In this paper we propose a mainstream reformulation of the original Walras’ model of capital accumulation. First, we prove the existence of intertemporal competitive equilibria. Our proof combines a well known theorem due to Yannelis and Prabhakar (J Math Econ 12:233–245, 1983) with a lemma due to Geanakoplos (Econ Theory 21:585–603, 2003). Moreover, we remedy the indeterminacy of allocation of savings across multiple types of capital goods by introducing a storage technology. Finally, we show that, for stored capital goods, the equality of rates of returns emerges endogenously in equilibrium, while it was imposed by Walras from the outset in his original contribution
a b s t r a c tIn this study we offer a new approach to proving the differentiability of the value function, which complements and extends the literature on dynamic programming. This result is then applied to the analysis of equilibrium in the recent class of monetary economies developed in [Lagos, R., Wright, R., 2005. A unified framework for monetary theory and policy analysis. Journal of Political Economy 113, . For this type of environments we demonstrate that the value function is differentiable and this guarantees that the marginal value of money balances is well defined.
We revisit a classical theme of general equilibrium theory, namely the continuity of the Walras correspondence. Using a remarkable theorem due to Fort (Publ Math Debr 2:100-102, 1951) which has widely been used in recent literature on game theory, we prove the generic continuity of the price equilibrium-set correspondence under very general assumptions on the exchange economy.
In this study we offer a new approach to proving the differentiability of the value function, which complements and extends the literature on dynamic programming. This result is then applied to the analysis of equilibrium in the recent class of monetary economies developed in [14]. For this type of environments we demonstrate that the value function is differentiable and this guarantees that the marginal value of money balances is well defined.JEL classification: E00, C61
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