Theoretical description of the agri-food market allows for identification of three entities whose interactions determine the market balance. In this perspective, we can distinguish consumers, agri-food processors and agricultural producers. They form a kind of circular flow of interdependent entities. The behavior of each of them conditions the behavior of others. The goal of the paper is to evaluate the role of processor in the food supply chain. We also raise the question of food processors in the context of their impact on the producers through prices of agricultural raw materials. The considerations are made basing on formal analytical models referring to the standards on the reasoning in microeconomics which are expand by the empirical evidence of analyzed problems. The processor is crucial to the sustainability of growth in the agri-food sector, because by seeking to maximize his objective function he determines the price level of agricultural products produced by the producers, under the assumption that the price of agricultural raw materials is determined by their marginal utility for the processor. It is also the basis for isolating the intermediate demand, which is reported by the agri-food processor for agricultural raw materials and direct (final) demand reported by the consumer.