On Intertemporal Preferences in Continuous Time: The Case of Certainty (Classic Reprint) - Softcover
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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.
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On Intertemporal Preferences in Continuous Time: The Case of Certainty
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Paperback. Zustand: 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. Bestandsnummer des Verkäufers 9781332272983_0
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On Intertemporal Preferences in Continuous Time The Case of Certainty Classic Reprint
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