AGGREGATION IN PRODUCTION RELATIONSHIPS

CRAIG SCOTT MARCOTT, Purdue University

Abstract

Traditional approaches to the aggregation of microeconomic objective functions and the arguments of these objective functions center around the problem of deriving conditions for functional separability. The resulting aggregates provide weak orders on the space of the arguments, with the aggregate objective function expressed as a monotonically increasing function of the aggregates. Within this general aggregation framework, Houthakker has suggested a technique in which an aggregate objective function is obtained as the expected value, over a distribution of characteristics, of microeconomic fixed factor proportion objective functions. The first part of this study is set in the above-outlined traditional aggregation framework. Houthakker's aggregation technique is presented in the context of modern duality theory, yielding new interpretations of his aggregation problem and extensions for the case of homothetic production relationships. Recognizing that traditional aggregation techniques fall short of what is needed for almost all theoretical and empirical purposes, the second part of this study introduces axioms of difference measurement as appropriate desiderata for an aggregate. A quaternary relation on a topological space of outputs satisfying three Difference Structure axioms is used to derive a dual quaternary relation, which preserves the axioms, on an arbitrary space of inputs. A class of Separable Doubly-Homothetic distance functions is introduced and a complete characterization of the measurement problem is given for this class of technologies. The major result is that when the primal difference structure is represented by a homothetic difference scale and technology is represented by a separable doubly-homothetic distance function, the resulting input aggregates are preference general and technology specific. The primary importance of this result is that it is possible for a group of social planners who are in broad disagreement on the ordering and measurement of outputs to be in total agreement on the ordering and measurement of inputs. Moreover, with the above specification of preferences and technology, the measurement of inputs is cardinal in the sense that the representation of the dual order is unique up to a similarity transformation.

Degree

Ph.D.

Subject Area

Economic theory

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