There is a large body of evidence indicating that cross-country differences in income levels are associated with differences in productivity. If workers are much more productive in one country than in another, restrictions on immigration lead to large efficiency losses. The paper quantifies...

The square root function has a unique positive fixed point. This function has the following properties: it is strictly increasing and strictly concave, with f(0)=0, and there are points a0 and b0 such that f(b)a and bf(b). It is shown that any function from Rn to Rn satisfying these properties...