Mathematics and Modern Economics Edited by Geoffrey M. Hodgson Research Professor University of Hertfordshire Business School, UK THE INTERNATIONAL LIBRARY OF CRITICAL WRITINGS IN ECONOMICS An Elgar Research Collection Cheltenham, UK • Northampton, MA, USA Contents Acknowledgements Introduction Geoffrey M. Hodgson PART I FROM THE FORMALIST REVOLUTION TO THE AEA COMMISSION 1. Mark Blaug (2003), 'The Formalist Revolution of the 1950s', in Warren J. Samuels, Jeff E. Biddle and John B. Davis (eds), A Companion to the History of Economic Thought, Chapter 25, Maiden, MA and Oxford, UK: Blackwell Publishing, 395-410 2. John M. Clark (1947), 'Mathematical Economists and Others: A Plea for Communicability', Econometrica, 15 (2), April, 75-8 3. Kenneth E. Boulding (1948), 'Samuelson's Foundations: The Role of Mathematics in Economies', Journal of Political Economy, LVI (3), June, 187-99 4. Morris A. Copeland (1951), 'Institutional Economics and Model Analysis', American Economic Review, 41 (2), May, 56—65 • 5. David Novick (1954), 'Mathematics: Logic, Quantity, and Method', Review of Economics and Statistics, XXXVI (4), November, 357-8 6. Paul A. Samuelson (1954), 'Some Psychological Aspects of Mathematics and Economies', Review of Economics and Statistics, XXXVI (4), November, 380-86 7. Stephen Enke (1955), 'More on the Misuse of Mathematics in Economics: A Rejoinder', Review of Economics and Statistics, XXXVII (2), May, 131-3 8. Wassily Leontief (1971), 'Theoretical Assumptions and Nonobserved Facts', American Economic Review, 61 (1), March, 1-7 9. Alan Coddington (1975), 'Creaking Semaphore and Beyond: A Consideration of Shackle's "Epistemics and Economies'", British Journal for the Philosophy of Science, 26 (2), June, 151—63 10. Alexander Rosenberg (1975), 'The Nomological Character of Microeconomics', Theory and Decision, 6 (1), 1-26 ' 11. Herbert G. Grubel and Lawrence A. Boland (1986), 'On the Efficient Use of Mathematics in Economics: Some Theory, Facts and Results of an Opinion Survey', Kyklos, 39 (3), 4 1 9 ^ 2 12. Gerard Debreu (1986), 'Theoretic Models: Mathematical Form and Economic Content', Econometrica, 54 (6), November, 1259-70 13. Herbert A. Simon (1986), 'The Failure of Armchair Economics [Interview]', Challenge, 29 (5), November-December, 18-25 ix xiii 3 19 23 36 46 48 55 58 65 78 104 128 140 Mathematics and Modern Economics 14. 15. 16. PART II PART III Gerard Debreu (1991), 'The Mathematization of Economic Theory', American Economic Review, 81 (1), March, 1-7 Anne 0 . Krueger (1991), 'Report of the Commission on Graduate Education in Economies', Journal of Economic Literature, XXIX (3), September, 1035-53 Alan S. Blinder (1990), 'Discussion', American Economic Review, 80 (2), May, 445 MATHEMATICS, FIN DE SIECLE: 1991-1999 17. Frank Hahn (1991), 'The Next Hundred Years', Economic Journal, 101 (404), January, 47-50 18. Donald N. McCloskey (1991), 'Economics Science: A Search Through the Hyperspace of Assumptions?', Methodus, 3 (1), June, 6-16 19. Philip Mirowski (1991), 'The When, the How and the Why of Mathematical Expression in the History of Economic Analysis', Journal of Economic Perspectives, 5 (1), Winter, 145-57 20. E. Roy Weintraub and Philip Mirowski (1994), 'The Pure and the Applied: Bourbakism Comes to Mathematical Economies', Science in Context, 7 (2), Summer, 245-72 21. Munir Quddus and Salim Rashid (1994), 'The Overuse of Mathematics in Economics: Nobel Resistance', Eastern Economic Journal, 20(3), Summer, 251-65 22. Robert W. Clower (1995), 'Axiomatics in Economies', Southern Economic Journal, 62 (2), October, 307-19 23. Mark Blaug (1997), 'Ugly Currents in Modern Economies', Policy Options, 18(17), September, 3-8 24. Peter J. Boettke (1997), 'Where Did Economics Go Wrong? Modern Economics as a Flight from Reality', Critical Review, 11(1), Winter, 11-64 25. Paul Krugman (1998), 'Two Cheers for Formalism', Economic Journal, 108 (451), November, 1829-36 26. Roger E. Backhouse (1998), 'If Mathematics is Informal, Then Perhaps We Should Accept that Economics Must be Informal Too', Economic Journal, 108 (451), November, 1848-58 27. Victoria Chick (1998), 'On Knowing One's Place: The Role of Formalism in Economies', Economic Journal, 108 (451), November, 1859-69 MILLENNIAL MATHEMATICS: METHODOLOGY AND ONTOLOGY 28. Robert Sugden (2000), 'Credible Worlds: The Status of Theoretical Models in Economies', Journal of Economic Methodology, 7 (1), 1-31 148 155 174 177 181 192 205 233 248 261 267 321 329 340 353 Mathematics and Modern Economics 29. 30. 31. 32. 33. 34. 35. 36. 37. PART IV James M. Buchanan (2001), 'Game Theory, Mathematics, and Economies', Journal of Economic Methodology, 8 (1), 27-32 Victoria Chick and Sheila C. Dow (2001), 'Formalism, Logic and Reality: A Keynesian Analysis', Cambridge Journal of Economics, 25 (6), 705-21 Ken Dennis (2002), 'Nominalising the Numeric: An Alternative to Mathematical Reduction in Economies', Cambridge Journal of Economics, 26 (1), January, 63-80 Tony Lawson (2004), 'Reorienting Economics: On Heterodox Economics, Themata and the Use of Mathematics in Economies', Journal of Economic Methodology, 11 (3), September, 329—40 Uskali Maki (2005), 'Models are Experiments, Experiments are Models', Journal of Economic Methodology, 12 (2), June, 303-15 K. Vela Velupillai (2005), 'The Unreasonable ineffectiveness of Mathematics in Economies', Cambridge Journal of Economics, 29 (6), November, 849-72 D. Wade Hands (2007), '2006 HES Presidential Address: A Tale of Two Mainstreams: Economics and Philosophy of Natural Science in the Mid-Twentieth Century', Journal of the History of Economic Thought, 29 (1), March, 1-13 Geoffrey M. Hodgson (2006), 'The Problem of Formalism in Economics', in Economics in the Shadows of Darwin and Marx: ' Essays on Institutional and Evolutionary Themes, Chapter 7, Cheltenham, UK and Northampton, MA: Edward Elgar, 116-34 Simon Mohun and Roberto Veneziani (2010),'Reorienting Economics?', Philosophy of the Social Sciences, XX (X), 1—20 and later, March (2012), 42, 126-45, doi: 10.1177/0048393110376218 MATHEMATICAL ECONOMICS AND THE GREAT CRASH OF 2008 38. David Colander, Hans Follmer, Armin Haas, Michael Goldberg, Katarina Juselius, Alan Kirman, Thomas Lux and Brigitte Sloth (2008), 'The Financial Crisis and the Systemic Failure of Academic Economies', Kiel Working Paper, 1489, 1-17 39. Tony Lawson (2009), "The Current Economic Crisis: Its Nature and the Course of Academic Economies', Cambridge Journal of Economics, 33 (4), 759-77 40. Timothy Besley and Peter Hennessy (2009), 'The Global Financial Crisis - Why Didn't Anybody Notice?', British Academy Review, 14,8-10 41. Sheila C. Dow, Peter E. Earl, John Foster, Geoffrey C. Harcourt, Geoffrey M. Hodgson, J. Stanley Metcalfe, Paul Ormerod, Bridget Rosewell, Malcolm C. Sawyer and Andrew Tylecote (2009), 'Letter to the Queen, 10 August', 1-3 384 390 407 425 437 450 474 487 506 529 546 565 568 Mathematics and Modern Economics 42. 43. 44. 45. 46. Tony Lawson (2009), 'Contemporary Economics and the Crisis', Real-World Economics Review, 50, 122-31 571 David Colander, Hans Foellmer, Armin Haas, Alan Kirman, Katarina Juselius, Brigitte Sloth and Thomas Lux (2009) 'How Should the Collapse of the World Financial System Affect Economics?', Real-World Economics Review, 50, 118-21 581 Philip Mirowski (2010), "The Great Mortification: Economists' Responses to the Crisis of 2007-(and counting)', Hedgehog Review, 12 (2), Summer, 28-41 585 Peter E. Earl (2010), 'Economics Fit for the Queen: A Pessimistic Assessment of its Prospects', Prometheus, 28 (3), September, 209-25 599 Geoffrey Hodgson (2011), 'Reforming Economics after the Financial Crisis', Global Policy, 2 (2), May, 190-95 616