While there has been intense debate in the empirical literature about the effects of minimum wages on inequality in the US, its general equilibrium effects have been given little attention. In order to quantify the full effects of a decreasing minimum wage on inequality, I build a dynamic general equilibrium model, based on a two-sector growth model where the supply of high-skilled workers and the direction of technical change are endogenous. I find that a permanent reduction in the minimum wage leads to an expansion of low-skilled employment, which increases the incentives to acquire skills, thus changing the composition and size of high-skilled employment. These permanent changes in the supply of labour alter the investment flow into R&D, thereby decreasing the skill-bias of technology. The reduction in the minimum wage has spill-over effects on the entire distribution, affecting uppertail inequality. Through a calibration exercise, I find that a 30 percent reduction in the real value of the minimum wage, as in the early 1980s, accounts for 15 percent of the subsequent rise in the skill premium, 18.5 percent of the increase in overall inequality, 45 percent of the increase in inequality in the bottom half, and 7 percent of the rise in inequality at the top half of the wage distribution.