The Solow Model

Abstract

The research will be carried out within the following framework. Firms manufacture a homogeneous commodity by employing capital and labour. Let the production function be of the Cobb-Douglas variety ${\hbox{Y}} = {{\hbox{K}}^{\upalpha }}{{\hbox{N}}^{\upbeta }}$. Output can be devoted to consumption, investment, government purchases and net exports Y = C + I + G + H. Let labour grow at the natural rate $\dot{N}$ = nN with n = const. For the small open economy, the foreign interest rate is given r* = const. Under perfect capital mobility, the domestic interest rate coincides with the foreign interest rate r = r*. Firms maximize profits under perfect competition, so the marginal product of capital corresponds to the interest rate $\upalpha$Y/K = r. This in turn yields the stock of capital. By way of contrast, the wage rate harmonizes with the marginal product of labour w = $\upbeta$Y/N.