The dynamics of export-import interaction

Abstract

This work is devoted to the dynamic interpretation of the basic provisions of the quantitative theory of money. Namely, the construction of models of price changes for marketable products in the performance of export-import activities both in discrete and continuous time. A number of hypotheses are used to determine the conditions for the violation of the equilibrium states of the trade balance using the classical macroeconomic Fisher equation. An overview of scientific works is presented, which highlights the main factors for the implementation of foreign economic activity: exchange rates and devaluation. The analysis of the considered sources testifies to the presence of the problem of stability of the observed dynamic processes in the vicinity of the state of equilibrium, which have the traditional name of the Marshall-Lerner condition. A detailed study of the stability criteria of a discrete dynamic model with quadratic nonlinearity demonstrates a significant variety of trajectories of the studied process. These are, in particular, increasing or decreasing aperiodic behavior, oscillating processes of a fixed period, bifurcations of doubling the period and chaotic trajectories. The limits of distribution of various types of evolutionary changes in terms of elasticities as important indicators of export-import operations are indicated. For models of pricing dynamics in continuous time, a detailed analysis of the structural instability of equilibrium states was performed. Saddle-nodal bifurcation and no less important Andronov-Hopf bifurcation, which is associated with the formation of a boundary cycle around the equilibrium state, are distinguished. It is proved that the found cycle is unique and stable. For a discrete model of price formation, appropriate calculations are performed to demonstrate different types of evolutionary behavior. The given discrete model based on the Fisher equation can be used for qualitative forecasting (by trajectories) of the dynamics of internal pricing without the use of traditional methodology of econometric analysis of time series. This model is characterized by the fact that it is reduced to a single complex parameter and this greatly simplifies the definition of the corresponding types of dynamical regimes in the vicinity of equilibrium states.