This paper studies how the internal structure of agriculture export markets and the level of competition affect poverty and welfare in rural areas in Africa. We develop a game-theory model of supply chains in cash crop agriculture between many atomistic smallholders and a few exporters. The model provides the tools needed to simulate the changes in farm-gate prices of export crops given hypothetical changes in the structure of the supply chain. Using household surveys, we assess the poverty impacts of those changes in the value chains for twelve case studies. We investigate the average impact for all rural households, the distribution of these impacts for poor vis-à-vis non-poor households, and the differences in impacts between male- and female-headed households. Overall we find that an increase in competition among processors is good for the farmers. However, small changes to the level of competition are unlikely to have significant effects on farmers’ livelihood. We also find that, on average, non-poor, male headed household are the ones that benefit the most from an increase in competition. The introduction of outgrower contracts in our model only produces significant changes in the simulations of one of our case studies.