This paper studies the role of buyer market power in determining the response of international prices to exchange rate changes (i.e., exchange rate pass-through). Using a novel dataset of the universe of Colombian export transactions that links Colombian exporters (sellers) to their foreign importers (buyers), I document three facts: i) most Colombian exports are concentrated in a few foreign buyers in each market, ii) the same seller charges different prices to different buyers in the same product and destination, and iii) markets with a higher concentration of sales among buyers display lower exchange rate pass-through. Motivated by these stylized facts, I propose an open economy model of oligopsony, a market with large number of sellers and a few buyers, that accounts for buyer market power in international markets and its consequences for price determination in international transactions. The model shows that larger foreign buyers pay a marked-down price, i.e., a price below the marginal product value for the buyer. Most importantly, these markdowns are flexible and play a role when adjusting prices to exchange rate shocks. I derive a model-based equation relating pass-through to buyer size and estimate it on the micro transaction level data for Colombia. I find that after an exchange rate shock, sellers connected to larger buyers face more moderate changes in their prices in the seller currency (i.e., lower exchange rate pass-through) than those connected to small buyers. Pass-through ranges from 1% for firms connected with the largest buyers to 17% for firms connected with the smallest buyers. I use the estimates from the empirical analysis to calibrate the model and propose a counterfactual where buyer market power is eliminated. Under this scenario, sellers‘ revenues increase; however, the price in seller currency is more responsive to exchange rate shocks.