Outfoxing a paradox. (English) Zbl 0961.91026
Summary: This paper addresses a paradox noted by Kevin Fox, that ‘using a standard definition of cost efficiency, a multi-product firm may be more efficient in producing each product than any other firm, yet it may not be the most efficient firm overall.’ We show why the paradox arises and how to avoid the paradox. Specifically we use the duality between cost functions and the directional distance function to provide a cost measure of efficiency that is nonparadoxical.
MSC:
| 91B38 | Production theory, theory of the firm |
| 91B32 | Resource and cost allocation (including fair division, apportionment, etc.) |
| 91B82 | Statistical methods; economic indices and measures |
References:
| [1] | Aczél, J., Lectures on Functional Equations and Their Application (1966), Academic Press: Academic Press New York, London · Zbl 0139.09301 |
| [2] | Chambers, R. G.; Chung, Y.; Färe, R., Benefit and distance functions, Journal of Economic Theory, 70, 407-419 (1996) · Zbl 0866.90027 |
| [3] | Fox, K. J., Efficiency at different levels of aggregation: public vs. private sector firms, Economics Letters, 65, 2, 173-176 (1999) · Zbl 1037.91538 |
| [4] | Luenberger, R. G., Benefit functions and duality, Journal of Mathematical Economics, 21, 461-481 (1992) · Zbl 0766.90011 |
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