The Z-transform method for multidimensional dynamic economic systems

Abstract

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

Keywords:

• Z-transform
• steady-state comparisons
• discrete-time systems
• multi-sector model

JEL Classifications:

• C63
• E20
• H20

Acknowledgments

This paper is sponsored by the National Science Foundation for Distinguished Young Scholars of China under project 70725006 and the National Science Foundation for Young Scientists Fund of China under project 71103208.

Notes

¹ Here after, when taking differentiations on , we always evaluate at .

² We have used