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Ordinal Approach to Characterizing Efficient Allocations, An

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  • Hennessy, David A.
  • Lapan, Harvey E.

Abstract

The invisible hand theorem relates nothing about the attributes of the optimal allocation vector. In this paper, we identify a convex cone of functions such that order on vectors of exogenous heterogeneity parameters induces component-wise order on allocation vectors for firms in an efficient market. By use of functional analysis, we then replace the vectors of heterogeneities with asymmetries in function attributes such that the induced component-wise order on efficient allocations still pertains. We do so through integration over a kernel in which the requisite asymmetries are embedded. Likelihood ratio order on the measures of integration is both necessary and sufficient to ensure component-wise order on efficient factor allocations across firms. Upon specializing to supermodular functions, familiar stochastic dominance orders on normalized measures of integration provide necessary and sufficient conditions for this component-wise order on efficient allocation. The analysis engaged in throughout the paper is ordinal in the sense that all conclusions drawn are robust to monotone transformations of the arguments in production.

Suggested Citation

  • Hennessy, David A. & Lapan, Harvey E., 2002. "Ordinal Approach to Characterizing Efficient Allocations, An," Staff General Research Papers Archive 10036, Iowa State University, Department of Economics.
  • Handle: RePEc:isu:genres:10036
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    File URL: http://www2.econ.iastate.edu/papers/p3812-2002-09-20.pdf
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    Keywords

    arrangement monotone; functional analysis; market structure; ordinal analysis; simplex; symmetry;

    JEL classification:

    • D20 - Microeconomics - - Production and Organizations - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General

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