Dominique, CRene (2014): On Market Economies: How Controllable Constructs Become Complex.

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Abstract
Since Lėon Walras neoclassical economists hold an inalterable belief in a unique and stable equilibrium for the economic system, which remains to this day unobservable. Yet that belief is the corner stone of other theories such as the ‘Efficient Market Hypothesis’ as well as the philosophy of neoliberalism, whose outcomes are shown by recent events to be flawed. A modern market economy is indeed a nonlinear controllable construct, but this paper uses 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. In a complex nonlinear deterministic systems, equilibria, whether multiple or deterministically chaotic, depends on their parameter values and uncertainties. The best approach suggested is to focus on endurable patterns thrownoff by such systems.
Item Type:  MPRA Paper 

Original Title:  On Market Economies: How Controllable Constructs Become Complex 
English Title:  On Market Economies: How Controllable Constructs Become Complex 
Language:  English 
Keywords:  Equilibrium, nonlinearity, controllability, nonlinearfeedback, H∞control, data requirement, complexity. 
Subjects:  C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C67  InputOutput Models 
Item ID:  56579 
Depositing User:  CRene Dominique 
Date Deposited:  13 Jun 2014 08:23 
Last Modified:  29 Sep 2019 04:31 
References:  [1] Dominique, CR. (2008).”Walrasian solutions without utility functions.”, EERI Research Paper Series EERI RP10, Economics and Econometrics Research Institute (EERI), Brussels. [2] Sonnenschein, H. (1972).”Market excessdemand functions.” Econometrica, 40 (3), 549563. [3] (1973).”Do Walras’ identity and continuity characterize the class of community excessdemand functions.” Journal of Economic Theory, 6, 345354. [4] Mantel, R. (1974).”On the characterization of aggregate excessdemand.” Journal of Economic Theory, 7, 348353. [5] Debreu, G (1970).”Economies with finite sets of equilibria.” Econometrica, 38, 387392. [6] Debreu, G. (1974).”Excessdemand functions.” Journal of mathematical economics, 1, 1521. [7] Zames, G. (1981).”Feedback and optimal sensitivity, model reference transformations, multiplicative seminorm and approximative inverses.” IEEE Transactions on Automatic Control, 38, 546559. [8] Francis, B. C. (1987). A course in Hcontrol, Lecture Notes and Information. Springerverlag: New York. [9] Isidori, A. (1997).Nonlinear Control Systems, 3rd ed., Springerverlag: Berlin. [10] Isidori, A. and Altolfi, A. (1992).”Disturbance attenuation and Hcontrol via measurement feedback in nonlinear systems.” IEEE Transactions on Automatic Control, 37, 12831293. [11] Doyle, J. C., Glover, P. et al. (1989).” Statespace solutions to standard H2 and H control problems: IEEE transactions on Automatic Control, 34, 831847. [12] van der Schaft, A. (1991).”On a statespace approach to nonlinear Hcontrol.” Systems and Control Letters, 16, 18. [13] (1992).”L2gain analysis of nonlinear systems and nonlinear state feedback Hcontrol.” IEEE Transactions on Automatic Control, 37, 770784. [14] Basar, T. and Bernhard, P. (1995).”Hoptimal control and related minimax design problems.” Systems and Control Foundations and Applications, 2nd ed., Birkhauser: Boston. [15] Aliyu, M. S. (2011). Nonlinear HControl, Hamiltonian Systems, and HamiltonJacobi Equations. CRC Press: New York. [16] Ball, J. A., and Walker, M.L. (1993).”Hcontrol for nonlinear systems via ouput feedback.” IEEE Transactions on Automatic Control, 38, 546559. [17] Scheinkman, J. A. (1976).”On optimal steadystate of nsector growth models.” Journal of Economic Theory, 12, 1130. [18] 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, 421444. [19] Blatt,J. M. (1983). Dynamic Economic Systems, Armouk, NY: M. C. Shape . [20] Boldrin, M. and Montruccio, L. (1986).”On the indeterminacy of capital accumulation paths.” Journal of Economic Theory, 40, 2639. [21] Frieling, G.,Jank, G. and Aboukandil, H. (1996).”On the global existence of solutions to coupled matrix Riccati equations in closedloop Nah games.” IEEE Transactions on Automatic Control, 41, 264269. 22] Anderson, B. D. O. et al. (1998).”Robust stabilization of nonlinear systems via normalized coprime factor representation 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/56579 