The point is not that the basic idea behind the law of one price is wrong; of course people have incentives to arbitrage price differences “in the absence of barriers.” But in the real world, barriers of some kind almost always exist, whether it is the fact that no one has the time to search all the stores in an area for the lowest-priced ketchup, or whether there are still various transaction costs and transport, legal and other issues affecting trade in the European Union. In fact, the scientifically interesting question around price convergence is the dynamic interplay over time between the
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