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Rational Bubbles on Dividend-Paying Assets: A Comment on Tirole (1985)

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  • Ngoc-Sang Pham
  • Alexis Akira Toda

Abstract

Tirole (1985) studied an overlapping generations model with capital accumulation and showed that the emergence of asset bubbles solves the capital over-accumulation problem. His Proposition 1(c) claims that if the dividend growth rate is above the bubbleless interest rate (the steady-state interest rate in the economy without the asset) but below the population growth rate, then bubbles are necessary in the sense that there exists no bubbleless equilibrium but there exists a unique bubbly equilibrium. We show that this result (as stated) is incorrect by presenting an example economy that satisfies all assumptions of Proposition 1(c) but its unique equilibrium is bubbleless. We also restore Proposition 1(c) under the additional assumptions that initial capital is sufficiently large and dividends are sufficiently small. We show through examples that these conditions are essential.

Suggested Citation

  • Ngoc-Sang Pham & Alexis Akira Toda, 2025. "Rational Bubbles on Dividend-Paying Assets: A Comment on Tirole (1985)," Papers 2507.12477, arXiv.org, revised Oct 2025.
    • Handle: RePEc:arx:papers:2507.12477
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    References listed on IDEAS

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    1. Andrew B. Abel & N. Gregory Mankiw & Lawrence H. Summers & Richard J. Zeckhauser, 1989. "Assessing Dynamic Efficiency: Theory and Evidence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(1), pages 1-19.
    2. Gadi Barlevy & Douglas Gale & Franklin Allen, 2017. "On Interest Rate Policy and Asset Bubbles," 2017 Meeting Papers 489, Society for Economic Dynamics.
    3. Chattopadhyay, Subir, 2008. "The Cass criterion, the net dividend criterion, and optimality," Journal of Economic Theory, Elsevier, vol. 139(1), pages 335-352, March.
    4. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
    5. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, December.
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    Cited by:

    1. Pham, Ngoc Sang & Le Van, Cuong & Bosi, Stefano, 2025. "To Bubble or Not to Bubble: Asset Price Dynamics and Optimality in OLG Economies," MPRA Paper 125772, University Library of Munich, Germany.
    2. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2025. "To Bubble or Not to Bubble: Asset Price Dynamics and Optimality in OLG Economies," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05199274, HAL.

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