Especialización En Matemática Aplicada
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- ÍtemPropuesta metodológica del modelamiento y solución de un sistema de ecuaciones en diferencia lineales de primer orden de la Teoría del Duopolio de Cournot.(2023-06-04) Medina Cuzpoca, Fredy Ricardo; Pinto Cruz, Edgar Antonio; Ramos Ramos, Carlos JulioThe study of time invariant systems (LTI) is very important and as an example of its application, Cournot’s Duopoly Theory, since these LTI systems facilitate the understanding and analysis of very complex systems. In this regard Blanco (2017), in his article "The scientific method in the economic theory of A. A. Cournot" analyzes the impact of this theory to economics and describes Cournot’s methodological contributions, finding that mathematics is in the theoretical basis of other knowledge. In the field of difference equations applied to economic models, Romero (2012), in his work "Ordinary differential equations and difference equations oriented to economic modeling", describes the obtaining of economic models through differential equations (continuous analysis) and difference equations (discrete analysis). In this article a methodological proposal is made for the solution of a system of equations in difference, proper of a Duopoly model of the Cournot theory in discrete time that can optimize the learning curves of the students in the previously mentioned domains. We start from a hypothetical exercise to make a toy model that allows us to propose a general methodological proposal for the solution of economic models of Cournot Duopoly with initial conditions of demand and prices per unit of production. In addition, an implementation in the programming language Phyton is made.