Abstract
Properties of the directional technology distance function have been given in a paper by Chambers, Chung, and Färe (1998). This function, \( \vec D \) (x,y;g x ,g y ), is an implicit representation of an M-outptit, N-input production technology. An input-output vector, (x, y), is feasible if and only if \( \vec D \), where (g x , g y ) is a “direction” vector to be described later. An important antecedent of the directional technology distance function is the shortage function, introduced by Luenberger (1992, 1995).
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References
Blackorby, Charles, Daniel Primont, and R. Robert Russell, Duality, Separability, and Functional Structure: Theory and Economic Applications, New York: Elsevier North-Holland, 1978.
Chambers, Robert, “Input and Ouput Indicators,” in Rolf Färe, Shawna Grosskopf, and R. Robert Russell, editors, Index Numbers: Essays in Honour of Sten Malmquist, Boston: Kluwer Academic Publishers, 1998.
Chambers, Robert, Yangho Chung, and Rolf Färe, “Profit, Directional Distance Functions, and Nerlovian Efficiency,” Journal of Optimization Theory and Applications, 98(2) (1998), 351–364.
Fare, Rolf, and Shawna Grosskopf, “Theory and Application of Directional Distance Functions,” Journal of Productivity Analysis, 13(2) (2000), 93–103.
Färe, Rolf, Shawna Grosskopf, and Osman Zaim, “Hyperbolic. Efficiency and Return to the Dollar,” European Journal of Operational Research, 136 (2002), 671–679.
Färe, Rolf, Shawna Grosskopf, Dong-Woon Noh, and William Weber, “Characteristics of a Polluting Technology: Theory and Practice,” Journal of Econometrics 126 (2005), 469–492.
Färe, Rolf, Shawna Grosskopf, and William Weber, “Shadow Prices of Missouri Public Conservation Land,” Public Finance Review, 29(6) (2001), 444–460.
Färe, Rolf, and Anders Lundberg, “Parameterizing the Shortage Function,” unpublished paper, 2004.
Färe, Rolf and Daniel Primont, “Luenberger Productivity Indicators: Aggregation Across Firms” forthcoming, Journal of Productivity Analysis, 2003.
Lau, Lawrence J., “Complete Systems of Consumer Demand Functions Through Duality,” in Michael D. Intriligator, editor, Frontiers of Quantitative Economics, Volume IIIA, Amsterdam: North-Holland, 1977.
Luenberger, David G., “New Optimality Principles for Economic Efficiency and Equilibrium,” Journal of Optimization Theory and Applications, 75(2) (1992), 221–264.
Luenberger, David G., Microeconomic Theory, New York: McGraw-Hill, 1995.
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Hudgins, L.B., Primont, D. (2007). Derivative Properties of Directional Technology Distance Functions. In: Färe, R., Grosskopf, S., Primont, D. (eds) Aggregation, Efficiency, and Measurement. Studies in Productivity and Efficiency. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-47677-3_2
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DOI: https://doi.org/10.1007/978-0-387-47677-3_2
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