The model used in this paper has two types of capital, K and H.  Under financial autarky, the situation studied in this subsection, there is little difference in the characteristics of K and H but, as discussed below, an important difference exists when international borrowing and lending occurs. The production function for this economy includes K and H, as well as L, the number of workers, and E, the efficiency of labor, and is given by

where Y is output and both α and β are between 0 and 1. We study the model with the variables expressed in terms of effective units of labor, and define y = Y / EL, k = K / EL and h = H / EL. Using these variables, the production function is

The model attempts to capture the fact that poor institutions lower the return to capital because, with poor institutions, some savings of domestic residents fail to translate to investment because of the malfeasance of governmental or private actors who are not appropriately constrained by law.  Institutional quality is negatively related to the amount of expropriation that occurs.  This model includes the parameter τ which represents the rate of expropriation of both types of capital by the government or others (0 < τ < 1), and, therefore, an index for the quality of institutions is (1 – τ).

The parameter τ appears in the capital accumulation equations for both K and H under autarky, when both types of capital can only be accumulated only through domestic savings.  The capital accumulation equations, expressed in terms of k and h, are