The Samuelson macroeconomic model as a singular linear matrix difference equation

Fernando Ortega,María Filomena Lopes De Barros

doi:10.1186/s40008-020-00207-3

Fernando Ortega, María Filomena Lopes De Barros

Open Access

https://doi.org/10.1186/s40008-020-00207-3

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Abstract

In this paper, we revisit the famous classical Samuelson’s multiplier–accelerator model for national economy. We reform this model into a singular discrete time system and study its solutions. The advantage of this study gives a better understanding of the structure of the model and more deep and elegant results.

Highlights

We propose an alternative view of the model by reforming it into a singular discrete time system
We proved the following theorem: Theorem 3.1 The difference equation (1) can be written in the form of the following singular discrete time system: FYk+1 = GYk + Vk, k = 2, 3, . . . , (4)
We will provide the solution to the system (4) and we will derive the sequence for the national income, the consumption and the private investment

Summary

Introduction

Many authors have studied generalized discrete, see (Apostolopoulos and Ortega 2019; Dassios 2015a; Dassios and Kalogeropoulos 2013; Ogata 1987; Ortega and Apostolopoulos 2018), and continuous time systems, see (Dassios et al 2019, 2020; Lewis 1986, 1987, 1992; Liu et al 2019; Milano and Dassios 2016, 2017), and their applications especially in cases where the memory effect is needed including generalized discrete, see (Dassios and Baleanu 2015; Dassios and Kalogeropoulos 2014; Dassios and Szajowski 2016), and continuous time systems with delays, see (Liu et al 2017, 2019, 2020; Tzounas et al 2020). Many more sophisticated models have been proposed by other researchers, see (Barros and Ortega 2019; Dassios and Devine 2016; Dassios and Zimbidis 2014; Dassios et al 2014; Dorf 1983; Kuo 1996; Puu et al 2004; Rosser 2000). All these models use superior and more delicate mechanisms involving monetary aspects, inventory issues, business expectation, borrowing constraints, welfare gains and multi-country consumption correlations. Ortega and Barros Economic Structures (2020) 9:36 parameters (multiplier and accelerator parameters) are entered into the system of equations This statement contradicts with the empirical evidence which supports temporary or long-lasting business cycles. See (Samuelson 1939) for the needed theory of difference equations that lead to the solution of the above equation

The reformulation

Results and discussion

Conclusions

Methods