlinear systems via ouput feedback. IEEE Transactions on Automatic Control, 38, pp.546-559.
  4. Basar, T. and Bernhard, P., 1995. H¥-optimal control and related minimax design problems.” Systems and Control Foundations and Applications, 2nd ed., Birkhauser: Boston.
  5. Blatt,J. M. 1983. Dynamic Economic Systems, Armouk, New York: M. C. Shape .
  6. Benhabib, J. and Nichimura, K., 1979. The Hoft bifurcation and the existence and stability of closed orbits in Multisector models of optimal growth. Journal of Economic Theory, 21, pp.421-444.
  7. Boldrin, M. and Montruccio, L., 1986. On the indeterminacy of capital accumulation paths. Journal of Economic Theory, 40, pp.26-39.
  8. Debreu, G., 1970. Economies with finite sets of equilibria. Econometrica, 38, pp.387-392.
  9. Debreu, G., 1974.Excess-demand functions. Journal of mathematical economics, 1, pp.15-21.
  10. Dominique, C-R., 2008. Walrasian solutions without utility functions. EERI Research Paper Series EERI- RP-10, Economics and Econometrics Research Institute EERI, Brussels.
  11. Doyle, J. C., Glover, P. et al., 1989. State-space solutions to standard H2 and H¥- control problems. IEEE transactions on Automatic Control, 34, pp.831-847.
  12. Francis, B.C., 1987. A course in H¥-control, Lecture Notes and Information. Springer-verlag: New York.
  13. Frieling, G.,Jank, G. and Aboukandil, H. 1996. On the global existence of solutions to coupled matrix Riccati equations in closed-loop Nah games. IEEE Transactions on Automatic Control, 41, pp.264-269.
  14. Isidori, A., 1997.Nonlinear Control Systems, 3rd ed., Berlin: Springer-verlag.
  15. Isidori, A. and Altolfi, A., 1992.Disturbance attenuation and H¥-control via measurement feedback in nonlinear systems. IEEE Transactions on Automatic Control, 37, pp.1283-1293.
  16. Mantel, R., 1974. On the characterization of aggregate excess-demand. Journal of Economic Theory, 7, pp.348-353.
  17. Scheinkman, J.A., 1976. On optimal steady-state of n-sector growth models. Journal of Economic Theory, 12, pp.11-30.
  18. Sonnenschein, H., 1972. Market excess-demand functions. Econometrica, 40(3), pp.549-563.
  19. Sonnenschein, H., 1973. Do Walras’ identity and continuity characterize the class of community excess-demand functions. Journal of Economic Theory, 6, pp.345-354.
  20. Van der Schaft, A., 1991. On a state-space approach to nonlinear H¥-control. Systems and Control Letters, 16, pp.1-8.
  21. Van der Schaft, A., 1992. L2-gain analysis of nonlinear systems and nonlinear state feedback H¥-control. IEEE Transactions on Automatic Control, 37, pp.770-784.
  22. Zames, G. 1981. Feedback and optimal sensitivity, model reference transformations, multiplicative semi-norm and approximative inverses. IEEE Transactions on Automatic Control, 38, pp.546-559.

Article Rights and License
© 2014 The Authors. Published by Sprint Investify. ISSN 2359-7712. This article is licensed under a Creative Commons Attribution 4.0 International License. Creative Commons License
Corresponding Author
C-René Dominique, Formerly Professor of Applied Economics, Laval University, Quebec, Canada
Download PDF


Laval University, Quebec, Canada

Dowling College, New York, United States