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The Existence of Input and Output Aggregates in Aggregate Production Functions
Charles Blackorby
William Schworm
Abstract
It is well-known that capital can be aggregated in an economy only under very restrictive conditions. What is not so widely understood is that these same problems exist when aggregating goods that are efficiently allocated in an economy. For example, suppose there are many types of labor in an economy and each type of labor is efficiently allocated among firms. To form a labor aggregate in the economy requires that certain aggregation restrictions be satisfied; these are the subject of this paper. 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.
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