On Some Important Ordinary Differential Equations of Dynamic Economics

Abstract

Mathematical modeling in economics became central to economic theory during the decade of the Second World War. The leading figure in that period was Paul Anthony Samuelson whose 1947 book, Foundations of Economic Analysis, formalized the problem of dynamic analysis in economics. In this brief chapter some seminal applications of differential equations in economic growth, capital and business trade cycles are outlined in deterministic setting. Chaos and bifurcations in economic dynamics are not considered. Explicit analytical solutions are presented only in relatively straightforward cases and in more complicated cases a path to the solution is outlined. Differential equations in modern dynamic economic modeling are extensions and modifications of these classical works. Finally we would like to stress that the differential equations presented in this chapter are of the “stand-alone” type in that they were solely introduced to model economic growth and trade cycles. Partial differential equations such as those which arise in related fields, like Bioeconomics and Differential Games, from optimizing the Hamiltonian of the problem, and stochastic differential equations of Finance and Macroeconomics are not considered here.

Parameter estimation of the Solow–Swan fundamental differential equation

“…the outline in Spear and Young, 2014 ), or the Mankiw–Romer–Weil model, which extends the classical model by augmenting the production function with human capital ( Mankiw et al., 1992 ). The differential equations of these and related models are summarized in Tsoularis (2021) .…”