A basic income can raise employment and welfare for a majority

With growing interest in a universal basic income (BI), we provide new results for a majority to benefit from replacing (some) unemployment benefits with BI. Given any income distribution and an extensive margin, such a replacement always benefits those remaining unemployed, raises utilitarian welfare, and benefits a poor - or even a working - majority. Similar results follow with involuntary unemployment, and joint distributions of wages and costs of work. Moreover, using quasi-linear utility with intensive margins, marginal introduction of BI can still benefit a large proportion of the poor whose productivities are below the average, without raising unemployment.