Skip to main content
Log in

Fiat money and the value of binding portfolio constraints

  • Research Article
  • Published:
Economic Theory Aims and scope Submit manuscript


We establish necessary and sufficient conditions for the individual optimality of a consumption-portfolio plan in an infinite horizon economy where agents are uniformly impatient and fiat money is the only asset available for intertemporal transfers of wealth. Next, we show that fiat money has a positive equilibrium price if and only if for some agent the zero short sale constraint is binding and has a positive shadow price (now or in the future). As there is always an agent that is long, it follows that marginal rates of intertemporal substitution never coincide across agents. That is, monetary equilibria are never full Pareto efficient. We also give a counter-example illustrating the occurrence of monetary bubbles under incomplete markets in the absence of uniform impatience.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  • Araujo A., Fajardo J., Páscoa M.R.: Endogenous collateral. J. Math. Econ. 41, 439–462 (2005)

    Article  Google Scholar 

  • Araujo, A., Páscoa, M.R., Torres-Martínez, J.P.: Long-lived collateralized assets and bubbles. Working paper (2009).

  • Bewley T.: The optimal quantity of money. In: Kareken, J., Wallace, N. (eds) Models of Monetary Economics, Federal Reserve Bank,   Minneapolis (1980)

    Google Scholar 

  • Clower R.: A reconsideration of the microfundations of monetary theory. West. Econ. J. 6, 1–9 (1967)

    Google Scholar 

  • Giménez E.: On the positive fundamental value of money with short-sale constraints: a comment on two examples. Ann. Finance 3, 455–469 (2007)

    Article  Google Scholar 

  • Grandmont J.M., Younés Y.: On the role of money and the existence of a monetary equilibrium. Rev. Econ. Stud. 39, 355–372 (1972)

    Article  Google Scholar 

  • Grandmont J.M., Younés Y.: On the efficiency of a monetary equilibrium. Rev. Econ. Stud. 40, 149–165 (1973)

    Article  Google Scholar 

  • Hahn F.H.: On transaction costs, inessential sequence economies and money. Rev. Econ. Stud. 40, 449–461 (1973)

    Article  Google Scholar 

  • Hernández A., Santos M.: Competitive equilibria for infinite-horizon economies with incomplete markets. J. Econ. Theory 71, 102–130 (1996)

    Article  Google Scholar 

  • Jouini E., Kallal H.: Arbitrage in security markets with short-sales constraints. Math. Finance 5, 197–232 (1995)

    Article  Google Scholar 

  • Laibson D.: Life-cycle consumption and hyperbolic discount functions. Eur. Econ. Rev. 42, 861–871 (1998)

    Article  Google Scholar 

  • Magill M., Quinzii M.: Incomplete markets over an infinite horizon: long-lived securities and speculative bubbles. J. Math. Econ. 26, 133–170 (1996)

    Article  Google Scholar 

  • Páscoa, M.R., Petrassi, M., Torres-Martínez, J.P.: Fiat money and the value of binding portfolio constraints. Working paper series, 176. Banco Central do Brasil (2008)

  • Rincón-Zapatero J.P., Santos M.: Differentiability of the value function without interiority assumptions. J. Econ. Theory 144, 1948–1964 (2009)

    Article  Google Scholar 

  • Rockafellar R.T.: Convex Analysis. Princeton University Press, Princeton (1997)

    Google Scholar 

  • Samuelson P.: An exact consumption-loan model of interest with or without the social contrivance of money. J. Political Econ. 66, 467–482 (1958)

    Article  Google Scholar 

  • Santos M.: The value of money in a dynamic equilibrium model. Econ. Theory 27, 39–58 (2006)

    Article  Google Scholar 

  • Santos M., Woodford M.: Rational asset pricing bubbles. Econometrica 65, 19–57 (1997)

    Article  Google Scholar 

  • Starret D.A.: Inefficiency and the demand for “money” in a sequence economy. Rev. Econ. Stud. 40, 437–448 (1973)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Juan Pablo Torres-Martínez.

Additional information

Previous working paper versions of this article appeared under the titles: “On the role of debt constraints in monetary equilibrium” and “Welfare improving debt constraints”. Although in this article we avoid short-sales of money, more general debt constraints were studied in the previous working paper versions (see, for instance, Páscoa, Petrassi and Torres-Martínez (2008)). M. Petrassi wants to disclaim that the views expressed in this work do not necessarily reflect those of the Banco Central do Brasil or its members.

We are grateful to the Co-Editor Timothy Kehoe and two anonymous referees for their insights and suggestions. Mário R. Páscoa acknowledges support from FCT and FEDER (project PTDC/ECO/64968/2006). J.P. Torres-Martínez acknowledges support from the Brazilian research council, CNPq, through project 307554/2004-0. Petrassi and Torres-Martínez also want to thank the Department of Economics, PUC-Rio, Brazil, where this research was partly undertaken.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Páscoa, M.R., Petrassi, M. & Torres-Martínez, J.P. Fiat money and the value of binding portfolio constraints. Econ Theory 46, 189–209 (2011).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


JEL Classification