Abstract: We ask what level of migration would maximize world welfare. We find that skill-neutral policies are never optimal. An egalitarian welfare function induces a policy that entails moving mainly unskilled immigrants into the rich countries, whereas a welfare function skewed highly towards the rich countries induces an optimal policy that entails a brain-drain from the poor countries. For intermediate welfare functions that moderately favor the rich however, it is optimal to have no migration at all.
Commentary: I admit my eyes glazed over at some of the math. Despite two courses in real analysis, two in econometrics, two in mathematical economics, plus discrete, differential equations, and some other math courses, I find I remain continually unsatisfied with my ability to adapt to unfamiliar notation. I was struggling with the first equation.
However, the paper is quite interesting. The abstract summarizes the conclusions well, and I was able to get an intuitive feel fairly easily. To a certain extent, I found the assumptions were predetermining the outcome too much: almost if I could sense the outcome a priori to the model being derived. I stress this comes from pure intuition and no ability to actually critique their efforts in any way.
The results also coincide with Canada's world leadership in point-based immigration, which the paper implies is synonymous with Canada leading the world in exploiting immigration for its own purposes and not as a method to make the whole world better off. This falls in nicely with my own views that government cannot make policy that gives non-citizens equal standing as citizens.
Sadly, I wasn't able to grasp the concepts firmly enough to build them into my continuing inner debate on the merits of population.