Abstract
Modern microeconomics and macroeconomics study dynamic phenomena. Dynamics could predict future states of an economy based on its structural charac teristics. Dynamic models in discrete time discrete state economic systems may take the form of one sin gle linear difference equation or a system of linea r difference equations. In this study we use Xcas and Mathematica as software tools in order to generate results concerning the dynamic properties of the so lutions of the difference equation(s) and, determin e whether an economic equilibrium exists. Our computational approach does not require solving the difference equation(s) and makes no assumptions for initial conditions. The results provide quantitati ve information based on the qualitative properties of the mathematical solutions rather than on their quantifiable ones. The relevant output of CAS softw are is created in a way as to be interpreted withou t the knowledge of advanced mathematics. The computer codes are fully presented and can be reproduced as they are in computational-based research practic e and education.
Highlights
Dynamic models in discrete time discrete state economic systems may take the form of one single linear difference equation or a system of linear difference equations
In this study we use Xcas and Mathematica as software tools in order to generate results concerning the dynamic properties of the solutions of the difference equation(s) and, determine whether an economic equilibrium exists
Dynamic economic analysis is to determine whether, given sufficient time, economic variables tend to converge to certain equilibrium values
Summary
Dynamic economic analysis is to determine whether, given sufficient time, economic variables tend to converge to certain equilibrium (steady state) values. Time is considered as a discrete variable, meaning that any variable undergoes a change only once within a period of time. Linearity is not restrictive in economic applications since it may be imposed on a model through means of a first order taylor approximation. In discrete time discrete state dynamic economic systems, only a subset of elements is given, these are the state variables of the economy such as the capital stock and asset position. Classic discrete time discrete state economic models are the Cobweb model with memory of several periods, Samuelson multiplier-acceleration interaction model, inflationunemployment model in discrete time, dynamic market models, macroeconomic and macroeconometric models
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