So what's Krugman's answer? What undergrads need to know, he says, is just what Hume and Ricardo were saying, 200 years ago: If relative costs of production are different in two countries, then total world output, and consumption in each individual country, will always be greater with trade than without, and prices will adjust so that trade is balanced. Free trade is always beneficial for all countries involved.
Krugman's additions to this Ricardo-Hume catechism are mostly negative -- a list of things we don't need to talk about when talk about trade.
Don't worry about development. The idea that a country can benefit from changing the sectors or industries it specializes in is, he says "a silly concept." Yes, we look around the world and see workers in rich countries producing things like airplanes and software, which are worth a lot, and workers in poor countries putting the same effort into producing agricultural goods and textiles, which are worth much less. But
Does this mean the rich country's high standard of living the result of being in the right sector, or that the poorer country would be richer if it tried to emulate the other's pattern of specialization? Of course not.Of course not. This blanket dismissal is rather odd, since the work Krugman won the Nobel for explicitly supports an affirmative answer to both questions.  It's a case of esoteric versus exoteric knowledge, I guess -- some truths are not meant for everyone. Or as Krugman delicately puts it, "the innovative stuff is not a priority for undergrads."
Don't worry about demand. In debates over policy, "the central issue is employment" in the arguments on both sides. But this is wrong, he says:
The level of employment is a macroeconomic issue, depending in the short run on aggregate demand and depending in the long run on the natural rate of unemployment, with policies like tariffs having little net effect. Trade policy should be debated in terms of its impact on efficiency…It's not immediately obvious why the claim that employment depends on aggregate demand is inconsistent with the claim that trade flows have important employment effects. After all, net exports are a component of demand. The implicit assumption is evidently that the central bank (or some other domestic policymaker) is maintaining the level of demand at the full-employment level, and will offset any effects from trade. 
Don't worry about trade deficits, and the financing they require. "The essential things to teach students are still the insights of Ricardo and Hume. That is, trade deficits are self-correcting…"
The whole piece is frankly polemical -- it's clear that the goal is not to educate in the normal sense, but to equip students to take a particular side in public debates. This is not specific to Krugman, of course. If anything, most contemporary textbooks are even worse.  One reason I am using Caves and Frankel in my class is that it has less obnoxious editorializing than other texts I looked at. But less is still a lot.
Enough Krugman-bashing. What's the alternative? What should people know about international trade? Matias Vernengo has one good alternative list. Here is mine.
There are three frameworks or perspectives in which we can productively think about international trade. The questions we ask in each case will depend on whether we are thinking of trade flows as the adjusting variable, or as reflecting an exogenous change to which some other variable(s) must adjust.
1. Trade flows are part of aggregate expenditure. On the one hand, a good way to predict trade flows is to assume that a fixed fraction of each dollar of spending goes to imported goods. As Joan Robinson and others have stressed, in the short run at least, adjustment of trade balances comes mainly or entirely through income changes. (This is also the perspective developed in Enno Schroeder's work, which I've discussed here before.) On the other hand, if we can't assume there is some level of full employment or potential output to which to which the economy always returns, then we have to be concerned with trade flows as one factor determining the level of aggregate income. This might be only a short-run phenomenon, as in mainstream Keynesian analysis, or it might be important to economic growth rates over the long run, as in models of balance of payments constrained growth.
2. Trade flows are part of the balance of payments. In a capitalist world economy, there are many different money payments and obligations between countries, of which trade flows are just part. In a world of liquidity constraints, certain configurations of money payments or money commitments are costly, or cannot be achieved at all. That is, a country in the aggregate cannot in general borrow unlimited amounts at "the" world interest rate. The tighter the constraints on a country's financial position, the more positive a trade balance it must somehow achieve. On the other hand, for a given level of financing constraint, a more positive trade balance allows for more freedom on other dimensions. This interaction between trade flows and financial constraints is central to the balance of payments crises that are such a prominent feature of the modern world economy.
3. Trade flows involve specialization. Thinking now in terms of baskets of goods rather than money flows, the essential thing about international trade is that it allows a country's consumption and production decisions to be made independently. Given that productive capacities vary more between countries than the mix of consumption goods chosen at a given income and prices, in practice this means that trade allows for specialization in production. If we take productive capacities as given, it follows that trade raises world output and income by allowing countries to specialize according to comparative costs. This is the essential (and genuine) insight of Ricardo. On the other hand, if we think that inherent differences between countries are small and that differences in productive capacity arise mainly through production itself, then international trade will lead to a historically contingent pattern of international specialization in which some positions are more advantageous than others. If causality runs from trade patterns to productive capacities and not just vice versa, then there is a case for including activity trade policy in any development strategy.
The orthodox trade theory has legitimate value and deserves a place in the curriculum. As we'll discuss in the next post, simple textbook models of the Ricardo-Mill type can be used to tell stories with more interesting political implications than the usual free-trade morality tales. But they are only part of the picture. Much of what matters about trade depends on the fact that it involves flows of money and not just exchanges of goods.
 Have Krugman's views changed since he wrote this? As reflected in his textbooks, no they have not. As reflected in his blog, seems like sometimes yes, sometimes no. Someone should ask him.
 For example, one of Krugman's more widely cited articles is this one, which develops a model in which an innovating region ("the North") develops new products, which it exports to a non-innovating region ("The South"). In the model,
Higher Northern per capita income depends on the quasi-rents from the Northern monopoly of new products, so the North must continually innovate not only to maintain its relative position but even to maintain its real income in absolute terms.This is hard to distinguish from the arguments for industrial policy that Krugman dismisses as silly.
 What's especially odd here is that orthodox theory says that in a world of mobile capital, the only tool the central bank has to maintain full employment is changes in the exchange rate. In standard textbooks (including Krugman's own), it is impossible for monetary policy to boost employment unless it improves the trade balance.
 For example, David Colander's generally undogmatic intro textbook includes a section titled "If trade is so good, why do so many people oppose it?"The answer turns out to be, they're just confused.