Economic Dynamics and the Calculus of Variations in the Interwar Period

Pomini, Mario

doi:10.1017/s1053837217000116

Cited by 15 publications

(8 citation statements)

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“…Dimand (1988) had also shown this connection, and reexamined the importance of Roos on the early development of econometrics (see also Dimand and Veloce [2007] on this influence). The work of Roos and Evans has also been studied particularly from the point of view of intertemporal optimization in the interwar, in particular by Duarte (2016) and Pomini (2018). Boianovsky and Tarascio (1998) and Pomini and Tusset (2009) centered on the history of the "Paretian school," and its attempts to dynamize general equilibrium theory, the latter especially during the interwar.…”

Section: Introductionmentioning

confidence: 99%

Rupture and continuity in the original divide between microdynamics and macrodynamics

Carret

2022

The European Journal of the History of Economic Thought

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In 1933, Ragnar Frisch introduced a distinction between micro-dynamics and macro-dynamics in his paper on "Propagation problems and impulse problems in dynamic economics." His claim that he proposed the first macro-dynamic analysis and that micro-dynamic schemes were limited to the dynamics of specific markets or behaviors had a lasting impact on the field. But the introduction of this separation created a narrative hiding what had been done before and introduced a tension between the two approaches. By going back to the content of micro-dynamic analysis, we are led to two lines of research that were pursued during the 1920s and early 1930s: cobweb models and intertemporal optimization. A pivotal economist for going beyond micro-dynamics was Jan Tinbergen, who had contributed to both these approaches, and went beyond with new analytical tools. However, the idea of intertemporal optimization met with some opposition when it was scaled up to the whole economic system. This prompted Frisch to propose his new approach, which met with immediate success as more schemes were proposed. Tinbergen was himself one of the first converts to macro-dynamics, but the links between the two approaches and the new tensions created by their separation remained. This tension between the newly created categories can be viewed as a result of opposing views on causality, which were rooted in differing mathematical approaches, a point explicitly made by the next generation.

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Section: Introductionmentioning

confidence: 99%

Rupture and continuity in the original divide between microdynamics and macrodynamics

Carret

2022

The European Journal of the History of Economic Thought

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“…Numerous insights and debates concerning the broader interpretation of statics, dynamics and stationary state can be roughly divided into the 'objective', largely mathematical approaches based on analogies with mechanics, and the 'subjective', incorporating expectations and other psychological factors. The objective approach culminated in the correspondence principle of PaulSamuelson, e.g., Samuelson (1947), and the calculus of variations approach initiated by Evans and Roos and further developed by the Paretian school(Pomini 2018). While first wave cobweb theory largely advanced 'objective' considerations, development of the subjective dimension characterizes the second wave.Algebraic formulation of first wave cobweb graphs and conditions associated with market instability, adapted from Tinbergen, are illustrated in various sources, e.g.,Nerlove (1958b, pp.228-9),Ferguson (1960, p.300): This leads to the linear first order difference equation and solution for equilibrium price PE and quantity QE when Pt = Pt -1 = PE: The linear cobweb dynamics follow from starting in equilibrium and imposing a discontinuous perturbation such that PE P0 (due to an exogenous shift in supply or demand at t = 0) and observing the path of prices starting from P0 depends on the relative slopes of the supply and demand curves: explosive oscillation for | s1 | > | d1 |; alternating oscillation for | s1 | = | d1 |; and, converging oscillation for | s1 | < | d1 |.…”

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confidence: 99%

Cobweb Theory, Market Stability, and Price Expectations

Poitras¹

2023

J Hist Econ Thought

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Contributors to cobweb theory include many leading economists of the twentieth century. From early beginnings in 1930, cobweb theory played a key role in evolving perceptions of market stability arising from recursive linear models with endogenous dynamics. The focal point of this evolution in cobweb theory is the transition from naive to adaptive to rational price expectations. After a review of the prehistory, this paper examines the first wave of linear cobweb theory initiated by Jan Tinbergen, Henry Schultz, and Umberto Ricci and proceeds to consider the evolution of price expectations in the second wave of cobweb models associated with endogenous cycles in commodity markets. The role of modern cobweb theory in discussions about the stability of market equilibrium and the connection to processes with rational expectations is assessed.

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“…It should be noted that Volterra's interest in mathematical economics was quite brief. In this sense, Pomini (2018) argues that Volterra's influence on Evans's work in economics is mainly methodological (62-63).…”

Section: Chaptermentioning

confidence: 99%

“…The dynamics in his mathematical model, as did in Evans's 1924 article, came from the optimizing 50. Pomini (2018) notes that in solving this problem with the calculus of variations, La Volpe was aided by two Neapolitan mathematicians (Pomini 2018, 70). He also notes that La Volpe's decision to include expectations "reveals the influence of the Austrian school for which dynamic analysis was a multi-period analysis influenced by the expectations of economic agents" (69).…”

Section: Further Developments Using the Calculus Of Variationsmentioning

confidence: 99%

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History of the calculus of variations in economics

Reginatto¹

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Agradeço ao professor Pedro Garcia Duarte pela orientação neste tópico bastante instigante, que conciliou muitos dos meus interesses em economia. Seus conselhos e suas aulas foram determinantes para esta dissertação. Agradeço também ao professor Jorge Araújo que me acompanha desde os tempos de graduação na UFRGS. Agradeço muito aos colegas do IPE-USP pela convivência e parceria: as conversas, reflexões e risadas acalentaram mesmo os mais pesados dias do mestado. O encontro rotineiro com pessoas tão vivazes e sapientes era não só inspirador, como também se provou vital para meu desenvolvimento. Agradeço em particular aos colegas de salinha: Ahmad, Bernardo, Clara, Fábio, Felipe, João, Menon, Vitor-e também ao Matheus, meu colega expatriado do Rio Grande. Agradeço aos amigos queridos de Porto Alegre, que desde muito cedo na minha formação estiveram comigo, em especial ao Guilherme Leon e ao Vitor Cunha. Crescemos juntos e partilhamos muito da vida; agora seguimos distantes, mas ainda próximos. Agradeçoà Helena pelo carinho e apoio nestesúltimos anos. Agradeço tambémà Carla por desde sempre ser uma pessoa especial na minha vida. Agradeçoà minha mãe, ao meu pai, eà minha família pelo amor, ajuizamento e, também, pela paciência e apoio nestes anos tão turbulentos e difíceis. RESUMO Neste trabalho de dissertação, apresento uma história geral de como o cálculo variacional foi aplicado na economia no período dos anos 1920 até 1940. Durante o período do entreguerras, havia uma comunidade plural e vibrante de autores trabalhando com economia matemática. Trabalhos históricos sobre esse período se debruçaram sobre pontos específicos desses autores. O presente trabalho tem como foca a técnica matemática, i.e., o cálculo variacional e como ele foi utilizado na economia. Minha história também abarca o início da matematização da economia, os primeiros anos da econometria, e os desenvolvimentos de uma teoria dinâmica de economia dentro de um modelo de equilíbrio geral. Este trabalho segue de perto a obra do matemático estadunidense Griffith C. Evans (1887-1973), um autor seminal nesta literatura. Em 1924, Evans usa o cálculo variacional para dinamizar a análise clássica de monopólio de A. Cournot. Nas próximas décadas, a maior parte dos autores que usaram o cálculo variacional em economia seguiram a abordagem de Evans: eles encontraram aplicações para o cálculo de variações em teorias de depreciação, ciclos de negócios e equilíbrio geral. No final da década de 60, modelos matemáticos usando controleótimo e programação dinâmica se popularizaram em economia. Estas novas técnicas matemáticas têḿ ıntima relação com o cálculo variacional. 1. Pluralism here indicates the variety of methods, beliefs, and policy advice present throughout American economic theory throughout the interwar period. I use the term in the same sense as

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Economic Dynamics and the Calculus of Variations in the Interwar Period

Cited by 15 publications

References 41 publications

Rupture and continuity in the original divide between microdynamics and macrodynamics

Rupture and continuity in the original divide between microdynamics and macrodynamics

Cobweb Theory, Market Stability, and Price Expectations

History of the calculus of variations in economics

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