We draw on a dynamical two-sector model and on a calibration exercise to study the impact of a skill-biased technological shock on the growth path and income distribution of a developing economy. The model builds on the theoretical framework developed by Silverberg and Verspagen (1995) and on the idea of localised technological change (Atkinson and Stiglitz, 1969) with sector-level increasing returns to scale. We find that a scenario of catching-up to the high-growth steady state is predictable for those economies starting off with a high enough endowment of skilled workforce. During the transition phase, if the skill upgrade process for the workforce is relatively slow, the typical inverse-U Kuznets pattern emerges for income inequality in the long run. Small scale Kuznets curves, driven by sectoral business cycles, may also be detected in the short run. Conversely, economies initially suffering from significant skill shortages remain trapped in a low-growth steady state. Although the long-term trend is one of decreasing inequality, small-scale Kuznets curves may be detected even in this case, which may cause problems of observational equivalence between the two scenarios for the policy-maker. The underlying factors of inequality, and the evolution of a more comprehensive measure of inequality than the one normally used, are also analysed.