Is Economics Entering its Post-Witchcraft Era?

Potgieter, Petrus H. and Rosinger, Elemér E. (2007): Is Economics Entering its Post-Witchcraft Era?

Abstract

Recently, an awareness is emerging in economics about the fact that important problems are not solvable algorithmically, that is, by any finite number of steps. This statement can be made mathematically exact and this paper reviews the contributions that have been made in this regard, related to standard topics in economics.

• Item Type: MPRA Paper
• Institution: University of South Africa
• Language: English
• Keywords: Computability economics; general equilibrium theory; Arrow's impossibility theorem; Debreu's theorem; Malleus Maleficiarum
• Subjects: A - General Economics and Teaching > A1 - General Economics > A11 - Role of Economics ; Role of Economists ; Market for Economists; A - General Economics and Teaching > A1 - General Economics > A12 - Relation of Economics to Other Disciplines; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods

References

1 Baigger, Günter. 1985. Die Nichtkonstruktivität des Brouwerschen Fixpunktsatzes. Arch. Math. Logik Grundlag., 25(3-4):183-188.

2 BBC NEWS (Asia-Pacific): Vanuatu cargo cult marks 50 years. http://news.bbc.co.uk/2/hi/asia-pacific/6363843.stm (accessed March 31, 2007).

3 Brattka, Vasco. 2001. Recursion and Computability over Topological Structures. Electronic Notes in Theoretical Computer Science 40:5.

4 Bridges, Douglas S., and Fred Richman. 1991. A recursive counterexample to Debreu's theorem on the existence of a utility function. Mathematical Social Sciences 21, no. 2 (April): 179-182.

5 Canning, David. 1992. Rationality, Computability, and Nash Equilibrium. Econometrica 60, no. 4 (July): 877-888.

6 Debreu, Gerard. 1970. Economies with a Finite Set of Equilibria. Econometrica 38, no. 3 (May): 387-392.

7 Fishburn, Peter C. 1970. Arrow's impossibility theorem: Concise proof and infinite voters. Journal of Economic Theory 2, no. 1 (March): 103-106.

8 Gneezy, U., and A. Rustichini. 2000. A Fine is a Price. The Journal of Legal Studies 29 (1): 1-18. http://citeseer.ist.psu.edu/gneezy98fine.html (accessed March 29, 2007)

9 Government of South Africa. 2006. Report on Incentive Structures of Social Assistance Grants in South Africa. Pretoria: Department of Social Development. http://www.welfare.gov.za/documents/2006/gps.pdf (accessed March 31, 2007).

10 Feynman, Richard. 1974. Cargo Cult Science. http://calteches.library.caltech.edu/51/02/CargoCult.htm (accessed March 31, 2007).

11 Hayek, F. A. 1945. The Use of Knowledge in Society. The American Economic Review 35, no. 4 (September): 519-530.

12 Jeffry L. Hirst. Notes on Reverse Mathematics and Brouwer's Fixed Point Theorem. available online:- http://www.mathsci.appstate.edu/~jlh/snp/pdfslides/bfp.pdf.

13 Mihara, H. Reiju. 1999. Arrow's theorem, countably many agents, and more visible invisible dictators. Journal of Mathematical Economics 32, no. 3 (November): 267-287.

14 Orevkov, V.P. A constructive map of the square into itself, which moves every constructive point. Dokl. Akad. Nauk SSSR, 152:55-58, 1963.

15 Rassenti, Stephen, Stanley S. Reynolds, Vernon L. Smith, and Ferenc Szidarovszky. 2000. Adaptation and convergence of behavior in repeated experimental Cournot games. Journal of Economic Behavior & Organization 41, no. 2 (February): 117-146.

16 Wong, Kam-Chau and Richter, Marcel K. 1996. Bounded rationalities and computable economies. Discussion paper 297, Minnesota - Center for Economic Research, December 1996. Available online:- http://ideas.repec.org/p/fth/minner/297.html [accessed 2004-12-30].

17 Wong, Kam-Chau and Richter, Marcel K. 1999. Non-computability of competitive equilibrium. Economic Theory, 14(1):1-27.

18 Wong, Kam-Chau and Richter, Marcel K. 1999. Computable preference and utility. Journal of Mathematical Economics, 32(3):339-354.