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

La richesse dans la fonction de perte quadratique du modèle d'épargne optimale de Ramsey, Malinvaud, Cass et Koopmans

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

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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; Richesse; Consommation; Epargne; Rétroaction négative; Vitesse de convergence; Approximation linéaire quadratique (search for similar items in EconPapers)
Date: 2024-06
New Economics Papers: this item is included in nep-upt
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-04612845v1
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Published in 2024

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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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