This paper shows that income convergence in an open-economy setting hinges upon how the time-discount rate of the households is determined. As opposed to the case of constant time-discount rate where cross-country income divergence may emerge, the small-open economy may catch up with the rest of the world if the discount rate increases with consumption. In contrast, either if the discount rate decreases with consumption or if future-oriented investment of the household lowers the time- discount rate, then the small-open economy fails to catch up with the rest of the world under free trade of commodities.
