History of the calculus of variations in economics - Reginatto, Vinícius Oike (2019)
In this dissertation work, I present a broad historical account of how the calculus of variations was applied in economics in the 1920s up until the 1940s. In the interwar period, mathematical economics was a vibrant and plural community of authors. Previous historical works on this period have focused on specific points of these authors. The present dissertation focuses on the mathematical technique, i.e., the calculus of variations and how it was used in economics. This history also encompasses the early mathematization of economics, the early history of econometrics, and the struggles to devise a dynamic theory of economics in a general equilibrium framework. I follow mainly the works of American mathematician Griffith C. Evans (18871973) whom I argue is a seminal author in this literature. In 1924, Evans used the calculus of variations to put forward a dynamic version of A. Cournot\'s classic analysis of monopoly. In the following decades, a handful of authors followed Evans\'s approach and used the calculus of variations to research depreciation, business cycles, optimal savings, and general equilibrium. In the late 1960s, similar mathematical formulations became common place in the form of optimal control and dynamic programming. These new mathematical techniques shared intimate relations with the calculus of variations.