Using up to nine different ways to represent a homogeneous technology, this paper proves explicit one to one identity between most of those different representations of a technology, outlining the homogeneity properties of each representation. These identities, which allow to shift from one representation of a technology to another -and which are summarized in a matrix of identities - can be useful since they provide a tool to obtain explicit functional forms for homogeneous technologies. They can also be useful to simplify computational procedures when different representations of a technology are needed. Finally, the document also refers explicitly to some aspects of producer theory that are often neglected or treated in a marginal way in the literature, such as the inverse supply, the non-conditional cost and the inverse input demand functions.
