Some Properties of a Small Open Economy Version of the Solow-Swan Growth Model

In this paper we examine some properties of the Benge and Wells (B-W) (1998a,b) formulation of a small open economy version of the Solow-Swan growth model. We suggest a simple method for classifying economies as capital importers or exporters (net debtors or creditors) in the steady state and highlight the simple mathematical structure of the B-W formulation. Given the small open economy assumption the fundamental dynamic equation for wealth is a simple first order linear differential equation so closed form solutions are immediate. That greatly simplifies the analysis of the transitional dynamics. In addition we show that the transitional dynamics of the B-W formulation depends on the specification of saving as a function of current income. In that formulation the speed of adjustment coefficient is a function of both the saving ratio and the world real rate of interest. A debt trap is possible for some parameter values. When saving is specified as a function of permanent income (steady state income) the speed of adjustment coefficient reverts to a constant determined by the exogenous growth rate in effective labour. The threat of a debt trap disappears.