TITLE:
Nonlinear Differential Equation of Macroeconomic Dynamics for Long-Term Forecasting of Economic Development
AUTHORS:
Askar Akaev
KEYWORDS:
Long-Term Economic Trend, Cycles, Nonlinear Accelerator, Induced and Autonomous Investment, Differential Equations of Macroeconomic Dynamics, Bifurcation, Stability, Crisis Recession, Forecasting, Explosive Growth in the Prices of Highly Liquid Commodities as a Predictor of Crisis
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.5,
May
30,
2018
ABSTRACT: In this article we derive a general differential equation that describes
long-term economic growth in terms of cyclical and trend components. Equation
is based on the model of non-linear accelerator of induced investment. A
scheme is proposed for obtaining approximate solutions of nonlinear differential
equation by splitting solution into the rapidly oscillating business
cycles and slowly varying trend using Krylov-Bogoliubov-Mitropolsky averaging.
Simplest modes of the economic system are described. Characteristics
of the bifurcation point are found and bifurcation phenomenon is interpreted
as loss of stability making the economic system available to structural change
and accepting innovations. System being in a nonequilibrium state has a dynamics
with self-sustained undamped oscillations. The model is verified with
economic development of the US during the fifth Kondratieff cycle
(1982-2010). Model adequately describes real process of economic growth in
both quantitative and qualitative aspects. It is one of major results that the
model gives a rough estimation of critical points of system stability loss and
falling into a crisis recession. The model is used to forecast the macroeconomic
dynamics of the US during the sixth Kondratieff cycle (2018-2050). For
this forecast we use fixed production capital functional dependence on a
long-term Kondratieff cycle and medium-term Juglar and Kuznets cycles.
More accurate estimations of the time of crisis and recession are based on the
model of accelerating log-periodic oscillations. The explosive growth of the
prices of highly liquid commodities such as gold and oil is taken as real predictors
of the global financial crisis. The second wave of crisis is expected to
come in June 2011.