Cocoa yields in Ghana remain low. This has variously been attributed to low rates of fertilizer application, pollinator limitation, and particularly dry growing conditions. In this paper we use an African forest-agriculture landscape dominated by cocoa (Theobroma cacao) to develop an ecological production function, allowing us to identify key ecological and management limits acting on cocoa yields simultaneously. These included more consistent application of fertilizers inter-annually, distributing rotting biomass throughout the farm and reducing the incidence of capsid attacks. By relaxing these limits, we estimate plausible increases in yields and, by extension, farm incomes. Our analysis reveals that resulting increases in cocoa yields requiring both ecological and intensive management interventions could be significant (113 ± 60%); however, benefits are disproportionately realized by the wealthiest households. We found that wealthier households benefited proportionally more from ecological intensification methods (e.g., leaving more rotting biomass in their farms) and the poorest households benefited proportionally more from capital-intensive intensification methods (e.g., pesticide and fertilizer applications). We treated poverty as multi-dimensional, and show that only certain dimensions of poverty (school attendance, assets, and food security) are significantly related to cocoa incomes, while several other dimensions (access to clean water, sanitation and electricity, and infant mortality) are not. We explore how increased household cocoa incomes could impact different dimensions of poverty. Our findings suggest, that if all households adopted the optimal level of each of these management options, and in so doing had similar poverty profiles to those households already managing optimally, we would see the community-averaged probability: a child of a household misses school decrease from 47 to 31%, a household would be able to acquire assets increase from 40 to 59% and a household would have access to an adequate amount of food increase from 62 to 79%.