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Emergence of price-taking Behavior

  • Sjur Didrik FlåmEmail author
Research Article
  • 2 Downloads

Abstract

Price-taking behavior is the bedrock of much market theory. How might such behavior emerge? Addressing that old but still intriguing question, this paper uses a money commodity to denominate all rates of exchange and substitution. Out of equilibrium, some rates differ between agents, thereby driving trade. The simplest form of trade is bilateral; it needs no broker, center or supervisor. Yet, under broad conditions, that elementary institution can take the economy to competitive equilibrium. Proving convergence, this paper invokes minimal hypotheses as to agents’ behaviors, competences and deals. Moreover, agents may make boundary choices, appreciate relatively few commodities, choose within general domains and deploy non-smooth preferences. Convex analysis provides the chief tool kit.

Keywords

Money commodity Bilateral exchange Market equilibrium. 

JEL Classification

C63 D03 D51 

Notes

References

  1. Alchian, A.A.: Why money? J. Money Credit Bank. 9, 133–140 (1977)CrossRefGoogle Scholar
  2. Alós-Ferrer, C., Kirchsteiner, G.: Learning and market clearing: theory and experiments. Econ. Theory 60, 203–2421 (2015).  https://doi.org/10.1007/s00199-015-0885-8 CrossRefGoogle Scholar
  3. Arrow, K.J., Hahn, F.H.: General Competitive Analysis. Holden-Day, Inc., San Franciso (1971)Google Scholar
  4. Aubin, J.-P., Cellina, A.: Differential Inclusions. Springer, Berlin (2012)Google Scholar
  5. Bauschke, H.H., Borwein, J.M.: On the convergence of von Neumann’s alternating projection algorithm for two sets. Set-Valued Anal. 1, 185–212 (1993)CrossRefGoogle Scholar
  6. Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming. Wiley, New York (1993)Google Scholar
  7. Eckalbar, J.C.: Bilateral trade in a monetized pure exchange economy. Econ. Model. 3, 135–139 (1986) CrossRefGoogle Scholar
  8. Debreu, G.: Economies with a finite set of equilibria. Econometrica 38(3), 387–392 (1970)CrossRefGoogle Scholar
  9. Donzelli, F.: Marshall versus Walras on equilibrium and disequilibrium. Hist. Econ. Rev. 48, 1–38 (2008)CrossRefGoogle Scholar
  10. Dubey, P., Sahi, S., Shubik, M.: Repeated trade and the velocity of money. J. Math. Econ. 22, 125–137 (1993)CrossRefGoogle Scholar
  11. Feldman, A.M.: Bilateral trading processes, pair-wise optimality, and Pareto optimality. Rev. Econ. Stud. 4, 463–473 (1973)CrossRefGoogle Scholar
  12. Fisher, F.M.: Disequilibrium Foundations of Equilibrium Economics. Cambridge University Press, London (1983)CrossRefGoogle Scholar
  13. Flåm, S.D.: Bilateral exchange and competitive equilibrium. Set-Valued Var. Anal. 24, 1–11 (2016a)CrossRefGoogle Scholar
  14. Flåm, S.D.: Order books, markets, and convex analysis. Optimization 66, 1413–1424 (2016b)CrossRefGoogle Scholar
  15. Flåm, S.D.: On measures, pricing and sharing of risk. Rev. Investig. Oper. 39, 2 (2018)Google Scholar
  16. Foley, D.C.: A statistical equilibrium theory of markets. J. Econ. Theory 62, 321–345 (1994)CrossRefGoogle Scholar
  17. Friedman, D.: Money-mediated disequilibrium processes in a pure exchange economy. J. Math. Econ 6, 149–167 (1979)CrossRefGoogle Scholar
  18. Friedman, D.: The double auction market institution: a survey. In: Friedman, D., Rust, J. (eds.) SFI Studies in the Sciences and Complexity, Proceedings, vol. XIV, pp. 3–24. Addison-Wesley, London (1993)Google Scholar
  19. Gale, D.: Strategic Foundations of General Equilibrium. Cambridge University Press, London (2000)CrossRefGoogle Scholar
  20. Gintis, H.: The dynamics of general equilibrium. Econ. J. 117, 1280–1309 (2007)CrossRefGoogle Scholar
  21. Ghosal, S., Morelli, M.: Retrading in market games. J. Econ. Theory 115, 151–181 (2004)CrossRefGoogle Scholar
  22. Haavelmo, T.: What can static models of equilibrium tell? Econ. Inq 12, 27–34 (1974) CrossRefGoogle Scholar
  23. Hahn, F.H., Negishi, T.: A theorem on non-tâtonnement stability. Econometrica 30, 463–469 (1962)CrossRefGoogle Scholar
  24. Hiriart-Urruty, J.-B.: Bases, outils et principes pour l’analyse variationelle. Springer, Berlin (2012)Google Scholar
  25. Howitt, P.: Beyond search: fiat money in organized exchange. Int. Econ. Rev. 46(2), 405–429 (2005)CrossRefGoogle Scholar
  26. Hua, X., Yamashita, N.: Block coordinate proximal gradient methods for nonsmooth separable optimization. Math. Program. Ser. A 160, 1–32 (2016)CrossRefGoogle Scholar
  27. Jofré, A., Rockafellar, R.T., Wets, R.J.-B.: General economic equilibrium with financial markets and retainability. Econ. Theory 63, 309–45 (2017).  https://doi.org/10.1007/s00199-016-1031-y CrossRefGoogle Scholar
  28. Mandel, A., Gintis, H.: Decentralized pricing and strategic stability of Walrasian general equilibrium. J. Math. Econ. 63, 84–92 (2016)CrossRefGoogle Scholar
  29. McLennan, A., Sonnenschein, H.: Sequential bargaining as a noncooperative foundation for Walrasian equilibrium. Econometrica 59(5), 1395–1424 (1991)CrossRefGoogle Scholar
  30. Mertens, J.F.: The limit-price mechanism. J. Math. Econ. 39, 433–528 (2003)CrossRefGoogle Scholar
  31. Necoara, I., Nesterov, Yu., Glineur, F.: Random block coordinate descent methods for linearly constrained optimization over networks. J. Optim. Theory Appl. 173, 227–2354 (2017)CrossRefGoogle Scholar
  32. Negishi, T.: Welfare economics and the existence of an equilibrium for a competitive economy. Metroeconomica 12, 92–97 (1960)CrossRefGoogle Scholar
  33. Nesterov, Yu.: Efficiency of coordinate descent methods on huge-scale optimization problems. SIAM J. Optim. 22(2), 341–362 (2012)CrossRefGoogle Scholar
  34. Patinkin, D.: Money, Interest and Prices. Harper and Row, New York (1965)Google Scholar
  35. Penot, J.-P.: Calculus Without Derivatives. Springer, Berlin (2013)CrossRefGoogle Scholar
  36. Piccione, M., Rubinstein, A.: Equilibrium in the jungle. Econ. J. 117(522), 883–896 (2007)CrossRefGoogle Scholar
  37. Rubinstein, A., Wolinsky, A.: Equilibrium in a market with sequential bargaining. Econometrica 53, 1133–1150 (1985)CrossRefGoogle Scholar
  38. Ruszczynski, A.: Nonlinear Optimization. Princeton University Press, Princeton (2006)CrossRefGoogle Scholar
  39. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)CrossRefGoogle Scholar
  40. Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin (1998)CrossRefGoogle Scholar
  41. Samuelson, P.A.: Foundations of Economic Analysis. Harvard University Press, Cambridge (1947)Google Scholar
  42. Shapley, L.S., Shubik, N.: Trade using one commodity as means of payment. J. Polit. Econ. 85, 937–968 (1977)CrossRefGoogle Scholar
  43. Smale, S.: A convergent process of price adjustment and global Newton methods. J. Math. Econ. 4, 127–130 (1976)Google Scholar
  44. Smith, V.L.: Rationality in Economics. Cambridge University Press, Cambridge (2008)Google Scholar
  45. Starr, R.M.: Why is there money? Endogenous derivation of “money” as the most liquid asset: a class of examples. Econ. Theory 21, 455–474 (2003).  https://doi.org/10.1007/s00199-002-0326-3 CrossRefGoogle Scholar
  46. Vind, K.: A theorem on the core of an economy. Rev. Econ. Stud. 5, 165–177 (1965)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Informatics DepartmentUniversity of BergenBergenNorway

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