Reducing food imports and promoting domestically produced food commodities are long-standing goals for policymakers and other stakeholders in sub-Saharan African countries. For instance, Tanzania, after a long period of dependency on imported food commodities, such as sugar and edible oils, intends to meet its demand for these commodities through domestic production by transforming its agriculture sector to achieve this goal. Applying a general computable equilibrium (CGE) model, this study determines the multiplier effects of technological progress that is assumed to foster domestic edible oilseed crop production, other crops, and Tanzania’s economy in general. Findings from the model establish an increase in domestic production not only for the edible oilseed crops but also for other commodities from other sectors of the economy. In addition, there is a decrease in prices on domestically produced commodities sold in the domestic market, and an increase in disposable income is predicted for all rural and urban households, as well as government revenues. Based on model results, we recommend that the Tanzanian government invests in technological progress and interventions that increase production in sectors such as agriculture, where it has a comparative advantage. Interventions that increase smallholder farmer’s production, such as the use of improved seed and other modern technologies that reduce costs of production, are critical for reducing food imports and improving food security.