This is a nice post from Dani Rodrik. The short answer is it depends. Free trade increases the price of export goods and lowers the price of imports:
[A]nyone who understands comparative advantage knows that free trade affects relative prices, not the price level (the latter being the province of macro and monetary factors). When a country opens up to trade (or liberalizes its trade), it is the relative price of imports that comes down; by necessity, the relative prices of its exports must go up! Consumers are better off to the extent that their consumption basket is weighted towards importables, but we cannot always rely on this to be the case.
Consider your typical Argentinian for example, who consumes a lot of wheat and beef. Since these are export products for Argentina, free trade implies a rise in the relative price of the Argentine consumption basket….And in the U.S., the Wal-Mart effect has to be qualified to take into account the fact that the relative price of the goods that the U.S. exports (including for example agricultural commodities) is higher than it would have been absent trade. Similarly, when the U.S. gets better market access abroad for its agricultural exports (a key demand under the Doha round), you can be sure that this will raise domestic prices for these goods, not lower them.
Of course, if you are running a huge trade deficit like the U.S., you can have cheaper prices all around—for all to go on a consumption binge as long as the party lasts. But this is hardly the argument we make when we teach the benefits of free trade.
