The Z-Transform Method for Multidimensional Dynamic Economic Systems

This paper uses the Z-transform to develop a method for solving the linearized multidimensional discrete-time systems, which can be used to discuss the e¡èects of policies on economy (including the welfare gains and initial e¡èects on economy) raised by multi-sector perfect-foresight-discrete-time models. Our method is not restricted on the dimension of the dynamic system, and it cannot only analyze the effect of permanent policy change on the economy, but also it can be used to analyze the e¡èect of temporal policy change on the economy. As an application example, we analyze the effects of fiscal policy on the initial economy and social welfare in the discrete-time Uzawa-Lucas model.