In this paper we show that price equalization does not imply zero barriers to trade. There are many barrier combinations that deliver price equalization, but each combination implies a different volume of trade. We demonstrate this first theoretically in a simple two-country model and then quantitatively for the case of capital goods trade in a multi-country model. To be quantitatively consistent with the observed capital goods trade flows across countries, our model implies that trade barriers must be large, yet our model delivers capital goods prices that are similar across countries. The absence of barriers to trade in capital goods delivers price equalization in capital goods but cannot reproduce the observed trade flows.