The growth of urban areas adjacent to forest areas, as well as international trade growth, has accelerated the demand for food. These areas of growth have led to the deforestation of tropical forests, a process that contributes negatively to climate change, and a decline in the provision of environmental services and biodiversity. This article seeks to propose and simulate a theoretical model of optimal control at the household level. This model is used to explain the dynamics of forest loss by expansion of the agricultural frontier. Under these conditions, based on tradable permanent crops, farmers decide whether to install new areas for cultivation or manage existing ones in a context of increasing transportation costs. We simulate a theoretical model using data on permanent crops in the high forest of Peru. The results of the model establish that there is a limit to the expansion of the agricultural frontier of the rainforest due to transportation costs. This limit can be surpassed in the context of the free movement of labor whenever these costs cause a decrease and/or increase in the price of land cultivation. Finally, the main policy recommendations of this study emphasize the subordination of transport policy to agroforestry and the conservation of forest ecosystems policies. Agroforestry design forest policies should consider the differential impact of the construction of highways and rural roads on the loss of tree cover as well as on sustainable food production, given that deforestation is not accelerated by the mere existence of roads but by the incentives that are presented to settlers to guide their efforts toward clearing new forest areas.
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