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This paper presents amodel of the conditions thatmay lead a small open economy towards a middle income trap. This situation has shown to be pervasive in Latin America. As Argentina is a salient instance of this phenomenon, we develop a stylized model of its economy at the first decades of the XXth century. It consists of a general equilibrium model of an open emerging economy, which is a price-taking primary goods exporter. A growth process is triggered by an increase of commodity prices, due to an upward jump of theworld demand of these goods. The economy goes through several phases of growth, starting from a subsistence stage. Once decreasing returns set in, the economy reaches a steady state. Only a sustained high demand of its export products allows the economyto thrive. Otherwise, the economy gets entrapped in a middle income level.