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

Jean-Bernard Chatelain and Kirsten Ralf ()
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Kirsten Ralf: ESCE International Business School

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

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

Keywords: Linear quadratic approximation; wealth; consumption; savings; negative feedback; speed of convergence (search for similar items in EconPapers)
JEL-codes: C61 C62 E43 E44 E47 E52 E58 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2024-06
New Economics Papers: this item is included in nep-upt
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http://mse.univ-paris1.fr/pub/mse/CES2024/24006.pdf (application/pdf)
https://shs.hal.science/halshs-04612845

Related works:
Journal Article: Wealth in the Quadratic Loss Function of the Ramsey Malinvaud Cass Koopmans Model of Optimal Savings (2024)
Working Paper: Wealth in the Quadratic Loss Function of the Ramsey Malinvaud Cass Koopmans Model of Optimal Savings (2024)
Working Paper: Wealth in the Quadratic Loss Function of the Ramsey Malinvaud Cass Koopmans Model of Optimal Savings (2024)
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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:24006

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