The Generalized Linear Production Model: Solvability, Nonsubstitution and Productivity Measurement

This paper presents a very general linear production model which nevertheless shows an extremely regular behaviour. We can ensure the solvability of the associated equilibrium systems for quantities and prices and the nonsubstitution property, allowing for joint production and non-square systems. We also discuss the application of this model to the measurement of productivity differences. The assumptions we use are intuitive and very mild (e.g. they are necessary for the type of solvability we require). Proofs are simple and rely on geometrical arguments (the separation theorems), rather than on the use of the theory of determinants.