Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-19T18:24:32.892Z Has data issue: false hasContentIssue false

ECONOMIC DYNAMICS AND THE CALCULUS OF VARIATIONS IN THE INTERWAR PERIOD

Published online by Cambridge University Press:  15 February 2018

Mario Pomini*
Affiliation:
Department of Economics and Management, University of Padua, Italy.
*

Abstract

Analogies with rational mechanics played a pivotal role in the search for formal models in economics. In the period between the two world wars, a small group of mathematical economists tried to extend this view from statics to dynamics. The main result was the extensive application of calculus of variations to obtain a dynamic representation of economic variables. This approach began with the contributions put forward by Griffith C. Evans, a mathematician who, in the first phase of his scientific career, published widely in economics. Evans’s research was further developed by his student Charles Roos. At the international level, this dynamic approach found its main followers in Italy, within the Paretian tradition. During the 1930s, Luigi Amoroso, the leading exponent of the Paretian School, made major contributions, along with his student Giulio La Volpe, that anticipated the concept of temporary equilibrium. The analysis of the application of the calculus of variations to economic dynamics in the interwar period raises a set of questions on the application of mathematics designed to study mechanics and physics to economics.

Type
Articles
Copyright
Copyright © The History of Economics Society 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

I would like to thank two anonymous referees for helpful comments on an earlier draft.

References

REFERENCES

Allen, Roy George. 1937. Mathematical Analysis for Economists. London: Macmillan.Google Scholar
Amoroso, Luigi. 1912. “Contributo alla teoria matematica della dinamica economica.” Atti della Accademia dei Lincei 21: 341346.Google Scholar
Amoroso, Luigi. 1921. Lezioni di economia matematica. Bologna: Zanichelli.Google Scholar
Amoroso, Luigi. 1928. “Discussione del sistema di equazioni che definiscono l’equilibrio del consumatore.” Annali di Economia 4: 3041.Google Scholar
Amoroso, Luigi. 1929. “Le equazioni differenziali nella dinamica economica.” Giornale degli Economisti e Rivista di Statistica 28: 6779.Google Scholar
Amoroso, Luigi. 1932. “Contributo alla teoria matematica della dinamica economica.” In Nuova Collana degli Economisti V. Torino: UTET, pp. 419440.Google Scholar
Amoroso, Luigi. 1933. “La dinamica dell’impresa.” Rivista italiana di Statistica, Economia e Finanza 4: 442451.Google Scholar
Amoroso, Luigi. 1938. “La teoria matematica del programma economico.” In Amoroso, Luigi, ed., Cournot nella economia e nella filosofia. Padova: Cedam, pp. 7493.Google Scholar
Amoroso, Luigi. 1940. “The Transformation Value in the Productive Process.” Econometrica 8: 111.CrossRefGoogle Scholar
Amoroso, Luigi. 1942. Meccanica Economica. Città di Castello: Macrì.Google Scholar
Arfken, George, and Weber, Hans. 2001. Mathematical Methods for Physicists. New York: Harcourt Academic Press.Google Scholar
Boianovsky, Mauro, and Tarascio, Vincent. 1998. “Mechanical Inertia and Economic Dynamics: Pareto on Business Cycles.” Journal of the History of Economic Thought 20: 521.Google Scholar
Boumans, Marcel. 2005. How Economists Model the Word into Numbers. Abingdon: Routledge.Google Scholar
Boumans, Marcel. 2009. “Dynamizing Stability.” History of Political Economy 41 (Annual suppl.): 127146.Google Scholar
Cass, David. 1965. “Optimal Growth in an Aggregative Model of Capital Accumulation.” Review of Economic Studies 32: 233240.Google Scholar
De Pietri Tonelli, Alfonso. 1921. Trattato di Economia Razionale e Sperimentale. Rovigo: Cedam.Google Scholar
Dimand, Robert. 1988. “Early Mathematical Theories of Business Cycles.” In Moggridge, D. E., ed., Keynes, Macroeconomics and Method. London: Edward Elgar, pp. 155161.Google Scholar
Dimand, Robert, and Veloce, William. 2007. “Charles F. Roos, Harold T. Davis and the Quantitative Approach to Business Cycle Analysis at the Cowles Commission in the 1930s and Early 1940s.” The European Journal of the History of Economic Thought 13: 519541.Google Scholar
Di Matteo, Massimo. 1993. “Foreword Part II.” In Giulio La Volpe, Studies on the Theory of General Dynamic Economic Equilibrium. Edited by Morishima, Michio and Matteo, Massimo Di. Basingstoke: Macmillan.Google Scholar
Di Matteo, Massimo. 1998. “Giulio La Volpe.” Rivista Italiana degli Economisti 3: 157160.Google Scholar
Donzelli, Franco. 1997. “Pareto’s Mechanical Dream.” History of Economic Ideas 5: 127178.Google Scholar
Duarte, Pedro G. 2016. “A Path through the Wilderness: Time Discounting in Growth Models.” History of Political Economy 48 (2): 161181.CrossRefGoogle Scholar
Evans, Griffith C. 1922. “A Simple Theory of Competition.” American Mathematical Monthly 29: 371380.Google Scholar
Evans, Griffith C. 1924. “The Dynamics of Monopoly.” American Mathematical Monthly 31: 91117.Google Scholar
Evans, Griffith C. 1925. “The Mathematical Theory of Economics.” American Mathematical Monthly 32: 104110.Google Scholar
Evans, Griffith C. 1929. “Cournot on Mathematical Economics.” Bulletin of American Mathematical Society 35: 269271.CrossRefGoogle Scholar
Evans, Griffith C. 1930. Mathematical Introduction to Economics. New York: McGraw-Hill.Google Scholar
Fisher, Irving. 1930. “Mathematics in the Social Sciences.” The Scientific Monthly 30: 547557.Google Scholar
Fossati, Eraldo. [1937] 1953. “Ricerca sulle relazioni tra il tempo e l’utilità.” In Fossati, Eraldo, Frammenti di teoria dinamica. Bologna: Cappelli Editore, pp. 3552.Google Scholar
Frisch, Ragnar. 1933. “Propagation Problems and Impulses Problems in Dynamics Economics.” In Economic Essays in Honour of Gustav Cassel. London: Allen and Unwin, pp. 171205.Google Scholar
Frisch, Ragnar. 1936. “On the Notion of Equilibrium and Disequilibrium.” The Review of Economic Studies 3: 100105.Google Scholar
Gandolfo, Giancarlo. 2008. “Giuseppe Palomba and the Lotka–Volterra Equations.” Rendiconti Lincei: 347357.Google Scholar
Grattan-Guinness, Ivor. 2010. “How Influential Was Mechanics in the Development of Neoclassical Economics? A Small Example of Large Questions.” Journal of the History of Economic Thought 32: 531580.Google Scholar
Graziani, Augusto. 1991. “The Italian Economic Journals and Some Major Turning-Points in Economic Theory.” Economic Notes 21: 121133.Google Scholar
Guerraggio, Angelo, and Paoloni, Giovanni. 2011. Vito Volterra. Basel: Birkhäuser.Google Scholar
Hicks, John. 1939. Value and Capital. Oxford: Oxford University Press.Google Scholar
Hotelling, Harold. 1931. “Review of Mathematical Introduction to Economics.” Journal of Political Economy 39: 107109.Google Scholar
Ingrao, Bruna, and Israel, Giorgio. 1990. The Invisible Hand. Cambridge: MIT Press.Google Scholar
Kyun, Kim. 1988. Equilibrium Business Cycle Theory in Historical Perspective. Cambridge: Cambridge University Press.Google Scholar
Louçã, Francisco. 2007. The Years of High Econometrics. Abingdon: Routledge.Google Scholar
La Volpe, Giulio. [1936] 1993. Studies on the Theory of General Dynamic Economic Equilibrium. Houndmills: Macmillan. First published as Studi sulla teoria dell’equilibrio economico dinamico generale. Napoli: Jovene.Google Scholar
La Volpe, Giulio. 1938. Ricerche di dinamica economica corporativa: impostazioni e problemi. Padova: Cedam.Google Scholar
La Volpe, Giulio. 1967. “L’analisi variazionale come fondamento ei modelli econometrici.” Ricerche Economiche 21: 231252.Google Scholar
La Volpe, Giulio. 1977. “La dinamica eso-endogena e i problemi diretti e inversi nella ricerca economica.” Rivista di Politica Economica 67: 111152.Google Scholar
McLure, Michael. 2001. Pareto, Economy and Society: The Mechanical Analogy. London: Routledge.Google Scholar
Mirowski, Philip. 1989. More Heat than Light: Economics as a Social Physics, Physics as Nature Economics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Moore, Henry L. 1929. Synthetic Economics. New York: Macmillan.Google Scholar
Mordecai, Ezekiel. 1930. “Moore’s Synthetic Economics.” The Quarterly Journal of Economics 44 (4): 663679.Google Scholar
Morrey, Carl B. 1983. “Griffith Conrad Evans.” Biographical Memoirs. National Academy of Science 54: 127155.Google Scholar
Nicola, Pier Carlo. 2000. Mainstream Mathematical Economics in the 20th Century. Berlin: Springer.CrossRefGoogle Scholar
Palomba, Giuseppe. 1939. Introduzione allo studio della dinamica economica. Napoli: Jovene.Google Scholar
Palomba, Giuseppe. 1959. Fisica economica. Napoli: Jovene.Google Scholar
Pareto, Vilfredo. [1896–97] 1941. Corso di Economia Politica. Torino: Boringhieri.Google Scholar
Pareto, Vilfredo. 1901. “Le nuove teorie economiche con annessa appendice. Le equazioni dell’equilibrio dinamico.” Giornale degli Economisti 23: 235259.Google Scholar
Pomini, Mario. 2009. “Equilibrio dinamico ed aspettative in Giulio La Volpe.” Il Pensiero Economico Italiano XVII: 331349.Google Scholar
Pomini, Mario, and Tusset, Gianfranco. 2009. “Habits and Expectations: Dynamic General Equilibrium in the Italian Paretian School.” History of Political Economy 41: 311343.Google Scholar
Ramsey, Frank. 1928. “A Mathematical Theory of Saving.” Economic Journal 38: 543559.Google Scholar
Raybout, Alain. 2013. “H. L. Moore and the Dynamic Complement of Pure Economics.” Oeconomica 3: 221240.Google Scholar
Roos, Charles. 1925. “A Mathematical Theory of Competition.” American Journal of Mathematics 47: 163165.CrossRefGoogle Scholar
Roos, Charles. 1927. “A Dynamical Theory of Economics.” The Journal of Political Economy 35: 632656.Google Scholar
Roos, Charles. 1928. “Generalized Lagrange Problems in the Calculus of Variations.” American Mathematical Society 30: 360384.Google Scholar
Roos, Charles. 1930. “A Mathematical Theory of Price and Production Fluctuations and Economic Crisis.” Journal of Political Economy 38: 501522.Google Scholar
Roos, Charles. 1934. Dynamic Economics. Bloomington: The Principia Press.Google Scholar
Rosenstein-Rodan, Paul N. 1934. “The Role of Time in Economic Theory.” Economica 1: 7797.Google Scholar
Samuelson, Paul A. 1941. “The Stability of Equilibrium: Comparative Statics and Dynamics.” Econometrica 9: 97120.Google Scholar
Samuelson, Paul A. 1947. Foundations of Economic Analysis. Cambridge: Harvard University Press.Google Scholar
Samuelson, Paul, and Solow, Robert. 1956. “A Complete Capital Model Involving Heterogeneous Capital Goods.” The Quarterly Journal of Economics 70: 537562.Google Scholar
Sensini, Guido. 1955. Corso di Economia Pura. Roma: Maglione.Google Scholar
Tinbergen, Jan. 1933. “L’utilisation des équations fonctionelles et des nombres complexes dans les recherches économiques.” Econometrica 1: 3651.Google Scholar
Tinbergen, Jan. 1934. “Annual Survey of Significant Developments in General Economic Theory.” Econometrica 2: 1336.Google Scholar
Weintraub, Roy. 1991. Stabilizing Dynamics. Cambridge: Cambridge University Press.Google Scholar
Weintraub, Roy. 1998. “From Rigor to Axiomatics: The Marginalization of Griffith C. Evans.” History of Political Economy 30: 227259.Google Scholar
Weintraub, Roy. 2002. How Economics Became a Mathematical Science. Durham: Duke University Press.Google Scholar
Wulwick, Nancy. 1995. “The Hamiltonian Formalism and Optimal Growth Theory.” In Rima, Ingrid H., ed., Measurement, Quantification and Economic Analysis. New York: Routledge, pp. 157175.Google Scholar