# On the analysis of endogenous growth models with a balanced growth path

*Timo Trimborn* ()

*Journal of Mathematical Economics*, 2018, vol. 79, issue C, 40-50

**Abstract:**
This paper is the first that provides a comprehensive toolkit for analyzing deterministic, continuous-time, endogenous growth models with a balanced growth path. Since it is impossible to analyze the original dynamic system of growing variables, I suggest two different methods of transforming the model variables in order to derive a stationary system. The stationary system can then be used to test for the existence and uniqueness of transition paths and to derive transitional dynamics qualitatively (e.g. by phase diagram analysis) and quantitatively (e.g. by numerical simulation). I provide sufficient conditions under which the transformed dynamic system is autonomous, derive the functional form of the transformed system, and provide instructions of how to analyze the stability properties of the transformed system. Furthermore, I show that the class of models for which the method can be applied exhibits a specific pattern of transitional dynamics. Two identical economies that differ only with respect to the endowment of one state variable are shown to grow with the same balanced growth rate in the long-run, but at different levels.

**Keywords:** Continuous-time endogenous growth models; Transitional dynamics; Balanced growth; Knife-edge conditions (search for similar items in EconPapers)

**Date:** 2018

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:mateco:v:79:y:2018:i:c:p:40-50

**DOI:** 10.1016/j.jmateco.2018.09.003

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