Economic exchange is an important means of facilitating cooperation, but it is not the only means. Kinship, norms enforced by reputational effects, and state action also organize cooperation. It is neither irrational nor morally wrong for me to be more eager to benefit, and more reluctant to harm, those with whom I cooperate more, because they are my relatives, because they are my neighbors or my co-workers or my fellow-members of other groups that embody collective social capital, or because they are my fellow-citizens.The thing is, for my application I also had to make an opposing argument.
The sovereign state has the capacity to pay for public goods by compulsory taxation, thus avoiding the free-rider problem. Wages or profits earned by people or firms that pay U.S. taxes are more important to me than wages or profits earned by those who pay taxes elsewhere, because I get a share of those wages or profits in the form of greater expenditure on public goods or reduced taxation. But even putting that aside, the feeling of community among Americans or Mexicans or Germans or Thais has all sorts of beneficial results (along, of course, with some quite horrible ones).
Does that mean that nations should be entirely selfish? No, any more than the fact that parents care more about their own children than they do about other children means that families should be entirely selfish. In particular, a big, rich country like the U.S. ought to be a generous contributor both to world-scale public goods and to the needs of the global poor.
I agree that it seems very plausible to say that we have special, or additional, moral obligations to "those with whom [we] cooperate more", like relatives, co-workers, teammates, etc. Lumping all of those groups together, though, obscures the fact that even if that's true (and let's just assume it is), the degree of additional obligation is measured on a sliding scale. For example, however much extra weight my parents deserve in my moral calculations, odds are that the woman who lives in the apartment below mine deserves rather less, and that the clerk who checked my ID at Albertsons this evening should get less still. And the further removed an individual is from my day-to-day life, the harder it becomes to discern which features of our relationship warrant this sort of special moral attention. By the time we're talking about call center operators in Virginia, our actual relationship is pretty vague indeed and it seems to me that we've slid pretty far down that sliding scale. How much further down, really, is the Mexican factory worker?
What's more, even if interpersonal relationships create additional moral considerations, so do other factors. Most notably - as Kleiman himself mentions - we're way richer than the other people we're considering trading with. If liberalizing trade would benefit the citizens of other countries at some expense to American citizens, then surely it matters how much poorer than our own those other citizens are. Nobody thinks the rule is to promote your family's well-being at any cost to others.
Now, I think that Kleiman feels like he's accommodating that egalitarian concern by endorsing the idea that "a big, rich country like the U.S. ought to be a generous contributor both to world-scale public goods and to the needs of the global poor." But if it's OK to tax our relatively rich compatriots to help out relatively poor foreigners, why is it not OK to allow certain jobs to move across the border, instead of cash? Free trade, on this account, is just de facto foreign aid, with the additional likely benefit (in many cases) of bringing more, cheaper goods to American consumers.
P.S. - Of course, Brad DeLong's response to all of this is going to be much simpler. My understanding is that he's a pretty strict utilitarian, and so would reject from the start the suggestion that, say, family members "deserve" any special moral consideration at all. Sure, maybe as a rule of thumb it's good to make the well-being of one's family a higher priority than the well-being of strangers, because this will probably tend to create the greatest happiness overall. But it's not like your aunt, qua your aunt, is somehow more special than other peoples' aunts. After all, it's hard to imagine something more random than the fact of you being related to your aunt. As they say, you don't pick your family.