On the Definition of Differentiated Products in the Real World

  • Beth Allen
Part of the Studies in Economic Theory book series (ECON.THEORY, volume 25)


This paper proposes an abstract model of commodity differentiation that incorporates manufacturing imprecision and dimensioning and tolerancing standards. The potential consistency of such a model based on engineering consideration is analyzed. For a large pure exchange economy, competitive equilibria exist and are Pareto optimal. Production issues such as the derived demand for intermediate products, continuity of cost functions, and product selection and technology issues such as mass customization, agile manufacturing, and manufacturability are discussed.

Key words

Differentiated commodities General equilibrium Hausdorff metric topology 


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  1. 1.
    Allen, B.: The demand for (differentiated) information. Review of Economic Studies 53, 311–323 (1986a)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Allen, B.: General equilibrium with information sales. Theory and Design 21, 1–33 (1986b)zbMATHGoogle Scholar
  3. 3.
    Allen, B.: Approximating geometric designs with simple material removal processes and CAD/CAM tools. Transactions of the North American Manufacturing Research Institution/Society of Manufacturing Engineers 27, 215–220 (1999a)Google Scholar
  4. 4.
    Allen, B.: Regular sets and the Hausdorff topology. Mimeo, Department of Economics, University of Minnesota (1999b)Google Scholar
  5. 5.
    Allen, B.: A theoretical framework for geometric design. Mimeo, Department of Economics, University of Minnesota (1999c)Google Scholar
  6. 6.
    Allen, B.: A toolkit for decision-based design theory. Engineering Valuation & Cost Analysis 3, 85–106 (2000)Google Scholar
  7. 7.
    Aubin, J.-P.: Applied abstract analysis. New York: Wiley 1977Google Scholar
  8. 8.
    Berliant, M., Dunz, K.: A foundation of location theory: existence of equilibrium, the welfare theorems and core. Mimeo, Department of Economics, Washington University in St. Louis (1995)Google Scholar
  9. 9.
    Berliant, M., ten Raa, T.: A foundation of location theory: consumer preferences and demand. Journal of Economic Theory 44, 336–353 (1988)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Berliant, M., ten Raa, T.: Corrigendum. Journal of Economic Theory 58, 112–113 (1992)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Bewley, T.: Existence of equilibria in economies with infinitely many commodities. Journal of Economic Theory 4, 514–540 (1972)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Boyer, M., Stewart, N. F.: Modeling spaces for toleranced objects. International Journal of Robotics Research 10, 570–582 (1991)Google Scholar
  13. 13.
    Boyer, M., Stewart, N. F.: Imperfect form tolerancing on manifold objects: a metric approach. International Journal of Robotics Research 11, 482–490 (1992)Google Scholar
  14. 14.
    Cole, H. L., Prescott, E. C.: Valuation equilibrium with clubs. Research Department Staff Report 174, Federal Reserve Bank of Minneapolis (1995)Google Scholar
  15. 15.
    Debreu, G.: Theory of value. New Heaven, CT: Yale University Press 1959Google Scholar
  16. 16.
    Hausdorff, F.: Set theory. New York: Chelsea 1962Google Scholar
  17. 17.
    Hildenbrand, W.: Core and equilibria of a large economy. Princeton, NJ: Princeton University Press 1974Google Scholar
  18. 18.
    Hornstein, A., Prescott, E. C.: Insurance contracts as commodities: a note. Review of Economic Studies 58, 917–928 (1991)Google Scholar
  19. 19.
    Mas-Colell, A.: A model of equilibrium with differentiated commodities. Journal of Mathematical Economics 2, 263–295 (1975)zbMATHMathSciNetGoogle Scholar
  20. 20.
    Mas-Collel, A.: Indivisible commodities and general equilibrium theory. Journal of Economic Theory 16, 443–456 (1977)MathSciNetGoogle Scholar
  21. 21.
    Nadler, S. B., Jr.: Hyperspaces of sets. New York: Marcel Dekker 1978Google Scholar
  22. 22.
    Parthasarathy, K.: Probability measures on metric spaces. New York: Academic Press 1967Google Scholar
  23. 23.
    Peters, T. J., Rosen, D. W., Shapiro, V.: A topological model of limitations in design for manufacturing. Research in Engineering Design 6, 223–233 (1994)CrossRefGoogle Scholar
  24. 24.
    Prescott, E. C., Townsend, R. M.: General competitive analysis in an economy with private information. International Economic Review 25, 1–20 (1984)MathSciNetGoogle Scholar
  25. 25.
    Requicha, A. A. G.: Representations for rigid solids: theory, methods, and systems. ACM Computing Surveys 12, 437–464 (1980)CrossRefGoogle Scholar
  26. 26.
    Requicha, A. A. G.: Toward a theory of geometric tolerancing. International Journal of Robotics Research 2, 45–60 (1983)Google Scholar
  27. 27.
    Requicha, A. A. G.: Mathematical definition of tolerance specifications. Manufacturing Review 6, 269–274 (1993)Google Scholar
  28. 28.
    Requicha, A. A. G., Rossignac, J. R.: Solid modeling and beyond. IEEE Computer Graphics and Applications, pp. 31–44 (1992)Google Scholar
  29. 29.
    Rockafellar, T.: Convex analysis. Princeton, NJ: Princeton University Press 1970Google Scholar
  30. 30.
    Rosen, D.W., Peters, T. J.: Topological properties that model feature-based representation conversions within concurrent engineering. Research in Engineering Design 4, 147–158 (1992)CrossRefGoogle Scholar
  31. 31.
    Rosen, D.W., Peters, T. J.: The role of topology in engineering design research. Research in Engineering Design 8, 81–98 (1996)CrossRefGoogle Scholar
  32. 32.
    Shah, J., Mäntylä, M.: Parametric and feature-based CAD/CAM: concepts, techniques, and application. New York: Wiley 1995Google Scholar
  33. 33.
    Srinivasin, V.: Role of statistics in achieving global consistency of tolerances. IBM Research Report, T. J. Watson Research Center (1998)Google Scholar
  34. 34.
    Stewart, N. F.: Sufficient condition for correct topological form in tolerance specification. Computer-Aided Design 25, 39–48 (1993)CrossRefzbMATHGoogle Scholar
  35. 35.
    Tilove, R. B.: Set membership classification: a unified approach to geometric intersection problems. IEE Transactions on Computing C-29, 874–883 (1980)MathSciNetGoogle Scholar
  36. 36.
    Tilove, R. B., Requicha, A. A. G.: Closure of Boolean operations on geometric entities. Computer-Aided Design 12, 219–220 (1980)CrossRefGoogle Scholar
  37. 37.
    Yoshikawa, H.: General design theory and a CAD system. In: Sata, T., Warman, E. A. (eds.) Man-machine communication in CAD/CAM: Proceedings of the IFIP WG5.2/5.3 Working Conference 1980 (Tokyo), pp. 35–58. Amsterdam: North-Holland 1981Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Beth Allen
    • 1
  1. 1.Department of EconomicsUniversity of MinnesotaMinneapolisUSA

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