On Intertemporal Preferences in Continuous Time: The Case of Certainty (Classic Reprint) - Tapa blanda
Sinopsis
Excerpt from On Intertemporal Preferences in Continuous Time: The Case of Certainty
A continuous function can be nowhere differentiable take, for example, a Brownian motion sample path. In fact, most continuous functions are nowhere differentiable. This is perhaps not so counter-intuitive when time is not the characteristic of the commodity in question. When the commodities are indexed by time, our intuition certainly suggests that prices for consumption should be continuous functions of time. We also think that more should be true. Prices should not fluctuate over time in a nowhere differentiable fashion.2 In particular, we think that interest rates should exist in a reasonable economic intertemporal model. This condition is equivalent to the requirement that prices for consumptions be absolutely continuous functions of time. This additional requirement is what makes the results of the commodity differentiation literature unsatisfactory for our purposes.
We begin in Section 2 with a formulation of the consumption set and consumption space. For the set of feasible consumption patterns, we use the space of positive, increasing, right continuous functions on denoted X+.3 For given a: e X+ and t 6 x(i) denotes the cumulative consumption from time zero to time t under consumption pattern 1. In order to speak of net trades, the space of consumption bundles, or the commodity space, is the linear span of X+. Denoted X, this is the space of functions of bounded variation on [0, 1] that are right-continuous.
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Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Excerpt from On Intertemporal Preferences in Continuous Time: The Case of Certainty
A continuous function can be nowhere differentiable take, for example, a Brownian motion sample path. In fact, most continuous functions are nowhere differentiable. This is perhaps not so counter-intuitive when time is not the characteristic of the commodity in question. When the commodities are indexed by time, our intuition certainly suggests that prices for consumption should be continuous functions of time. We also think that more should be true. Prices should not fluctuate over time in a nowhere differentiable fashion.2 In particular, we think that interest rates should exist in a reasonable economic intertemporal model. This condition is equivalent to the requirement that prices for consumptions be absolutely continuous functions of time. This additional requirement is what makes the results of the commodity differentiation literature unsatisfactory for our purposes.
We begin in Section 2 with a formulation of the consumption set and consumption space. For the set of feasible consumption patterns, we use the space of positive, increasing, right continuous functions on denoted X+.3 For given a: e X+ and t 6 x(i) denotes the cumulative consumption from time zero to time t under consumption pattern 1. In order to speak of net trades, the space of consumption bundles, or the commodity space, is the linear span of X+. Denoted X, this is the space of functions of bounded variation on [0, 1] that are right-continuous.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from On Intertemporal Preferences in Continuous Time: The Case of Certainty
Different topologies on the space of certain consumption patterns in a continuous time setting are discussed. A family of topologies which give an economically reasonable sense of closeness and have an appropriate intertemporal flavor is suggested. The topological duals of our suggested topologies are essentially spaces of Lipschitz continuous functions. Any utility functional whose felicity function at any time t depends explicitly on the consumption at that time and is not linear in it is not continuous in any one of our topologies. A class of utility functionals that are continuous in the suggested topologies and that capture the intuitively appealing notion that consumptions at nearby dates are almost perfect substitutes is provided. We then give necessary and sufficient conditions for a consumption plan to be optimal for this class of utility functionals. We demonstrate our general theory by solving in closed form the optimal consumption problem for a particular utility function. The optimal solution consists of a (possible) initial "gulp" of consumption, or an initial period of no consumption, followed by consumption at the rate that maintains a constant ratio of wealth to an index of past consumption experience.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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On Intertemporal Preferences in Continuous Time: The Case of Certainty
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Paperback. Condición: New. Print on Demand. This book delves into the fascinating realm of intertemporal preferences, exploring how individuals make choices about consumption over time. The author argues that traditional models fail to adequately capture the dynamic nature of these preferences, particularly the tendency for individuals to substitute consumption across nearby dates. To address this shortcoming, the book introduces a novel family of preference topologies that more accurately reflect the interplay between time and preferences. These topologies are mathematically well-behaved and allow for preferences that exhibit a trade-off between delaying or advancing consumption for increasingly shorter periods. The author demonstrates how these preferences lead to surprising insights into optimal consumption behavior. For instance, optimal consumption plans may involve periods of no consumption followed by periods of rapid consumption, a pattern not predicted by traditional models. Overall, this book offers a significant contribution to the study of intertemporal preferences. Its innovative approach and thought-provoking insights challenge conventional wisdom and provide a deeper understanding of how individuals make consumption decisions over time. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781332272983_0
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On Intertemporal Preferences in Continuous Time The Case of Certainty Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332272983
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On Intertemporal Preferences in Continuous Time The Case of Certainty Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332272983
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