We give a geometric interpretation of the lens condition, proposed by Deardorff as a shortcut for checking the factor price equalization (FPE) condition. We identify the conditions under which the lens condition implies the FPE condition. If the FPE zone is not a neighborhood of the diagonal...

We give two optimization programs for determining whether Pareto improving local changes are possible. When they are, the programs compute them. Any procedure generating efficient and Pareto improving changes can be replicated by these programs. The two programs are dual to each other. We apply...