The Foundations of General Equilibrium

Abstract

This chapter introduces the primitive notions of a general equilibrium theory. Throughout this book I specifically focus on the problem of the social organization of pure barter or exchange processes. Therefore, I explicitly exclude production from the theory.¹ The theory is designed using the so-called axiomatic approach as developed in full extent for economic theory in Debreu (1959). The axiomatic approach is a general methodology underlying any mathematical modelling. It amounts to the reduction of a scientific object to a number of irreducible primitive notions and a number of axioms describing the relationship between those primitive notions. Thus, it describes how to model the object under consideration and explain certain phenomena as observed, in relation to the object. Consequently, the axiomatic method allows the modelling of a scientific object to be performed at several levels. Certain primitive concepts may be irreducible in the first instance of reduction, but may be subject to a second reduction.