Economic systems, due to their substantial effects on any society, are interesting research subject for a large family of researchers. Despite all attempts to study economic and financial systems, studies on discrete-time macroeconomic systems are rare. Hence, in the current study, we aim to investigate dynamical behavior and synchronization of these systems. At first, the discrete-time mathematical model of the macroeconomic system is presented. Then, the system is studied through topological classification, bifurcation analysis, Lyapunov exponents, and manifold theory, which are powerful too...