Textbook analysis tells us that in a competitive labor market, the introduction of a minimum wage above the competitive equilibrium wage will cause unemployment. This paper makes two contributions to the basic theory of the minimum wage. First, we analyze the effects of a higher minimum wage in terms of poverty rather than in terms of unemployment. Second, we extend the standard textbook model to allow for incomesharing between the employed and the unemployed. We find that there are situations in which a higher minimum wage raises poverty, others where it reduces poverty, and yet others in which poverty is unchanged. We characterize precisely how the poverty effect depends on four parameters: the degree of poverty aversion, the elasticity of labor demand, the ratio of the minimum wage to the poverty line, and the extent of incomesharing. Thus, shifting the perspective from unemployment to poverty leads to a considerable enrichment of the theory of the minimum wage.