Small-scale farmers are known to produce the greater proportion of food consumed in the Third World, especially in sub-Saharan Africa. The various national and international agricultural research centres located in these parts of the world have developed agricultural packages which have been proven, at experimental levels, to be highly productive. However, small-scale farmers in these areas continue to produce at levels far below the capacities of these packages as predicted from experimental results. Consequently, these farmers, despite their relatively large number, could not produce enough to feed themselves let alone the general population. To improve the quality of life of these farmers in particular, and the population of the Third World in general, there is a need to study the various factors responsible for low agricultural production at the household level. Models relating production to the various factors need to be formulated to improve our understanding of the functional relationships. This in turn could lead to relevant national and international policies with respect to small-scale farmers in the Third World. In this paper, we develop models to predict production given these factors. For simplicity, the parameters of the models are limited to land size (or herd size), environmental effect and management effect. A statistical examination of our model fitted to a set of survey data on this subject revealed that improving the farmers' management level could greatly enhance their production. Further statistical analysis of the data set showed that the various factors constituting the farmers' management level could broadly be classified into three groups: resources (labour and farm implements), personal characteristics (educational level and age) and external assistance (contact with extension agents/assistance) in that order of importance. We discuss the importance of these fmdings in the formulation of policies concerning small-scale farmers in sub-Saharan Africa.