Economic Dynamics and Computation—Resurrecting the Icarus Tradition

Metroeconomica

Volumn 55, Issue 2-3, 2004, Pages 239-264

  Velupillai, K Vela ^a,b  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^b UNIVERSITY OF TRENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34250863048     PISSN: 00261386     EISSN: 1467999X     Source Type: Journal    
DOI: 10.1111/j.0026-1386.2004.00192.x     Document Type: Article

References (33)

1. Allen R. G. D. (1959): Mathematical Economics, 2nd edn, Macmillan, London.
2. Allen R. G. D. (1967): Macro-Economic Theory: A Mathematical Treatment, Macmillan, London.
3. De Antoni E. (1999): ‘Clower's intellectual voyage: the “Ariadne's thread” of continuity through changes’, in Howitt P., de Antoni E., Leijonhufvud A. (eds): Money, Markets and Method: Essays in Honour of Robert W. Clower, Edward Elgar, Cheltenham, ch. 1, pp. 3–22.
4. Briggs K. M. (2000): ‘Another universal differential equation’, http://tantalum.bt-sys.bt.co.uk:tex/universal-ode.tex, 13 April.
5. Debreu G. (1974): ‘Excess demand functions’, reprinted in Mathematical Economics: Twenty Papers of Gerard Debreu, Cambridge University Press, Cambridge, 1983, ch. 16, pp. 203–9.
6. Duffin R. J. (1981): ‘Rubel's universal differential equation’, Proceedings of the National Academy of Sciences USA, 78 (8), pp. 4661–62.
7. Fisher J. (1892): ‘Mathematical investigations in the theory of value and prices’, Transactions of the Connecticut Academy, IX (July); reprinted by Augustus M. Kelley, Fuirfield, NJ, 1991.
8. Gödel K. (1946): ‘Remarks before the Princeton Bicentennial Conference on Problems in Mathematics’, reprinted in Davis M. (ed.): The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, Raven Press, New York, 1965, pp. 84–88.
9. Goodwin R. M. (1950): ‘A non-linear theory of the cycle’, Review of Economics and Statistics, XXXII (4), pp. 316–20.
10. Goodwin R. M. (1951): ‘Iteration, automatic computers, and economic dynamics’, Metroeconomica, III (1), pp. 1–7.
11. Goodwin, R. M. (1951a): ‘The nonlinear accelerator and the persistence of bussiness cycles’, Econometrica, 19, 1, January, pp. 1–17.
12. Goodwin R. M. (1990): Chaotic Economic Dynamics, Clarendon Press, Oxford.
13. Guckenheimer J. (1996): ‘Phase portraits of planar vector fields: computer proofs’, Experimental Mathematics, 4 (2), pp. 153–65.
14. Iserless A. (1996): A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Cambridge.
15. Iserless A., Peplow A. T., Stuart A. M. (1991): ‘A unified approach to spurious solutions introduced by time discretisation. Part I: Basic theory’, SIAM Journal of Numerical Analysis, 28 (6), pp. 1723–51.
16. Jones J. (1981): ‘Classification of quantifier prefixes over Diophantine equations’, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 27, pp. 403–10.
17. Lange O. (1970): Introduction to Economic Cybernetics, Pergamon Press, London.
18. Matiyasevich Y. V. (1993): Hilbert's Tenth Problem, MIT Press, Cambridge, MA.
19. McAnulty J. C., Naines J. B., Jr, Strotz R. H. (1953): ‘Goodwin's nonliinear theory of the business cycle: an electro-analog solution’, Econometrica, 21 (3), pp. 390–411.
20. Pareto V. (1927): Manual of Political Economy, translated by A. S. Schwier and edited by A. S. Schwier and A. N. Page, Macmillan, London, 1971.
21. Pour-El M. B. (1974): ‘Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers)’, Transactions of the American Mathematical Society, 199 (November), pp. 1–28.
22. Rubel L. A. (1981): ‘A universal differential equation’, Bulletin (New Series) of the American Mathematical Society, 4 (3), pp. 345–49.
23. Rubel L. A. (1988): ‘Some mathematical limitations of the general-purpose analog computer’, Advances in Applied Mathematics, 9, pp. 22–34.
24. Rubel L. A. (1989): ‘Digital simulation of analog computation and Church's thesis’, Journal of Symbolic Logic, 54 (3), pp. 1011–17.
25. Samuelson P. A. (1990): ‘Deterministic chaos in economics: an occurrence in axiomatic utility theory’, in K. Velupillai (ed.): Nonlinear and Multisectoral Macrodynamics: Essays in Honour of Richard Goodwin, ch. 5, pp. 42–63, Macmillan, London.
26. Sauer T., Yorke J. A. (1991): ‘Rigorous verification of trajectories for the computer simulation of dynamical systems’, Nonlinearity, 4, pp. 961–79.
27. Shannon C. E. (1941): ‘Mathematical theory of the differential analyzer’, Journal of Mathematics and Physics, XX (4), pp. 337–54.
28. Sonnenschein H. (1973): ‘The utility hypothesis and market demand theory’, Western Economic Journal, 2 (4), pp. 404–10.
29. Strotz R. H., Calvert J. F., Morehouse N. F. (1951): ‘Analogue computing techniques applied to economics’, Transactions of the American Institute of Electrical Engineers, 70 (1), pp. 557–63.
30. Stuart A. M., Humphries A. R. (1998): Dynamical Systems and Numerical Analysis, Cambridge University Press, Cambridge.
31. Temple G. (1981): 100 Years of Mathematics, Gerald Duckworth, London.
32. Turing A. (1936-37): ‘On computable numbers, with an application to the Entscheidungsproblem’, Proceedings of the London Mathematical Society, Series 2, 42, pp. 230–65; reprinted in Davis M. (ed.): The Undecidable, Raven Press, New York, 1965, pp. 116–51.
33. Tustin A. (1953): The Mechanism of Economic Systems: An Approach to the Problem of Economic Stabilisation from the Point of View of Control-System Engineering, Harvard University Press, Cambridge, MA.