Skip to main content

Multiple markets: new perspective on nonlinear pricing

Abstract

We discuss how linear equilibrium pricing in certain competitive market structures may represent nonlinear equilibrium pricing of Aliprantis et al. (J Econ Theory 100:22–72, 2001, J Econ Theory 121:51–74, 2005). Their work extends the theory of value beyond the scope of the Walrasian single market linear price model. Our arguments include a new and general result on the existence of linear price equilibrium with multiple markets. Each market has its own price vector (linear functional), and agents’ involvement in various markets is heterogeneous. As a result, price differences across markets may prevail in equilibrium. We present an example in which single market linear price equilibrium does not exist, but certain corresponding equilibrium with two markets does. This example is a particular instance of a prevalent nonexistence problem in atomless economies with differential information. Bypassing the nonexistence problem is one of the achievements of the nonlinear equilibrium theory. Our equilibrium with multiple markets, on the other hand, offers a solution with a more standard economic interpretation. Besides, our general framework is a model of multiple markets in their own right, and our results are related to the role of economic intermediation and bilateral trade.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3

References

  1. Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis: A Hitchhiker’s Guide. Springer, Berlin (2006)

    Google Scholar 

  2. Aliprantis, C.D., Brown, D.J., Burkinshaw, O.: Edgeworth equilibria. Econometrica 55, 1109–1137 (1987)

    Article  Google Scholar 

  3. Aliprantis, C.D., Brown, D.J.: Equilibria in markets with a Riesz space of commodities. J. Math. Econ. 11, 189–207 (1983)

    Article  Google Scholar 

  4. Aliprantis, C.D., Florenzano, M., Tourky, R.: General equilibrium analysis in ordered topological vector spaces. J. Math. Econ. 40, 247–269 (2004a)

    Article  Google Scholar 

  5. Aliprantis, C.D., Florenzano, M., Tourky, R.: Linear and non-linear price decentralization. J. Econ. Theory 121, 51–74 (2005)

    Article  Google Scholar 

  6. Aliprantis, C.D., Florenzano, M., Tourky, R.: Production equilibria. J. Math. Econ. 42, 406–421 (2006)

    Article  Google Scholar 

  7. Aliprantis, C.D., Monteiro, P.K., Tourky, R.: Non-marketed options, non-existence of equilibria, and non-linear prices. J. Econ. Theory 114, 345–357 (2004b)

    Article  Google Scholar 

  8. Aliprantis, C.D., Tourky, R.: Cones and Duality. American Mathematical Society, Graduate Studies in Mathematics (2007)

  9. Aliprantis, C.D., Tourky, R., Yannelis, N.C.: A theory of value with non-linear prices: equilibrium analysis beyond vector lattices. J. Econ. Theory 100, 22–72 (2001)

    Article  Google Scholar 

  10. Anderson, R.M., Zame, W.R.: Genericity with infinitely many parameters. B.E. J Theor. Econ. 1, 1–64 (2001)

    Google Scholar 

  11. Angelopoulos, A., Koutsougeras, L.C.: Value allocation under ambiguity. Econ. Theory 59, 147–167 (2015)

    Article  Google Scholar 

  12. Chavas, J.-P., Briec, W.: On economic efficiency under non-convexity. Econ. Theory 50, 671–701 (2012)

    Article  Google Scholar 

  13. Condie, S., Ganguli, J.V.: Ambiguity and rational expectations equilibria. Rev. Econ. Stud. 78, 821–845 (2011)

    Article  Google Scholar 

  14. Condie, S., Ganguli, J.V.: Informational efficiency with ambiguous information. Econ. Theory 48, 229–242 (2011)

    Article  Google Scholar 

  15. Correia-da-Silva, J., Hervés-Beloso, C.: Prudent expectations equilibrium in economies with uncertain delivery. Econ. Theory 39, 67–92 (2009)

    Article  Google Scholar 

  16. Dagan, N., Serrano, R., Volij, O.: Bargaining, coalitions and competition. Econ. Theory 48, 519–548 (2011)

    Article  Google Scholar 

  17. de Castro, L.I., Pesce, M., Yannelis, N.C.: Core and equilibria under ambiguity. Econ. Theory 48, 519–548 (2011)

    Article  Google Scholar 

  18. Finch, S.: Mathematical Constants. Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  19. Florenzano, M.: General Equilibrium Analysis: Existence and Optimality Properties of Equilibria. Springer, Berlin (2003)

    Book  Google Scholar 

  20. Florenzano, M., Marakulin, V.M.: Production equilibria in vector lattices. Econ. Theory 17, 577–598 (2001)

    Article  Google Scholar 

  21. Graziano, M.G.: Economies with public projects: efficiency and decentralization. Int. Econ. Rev. 48, 1037–1063 (2007)

    Article  Google Scholar 

  22. Habte, A., Mordukhovich, B.S.: Extended second welfare theorem for nonconvex economies with infinite commodities and public goods. Adv. Math. Econ. 14, 93–126 (2011)

    Article  Google Scholar 

  23. Hervés-Beloso, C., Martins-da-Rocha, V.F., Monteiro, P.K.: Equilibrium theory with asymmetric information and infinitely many states. Econ. Theory 38, 295–320 (2009)

    Article  Google Scholar 

  24. He, W., Yannelis, N.C.: Existence of Walrasian equilibria with discontinuous, non-ordered, interdependent and price-dependent preferences. Econ. Theory 61, 497–513 (2016)

    Article  Google Scholar 

  25. Klishchuk, B.: New conditions for the existence of Radner equilibrium with infinitely many states. J. Math. Econ. 61, 67–73 (2015)

    Article  Google Scholar 

  26. Koutsougeras, L.C., Yannelis, N.C.: Incentive compatibility and information superiority of the core of an economy with differential information. Econ. Theory 3, 195–216 (1993)

    Article  Google Scholar 

  27. Mas-Colell, A.: The price equilibrium existence problem in topological vector lattices. Econometrica 54, 1039–1053 (1986)

    Article  Google Scholar 

  28. Podczeck, K.: Equilibria in vector lattices without ordered preferences or uniform properness. J. Math. Econ. 25, 465–485 (1996)

    Article  Google Scholar 

  29. Podczeck, K., Tourky, R., Yannelis, N.C.: Non-existence of Radner equilibrium already with countably infinitely many states. Unpublished (2008)

  30. Podczeck, K., Yannelis, N.C.: Equilibrium theory with asymmetric information and with infinitely many commodities. J. Econ. Theory 141, 152–183 (2008)

    Article  Google Scholar 

  31. Radner, R.: Competitive equilibrium under uncertainty. Econometrica 36, 31–58 (1968)

    Article  Google Scholar 

  32. Tourky, R.: A new approach to the limit theorem on the core of an economy in vector lattices. J. Econ. Theory 78, 321–328 (1998)

    Article  Google Scholar 

  33. Tourky, R., Yannelis, N.C.: Private expectations equilibrium. Unpublished (2003)

  34. Wickstead, A.W.: Compact subsets of partially ordered Banach spaces. Math. Ann. 212, 271–284 (1975)

    Article  Google Scholar 

  35. Wolinsky, A.: Information revelation in a market with pairwise meetings. Econometrica 58, 1–23 (1990)

    Article  Google Scholar 

  36. Xanthos, F.: A note on the equilibrium theory of economies with asymmetric information. J. Math. Econ. 55, 1–3 (2014)

    Article  Google Scholar 

  37. Yannelis, N.C.: The core of an economy with differential information. Econ. Theory 1, 183–197 (1991)

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Bogdan Klishchuk.

Additional information

The idea of this paper occurred to the author while he studied examples of nonlinear price decentralization of Pareto efficient allocations in Tourky and Yannelis (2003). The author thanks his Ph.D. supervisor at the ANU, Professor Rabee Tourky, for kindly sharing this working paper, helpful comments, and discussions. Two anonymous referees and the editor are gratefully acknowledged for questions that led to significant improvements. The author appreciates valuable feedback at various stages from Patrick Beissner, Simon Grant, Tai-Wei Hu, M. Ali Khan, Jeff Kline, Kieron Meagher, Idione Meneghel, Romans Pancs, Martin Richardson, Ronald Stauber, Jan Werner, Nicholas Yannelis, Valentin Zelenyuk, and an ANU audience.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Klishchuk, B. Multiple markets: new perspective on nonlinear pricing. Econ Theory 66, 525–545 (2018). https://doi.org/10.1007/s00199-017-1071-y

Download citation

Keywords

  • Multiple markets
  • Nonlinear price
  • Equilibrium price
  • Equilibrium existence
  • Equilibrium nonexistence

JEL Classification

  • D4
  • D5
  • D6
  • D8