This study delves into the dynamics of price linkages and transaction costs in agricultural markets, emphasizing the sustainability of food supply chains. By exploring vertical and horizontal price linkages in agro-farming value chains of a developing country, it addresses the efficiency of market information transmission and the capacity for arbitrage among chain participants. The methodological core of the research involves analyzing price linkages in Chilean horticultural wholesale markets, focusing on key vegetables such as, onions, lettuce, maize, and tomatoes. This analysis is underpinned by a novel approach that models and estimates time-dependent, conditional threshold bands, extending the traditional cointegration models. This method allows a more nuanced understanding of how agricultural market linkages evolve over time, enhancing our comprehension of price transmission behavior and market integration. The results reveal significant non-linear relationships between fuel prices and vegetable prices, particularly in central Chilean regions. This finding challenges the traditional linear perspective, suggesting that factors such as storage capacity and arbitrage behavior can influence price signal transmission. Such insights are crucial for stakeholders in the agribusiness value chain, offering a deeper understanding of market dynamics and aiding in the development of more sustainable and efficient market strategies. This research contributes significantly to the field of agricultural economics by providing a more robust framework for analyzing market behaviors and transaction costs in the context of sustainability and value chains. Its findings have profound implications for both theory and practice, informing policy-making and strategic decision-making in the agribusiness sector.