A simple characterisation for sustained growth

Abstract

This article considers an inter-temporal optimization problem in a fairly general form and give sufficient conditions ensuring the convergence to infinity of the economy. These conditions are easy to verify and can be applied for a large class of problems in literature. As examples, some applications for different economies are also given.

Fifty years of mathematical growth theory: Classical topics and new trends

“…In particular, we do not touch the literature around the applicability of the contraction mapping theorems and alternatives (depending in particular on the boundedness of the utility functions). The reader can refer to Le Van and Morhaim [81] for more details, a representative JME contribution to this important literature being Ha-Huy and Thien Tran [64], among others. We now specialize in the traditional one-sector Ramsey model.…”

“…An increasing number of contributions is being devoted to theoretical normative and positive issues arising in the ongoing debate on sustainable growth. Differently from the research questions addressed within the traditional endogenous growth framework (still active, see for example Ha-Huy and Thien Tran [64] for a very recent contribution), this new literature intersects with the environmental literature and questions the long term viability of growth regime in the presence of environmental external effects (pollution and global warming) and availability of natural resources and backstop technologies. In response to the Meadows report published in 1972, a number of economic growth models incorporating natural resources as input into otherwise neoclassical production functions have been elaborated such like the famous DHSS (Dasgupta-Heal-Solow-Stiglitz) model, see for example Stiglitz [114].…”

Balanced growth and degrowth with human capital

“…Their social planner's solutions internalizes the external effects of human capital in production. However, the uniqueness proofs provided in Gourdel et al (2004) and the sustained growth result in Ha-Huy and Tran (2020) can not encompass positive human capital depreciation. Furthermore, both papers require a bounded utility function, while our contribution covers logarithmic preferences.…”

“…Ha-Huy and Tran (2020) also consider an unbounded utility function from below, but their condition (3.2) in Proposition 3.3 fails in the case of our article.…”