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Deforestation in the Amazon with its vast consequences for the ecosystem and climate is largely related to subsequent land use for cattle ranching. In addition to conservation policies, proposals to reduce deforestation include measures to intensify cattle ranching. However, the effects of land-use intensification on deforestation are debated in the literature. This paper introduces the abacra model, a stylized agent-based model to study the interplay of deforestation and the intensification of cattle ranching in the Brazilian Amazon. The model combines social learning and ecological processes with market dynamics. In the model, agents adopt either an extensive or semi-intensive strategy of cattle ranching based on the success of their neighbors. They earn their income by selling cattle on a stylized market. We present a comprehensive analysis of the model with statistical methods and find that it produces highly non-linear transient outcomes in dependence on key parameters like the rate of social interaction and elasticity of the cattle price. We show that under many environmental and economic conditions, intensification does not reduce deforestation rates and sometimes even has a detrimental effect on deforestation. Anti-deforestation policies incentivizing fast intensification can only lower deforestation rates under conditions in which the local cattle market saturates.