This paper examines the link between political support for basic income funded by linear income
taxation and income inequality by household and gender. We develop a model with an
increasingly right-skewed distribution of skill across households and a gender wage gap within
households. Household preference for basic income decreases as skill level increases and
female labour supply decreases with time spent rearing children. Majority voting supports the
basic income scheme as mean relative to median household skill increases. Household fertility
and skill level are inversely related under the scheme. An increase in the marginal tax rate to
fund required government revenue could excacerbate gender inequality by reducing female
labour supply. Quantitative illustrations suggest that the recent peak in the mean to median
wage gap would provide voting support for basic income from the majority of households in the
United States. Basic income of $12,000 conditional on below-median wages would increase
government spending by 10.8% which, if funded by progressive income taxation, could reduce
the adverse effects on gender inequality.