A complete characterization of equilibrium paths in a labour-less two-sector model of optimal growth

In this paper, I develop a two-sector growth model in which the output of each industry is obtained only by means of capital. From a theoretical perspective, this setting reveals that the determinacy of the equilibrium path is possible even when the production technology available in the industry of consumption goods is not necessarily convex. Moreover, form a numerical point of view, I show that whenever the first-best solution of the model is tailored on the US economy, such a theoretical framework relaxes the complementarity between the propensities to consume and to save and it is also consistent with the observed countercyclical pattern of the relative price of capital goods.