# The Buckingham’s π Theorem: Consequences for the Price Theory

### Abstract

The present article focuses on the possible interpretation of the pi theorem of physics in the field of the economics' general equilibrium analysis. The physical units of the exchanged goods are de ned as fundamental units and the neoclassical prices as dimensionless derived numbers. Thus, the general equilibrium does not need money metrics, unspeci ed money market and the complementing inappropriate incorporation of the Walras Law. Further, the main function of money is not that of a unit of account, but a means of exchange. If such type of a money market is introduced, the Walras symmetry holds but in the sense that the positive aggregate excess demand on the goods market matches the negative excess demand on the money market. Distinction is de ned between neoclassical, relative and monetary prices. Additional conditions must be met to allow for a closed monetary circulation.

### References

[2]. Aristotle. (350 BC). “Nicomachean Ethics”. (W. D. Ross, Trans.). https://www.constitution.org/ari/ethic_00.

[3]. Arrow, K. J. (1968). “Economic Equilibrium”. International Encyclopedia of Social Sciences, New York, Macmillan and Free Press.

[4]. Arrow, K. J. and Debreu, G. (1954). "Existence of an equilibrium for a competitive economy". Econometrica. 22 (3), pp 265–290.

[5]. Auckley, G. (1961). Macroeconomic theory. New York.

[6]. Batzias, F. A., & Sidiras, D. K. (2004). „Dye adsorption by calcium chloride treated beech sawdust in batch and fixed-bed systems“. Journal of Hazardous Materials, 114, pp167-174.

[7]. Bertrand, J. (1878). "Sur l'homogénéité dans les formules de physique". Comptes Rendus. 86 (15), pp 916–920.

[8]. Bluman, G. W. and Kumei, S. (1989). “Symmetries and Differential Equations”. Springer Science+Business Media, LLC.

[9]. Buckingham, E. (1914). "On physically similar systems; illustrations of the use of dimensional equations". Physical Review. 4 (4), pp 345–376.

[10]. Boulding, K. E. (1966). „Economic analysis“. (Fourth ed., Vol. II). New York.

[11]. Dixon, R. (2017). Walras’ Law, https://www.online.fbe.unimelb.edu.au/WalrasLaw.pdf, retrieved June 2017.

[12]. Clower, R. W. (1967). A Reconsideration of the Micro foundations of the Monetary Theory, Western Economic Journal (London), 6(4), 1–8.

[13]. Federman, A. (1911). On some general methods of integration of first-order partial differential equations, Proceedings of the Saint-Petersburg polytechnic institute. Section of technics, natural science, and mathematics.16 (1), pp 97–155.

[14]. Gale, D. (1955). “The Law of Supply and Demand”. Mathematics Scandinavica, 3, pp 155-169.

[15]. Ganchev, G. (2021). “The Money as the Necessary Link between Micro and Macro Levels”. In Kostis, P. C. (Eds.), Bridging Microeconomics and Macroeconomics and the Effects on Economic Development and Growth (pp. 123-147). IGI Global. http://doi:10.4018/978-1-7998-4933-9.ch007

[16]. Jevons, W. S. (1875). “Money and the Mechanism of Exchange”. London: Macmillan.

[17]. Hanche-Olsen, H. (2004). “Buckingham’s pi-theorem”. TMA4195 Mathematical modelling.

[18]. Jong, F. J. (1967). „Dimensional analysis for economists“. Amsterdam: North Holland Publ. Co.

[19]. Kopsidas, O. (2018). “The Analysis of Dimensionless Magnitudes in Economic Science”. Economics World, July-Aug. 2018, Vol. 6, No. 4, pp 279-285.

[20]. McKenzie, L. W. (1959). "On the Existence of General Equilibrium for a Competitive Economy". Econometrica. 27 (1), pp 54–71.

[21]. Nikaido, H. (1956). “On the Classical Multilateral Exchange Problem”. Microeconomica 8, pp 135-145.

[22]. Nussbaumer, T., & Neuenschwander, P. (2000). „A new method for an economic assessment of heat and power plants using dimensionless numbers“. Biomass Bioenerg, 18, pp181-188.

[23]. Penfold, D. M. (1968). The Mathematical Gazette. Volume 52, Issue 382, December 1968 , pp. 424

[24]. Pigou, A. C. (1917). “The Value of Money”. The Quarterly Journal of Economics, 32(1), 38–65.

[25]. Riabouchinsky, D. (1911). "Мéthode des variables de dimension zéro et son application en aérodynamique". L'Aérophile, pp 407–408.

[26]. Rayleigh (1892). "On the question of the stability of the flow of liquids". Philosophical Magazine. 34 (206), pp 59–70.

[27]. Samuelson, P. A. (1983). “Foundations of Economic Analysis”. Harvard University Press, 1947 (enlarged ed. 1983).

[28]. Takayama, A. (1990). “Mathematical Economics”, (2nd ed.). Cambridge University Press.

[29]. Vaschy, A. (1892). "Sur les lois de similitude en physique". Annales Télégraphiques. 19, pp 25–28.

[30]. Walras, L. (1874). “Elements of Pure Economics”, (1926 ed.). Allen & Unwin.

**Journal of Mathematical Economics and Finance**, [S.l.], v. 9, n. 1, p. 73 - 88, june 2023. ISSN 2458-0813. Available at: <https://journals.aserspublishing.eu/jmef/article/view/7988>. Date accessed: 28 sep. 2023. doi: https://doi.org/10.14505/jmef.v9.1(16).02.

**The Copyright Transfer Form to ASERS Publishing (The Publisher)**

This form refers to the manuscript, which an author(s) was accepted for publication and was signed by all the authors.

The undersigned Author(s) of the above-mentioned Paper here transfer any and all copyright-rights in and to The Paper to The Publisher. The Author(s) warrants that The Paper is based on their original work and that the undersigned has the power and authority to make and execute this assignment. It is the author's responsibility to obtain written permission to quote material that has been previously published in any form. The Publisher recognizes the retained rights noted below and grants to the above authors and employers for whom the work performed royalty-free permission to reuse their materials below. Authors may reuse all or portions of the above Paper in other works, excepting the publication of the paper in the same form. Authors may reproduce or authorize others to reproduce the above Paper for the Author's personal use or for internal company use, provided that the source and The Publisher copyright notice are mentioned, that the copies are not used in any way that implies The Publisher endorsement of a product or service of an employer, and that the copies are not offered for sale as such. Authors are permitted to grant third party requests for reprinting, republishing or other types of reuse. The Authors may make limited distribution of all or portions of the above Paper prior to publication if they inform The Publisher of the nature and extent of such limited distribution prior there to. Authors retain all proprietary rights in any process, procedure, or article of manufacture described in The Paper. This agreement becomes null and void if and only if the above paper is not accepted and published by The Publisher, or is with drawn by the author(s) before acceptance by the Publisher.