IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/24006.html
   My bibliography  Save this paper

Wealth in the Quadratic Loss Function of the Ramsey Malinvaud Cass Koopmans Model of Optimal Savings

Author

Listed:

Abstract

Using the second order Taylor expansion of the Lagrangian of the Ramsey model of optimal savings, wealth is included in the quadratic loss function, and not only consumption. Its weight is given by the degree of concavity of the decreasing returns to scale production function times the marginal utility of consumption. The weight of consumption is given by the degree of concavity of the utility function. This quadratic loss function implies that the speed of convergence is explicitly driven by the trade-off between wealth smoothing (fostering convergence, related to technology) versus consumption smoothing (delaying convergence, related to preferences). By contrast, the second order Taylor expansion of the utility instead of the Lagrangian leads to a quadratic loss function with a weight of wealth equal to zero, which is false for a decreasing returns to scale production function

Suggested Citation

  • Jean-Bernard Chatelain & Kirsten Ralf, 2024. "Wealth in the Quadratic Loss Function of the Ramsey Malinvaud Cass Koopmans Model of Optimal Savings," Documents de travail du Centre d'Economie de la Sorbonne 24006, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:24006
    as

    Download full text from publisher

    File URL: http://mse.univ-paris1.fr/pub/mse/CES2024/24006.pdf
    Download Restriction: no
    File URL: https://shs.hal.science/halshs-04612845
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    Linear quadratic approximation; wealth; consumption; savings; negative feedback; speed of convergence;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mse:cesdoc:24006. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.