Signaling and optimal sorting

I consider educational signaling of inherent ability that facilitates sorting of individuals between sectors. More able individuals are more productive in the primary sector, and less able individuals are more productive in the secondary sector. I find signaling may increase but never maximizes welfare, and is more likely to increase welfare the greater is productivity in the secondary sector, and, possibly, the lower is productivity in the primary sector. Consistent with recent increased undergraduate enrollment in the U.S, excessive signaling occurs by less able individuals. If education increases human capital, total welfare likely increases although more individuals may over-invest in education.