In this paper we show that price equalization alone is not sufficient to establish that there are no barriers to international trade. There are many barrier combinations that deliver price equalization, but each combination implies a different volume of trade. Therefore, in order to make statements about trade barriers it is necessary to know the trade flows. We demonstrate this first theoretically in a simple two-country model. We then extend the result quantitatively to a multi-country model with two sectors. We show that for the case of capital goods trade, barriers have to be large in order to be consistent with the observed trade flows. Our model also implies that capital goods prices look similar across countries, an implication that is consistent with data. Zero barriers to trade in capital goods will deliver price equalization in capital goods, but cannot reproduce the observed trade flows in our model.