Production Theory for Constrained Linear Activity Models

The purpose of this paper is to generalize the framework of activity analysis discussed in Villar (2003) and obtain similar results concerning solvability. We generalize the model due to Villar (2003), without requiring any dimensional requirements on the activity matrices and by introducing a model of activity analysis in which each activity may (or may not) have a capacity constraint i.e. a maximum level at which the activity can operate. It seems that in this significantly more general framework we are able to obtain the desired results concerning solvability and existence of an equilibrium price vector under weaker assumptions than the corresponding requirements in Villar (2003). We also prove a version of the Non-Substitution Theorem that establishes the existence of “efficiency price-vectors” as a joint product.



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