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 time discount rate increases with consumption. In contrast, if the time discount rate decreases with consumption, then the small open economy fails to catch up with the rest of the world under free trade of commodities.