The Existence of Input and Output Aggregates in Aggregate Production Functions

In this paper, we make two contributions to the literature on aggregating inputs and outputs in economy production functions. First, we present necessary and sufficient conditions for aggregating efficiently allocated goods under general assumptions on the technology. Second, we present a general theorem on the conditions for the existence of aggregates of both efficiently allocated goods and arbitrarily allocated goods. We use this theorem to elucidate the role of efficiency in determining the existence of aggregates.