In the GTAP model there are two types of produced commodities, goods produced for domestic markets and goods produced for export. In the base GTAPinGAMS model these goods are assumed to be imperfect substitutes produced as joint products with a constant elasticity of transformation.6 Specifically, if Dir is domestic output and Xir is exports, then
where Yir is the activity level for good i in region r. Producers are competitive, implying that given a value of Yir, supplies to the domestic and export markets are given by:7
Inputs to production include primary factors and intermediate inputs. Intermediate demands are proportional to the level of activity, so the total intermediate demand for good i in region r is:
In the core model we assume that all intermediate input coefficients (aijr) are fixed, unresponsive to price.8
Following Armington  intermediate demand is represented as a composite of imported and domestic goods as imperfect substitutes. Thus, we have:
in which DIir is domestic intermediate and MIir is imported intermediate demand.
A Cobb-Douglas production function relates activity level and factor inputs. Producers minimize unit cost given factor prices and applicable taxes. The factor demands solve:
taking Yir as given. Linear homogeneity of the production function implies that factor demands may be expressed as the product of an activity level and compensated demand function depending on factor prices and factor taxes: