The NBER Digest summarizes Christian Broda and David Weinstein’s work on international price differences:

Broda and Weinstein find that the law of one price and purchasing power parity, in their absolute forms, hold about as well across borders as within countries. The researchers confirm that the LOP is violated flagrantly in international data, but also across cities within the same country. Thus, for example, the observation that an identical can of soda sells at different prices in different countries is not very informative about border barriers, because prices vary substantially even within borders.