Smallness of a commodity and partial equilibrium analysis

Partial equilibrium analysis has a conceptual dilemma that its object should be negligibly small so as not to affect allocation of the other commodities but then the consumer does not care for it and the notion of willingness to pay for it does not make sense. In the setting of a continuum of commodities, we propose a limiting procedure which transforms the many-commodity environment into a partial singlecommodity environment. In the limit, the notion of willingness to pay for a commodity is established as a ‘density’ notion and the absence of income effect on it is established. As an application, we provide a general equilibrium foundation of partial equilibrium analysis.