The purpose of the analysis presented in this paper is to answer why a specific price level of agri-food products is determined and accepted by both the consumer and processor, as well as by the agricultural producer and processor. An answer to this question requires presenting a number of equations and functional relationships based on specific assumptions, which is a formal and analytical method of analysis. This method is based on the assumption that the acceptance involves maximizing the goal function of the processor and the goal function of the consumer and agricultural producer simultaneously, as well as that there are conditions for competitive equilibrium on these markets. The essence of this method is the choice of the processor in terms ofprices on the agri-food market. The importance of the procurement price level forthe choice of the processor is presented in an unusual and new manner by conducting an advanced analysis. The basic result of the analysis is a mechanism to determine the acceptable price level for these entities on the agri-food market. This is determined by introducing the admitting inequalities, which specify the ratio of expectations of these entities to the market equilibrium price. The conclusion is that the price level is mutually acceptable because the goal functions of the entities have been carried out. The analysis is analytical and formal and has a theoretical and cognitive value. It may contribute to the theory of prices in the agri-food sector and the conditions for the choice of the processor.