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Stationary Ordinal Utility and Time Perspective
... The essential difference between the characterization of valuations in the present paper and earlier studies (e.g., Koopmans (1960), Koopmans, Diamond, and Williamson (1964), Diamond (1965), Fishburn (1966), Koopmans (1972), Lauwers (1995), Chichilnisky (1996Chichilnisky ( , 1997, Chambers and Echenique (2018), Drugeon and Huy (2021)) is the adoption of the time value of money principle. The time value of money principle reflects the preference for expediting the receipt of positive payoffs: the faster the accumulation of payoffs, the better. ...
... Many writers, e.g., Debreu (1959Debreu ( , 1960, Koopmans (1960), Koopmans, Diamond, and Williamson (1964), Diamond (1965), Fishburn (1966), Koopmans (1972), Olson and Bailey (1981), Lauwers (1995), Chichilnisky (1996Chichilnisky ( , 1997, Fishburn and Edwards (1997), Chambers and Echenique (2018), Drugeon and Huy (2021), have studied the implications of various axioms on preferences over product sets, e.g., on sequences of consumptions or on streams of payoffs, and the representation of the preferences by ordinal utilities. ...
... It satisfies (S1.2) if and only if v is not a patient valuation (equivalently, v(e 1 ) > 0), and it satisfies S2 if and only if v(e t ) > 0 ∀t. (Koopmans (1960(Koopmans ( , 1972, Koopmans, Diamond, and Williamson (1964)) ...
This paper characterizes those preferences over bounded infinite utility streams that satisfy the time value of money principle and an additivity property, and the subset of these preferences that, in addition, are either impatient or patient. Based on this characterization, the paper introduces a concept of optimization that is robust to a small imprecision in the specification of the preference, and proves that the set of feasible streams of payoffs of a finite Markov decision process admits such a robust optimization.
... In those two largely overlapping articles, he attributed to Koopmans (1960) two arguments in favour of discounting the welfare of future generations. The first "strong" argument, set out also by Koopmans et al. (1964) as well as by Diamond (1965) on his own, was that, without giving less weight to utilities far in the future, no complete and transitive preference ordering on the entire space of infinite utility streams could satisfy the usual continuity and weak Pareto conditions. 1 The second "weak" argument was that failure to discount later generations' utilities would imply that earlier generations are condemned to make excessive sacrifices. ...
... The opening question in the quotation is a valuable addition inArrow (1999b) to the corresponding passage inArrow (1999a). The second "classic paper" is presumablyKoopmans et al. (1964).11 Stern (2014b, p. 472; 2015, p. 169) also quotes a recent personal communication in which Peter Diamond, a co-author ofKoopmans et al. (1964), had argued to the effect that the results of this line of work, if they would indeed preclude intergenerational equity, should not be applied to the issue of whether to discount the welfare of future generations. ...
... The second "classic paper" is presumablyKoopmans et al. (1964).11 Stern (2014b, p. 472; 2015, p. 169) also quotes a recent personal communication in which Peter Diamond, a co-author ofKoopmans et al. (1964), had argued to the effect that the results of this line of work, if they would indeed preclude intergenerational equity, should not be applied to the issue of whether to discount the welfare of future generations. Instead Diamond has argued in favour of the kind of "pragmatic" criteria discussed in Sects. ...
Ramsey famously condemned discounting “future enjoyments” as “ethically indefensible”. Suppes enunciated an equity criterion which, when social choice is utilitarian, implies giving equal weight to all individuals’ utilities. By contrast, Arrow (Contemporary economic issues. International Economic Association Series. Palgrave Macmillan, London, 1999a; Discounting and Intergenerational Effects, Resources for the Future Press, Washington DC, 1999b) accepted, perhaps reluctantly, what he called Koopmans’ (Econometrica 28(2):287–309, 1960) “strong argument” implying that no equitable preference ordering exists for a sufficiently unrestricted domain of infinite utility streams. Here we derive an equitable utilitarian objective for a finite population based on a version of the Vickrey–Harsanyi original position, where there is an equal probability of becoming each person. For a potentially infinite population facing an exogenous stochastic process of extinction, an equitable extinction biased original position requires equal conditional probabilities, given that the individual’s generation survives the extinction process. Such a position is well-defined if and only if survival probabilities decline fast enough for the expected total number of individuals who can ever live to be finite. Then, provided that each individual’s utility is bounded both above and below, maximizing expected “extinction discounted” total utility—as advocated, inter alia, by the Stern Review on climate change—provides a coherent and dynamically consistent equitable objective, even when the population size of each generation can be chosen.
... The calculus of variation and the optimal control theory have contributed to the enrichment of the literature on this theory. Initially, the applications of these methods were restricted to the assumption that time preferences remain unchanged over time, but later, as the structure of such preferences was scrutinized in the pioneering works of Koopmans (1960); Koopmans et al. (1964) and Uzawa (1968) the preferences that are recursive in nature and which allow the rate of time preference to vary endogenously have enriched the analysis of intertemporal behavior (Blackorby et al., 1978;Epstein and Hynes, 1983;Epstein, 1987a;1987b;Obstfeld, 1990). At the same time, along with this development, the MBF-hypothesis has continued to inspire many generations of researchers (Sargent, 1987;Baranzini, 2005;Deaton, 2005). ...
... Specifically, this paper shows how the three lines of development, namely, the structure of recursive preferences of Koopmans-Uzawa-Epstein kind (Koopmans, 1960;Koopmans et al., 1964;Uzawa, 1968), the Hamiltonian method and Pontryagin's maximum principle as a tool to analyze dynamic behavior, and the MBFhypothesis are interrelated. In particular, (1) we define the Fisherian and the Böhm-Bawerkian rates of time preferences and show that they are equivalent, whether they are defined along locally constant paths or inclusive of the effect of the first order change of consumption. ...
... Where and are assumed to be real-valued and twice continuously differentiable. The structure of recursive preferences and this utility functional representation of such preferences has been investigated by Koopmans (1960), Koopmans et al. (1964), Blackorby et al. (1978), Epstein and Hynes (1983), Epstein (1987a;1987b) and Obstfeld (1990). In the following analysis, will be referred to as the instantaneous utility function, and as the instantaneous discounting function. ...
... (2) impatience: discounting the future, e.g. featured in work of Diamond, Koopmans and Williamson (1962), Feldstein (1965), Koopmans (1960), Koopmans, Diamonds and Williamson (1964), Marglin (1963), and Strotz (1957); ...
... (4) time perspective: related to hyperbolic-discounting as in Koopmans et al. (1964) and Laibson (1997); ...
... (6) persistence: stationarity of a consistent preference structure in Diamond (1965), Koopmans (1960), Koopmans et al. (1964); and (7) variety: or nonpersistence as consistently varying preference structure as described in Wold (1952). ...
... 13 This paper assumes, as in Koopmans' (1960Koopmans' ( , 1964 classic analysis and a large subsequent literature, that generation 0's preference does not depend on past generations' consumption. Relaxing this assumption raises interesting challenges, discussed in Section 6. ...
... Despite its similarity with Axiom 9 when s = 1, time consistency is conceptually different because it involves multiple, possibly different, preference relations. 32 Indeed, Koopmans et al. (1964) write, "[Stationarity] does not imply that, after one period has elapsed, the ordering then applicable to the 'then' future will be the same as that now applicable to the 'present' future. All postulates are concerned with only one ordering, namely that guiding decisions to be taken in the present. ...
... It is straightforward to construct examples of preferences { t } ∞ t=0 that satisfy Axiom 9 but are not time consistent, and vice versa. of preferences as the time of choice changes is therefore extraneous to the present study." (Koopmans et al. (1964), p. 85, emphasis in the original) ...
Modeling intergenerational altruism is crucial to evaluate the long-term consequences of current decisions, and requires a set of principles guiding such altruism. We axiomatically develop a theory of pure, direct altruism: Altruism is pure if it concerns the total utility (rather than the mere consumption utility) of future generations, and direct if it directly incorporates the utility of all future generations. Our axioms deliver a new class of altruistic preferences, whose weight put on the consumption of a future generation generally depends on the consumption of other generations. The only preferences lacking this dependence correspond to the quasi-hyperbolic discounting model, which our theory characterizes. Our approach provides a framework to analyze welfare in the presence of altruistic preferences and addresses technical challenges stemming from the interdependent nature of such preferences.
... The answer is significant too for the analysis of decision trees, and for the discounted utility model of economics, which has an even longer history. Although the axiomatic foundations of that model are deterministic (Koopmans, 1960;Koopmans et al., 1964;Williams & Nassar, 1966;Koopmans, 1972), it is widely employed in stochastic settings. It is useful to imbed questions about MDPs, decision trees, and the discounted utility model in a general abstract setting and, thus, to obtain answers that encompass multiple types of models. ...
... It is standard practice in economics applications to use this model to encompass both time preference and attitude towards risk. It was suggested in Samuelson (1937) (which was foreshadowed by Ramsey, 1928) in a deterministic setting where it was axiomatized by Koopmans (1960Koopmans ( , 1972, Koopmans et al. (1964) whose postulates include (A1)-(A4) and (A2 c ). In the stochastic case, the model emerges from results concerning multiattribute preference orderings and utility functions that are unified and generalized by the axiomatization in Miyamoto and Wakker (1996) which includes (A1)-(A4) and (A2 c ). ...
A binary preference relation on a real vector space satisfying four (natural) axioms is shown to induce a utility function composed of a linear function to the reals and a weakly monotonic function. The key axiom is decomposition, and the utility function can be taken to be linear if and only if this axiom’s converse is also satisfied. Important consequences follow for risk-sensitive discounted Markov decision processes, decision trees, and the discounted utility model in economics. Since the four axioms imply that preferences correspond to discounting, the four axioms without the converse imply that preferences are consistent with discounting without risk neutrality.
... The next aggregator is a modification of the aggregator by Koopmans et al. (1964). ...
... Sometimes, a trick is needed. Koopmans et al. (1964) study the aggregator ...
In this paper, we consider the problem of the existence and the uniqueness of a recursive utility function defined on intertemporal lotteries. The purpose of this paper is to provide the results of the existence and the uniqueness of a recursive utility function. The utility function is obtained as the limit of iterations on a nonlinear operator and is independent on initial starting points, with iterations converging at an exponential rate. We also find the maximum utility and an optimal strategy by means of iterations of the Bellman operator.
... An inspiration which led to consider the above equation were some models in economics connected to the description of a special order in a space of sequences of preference of consumption outcomes called "impatience" (see [2]). Arsen Kochov in a private correspondence presented an idea that every sequence of consumption outcomes can be represented by an increasing homeomorphism with one fixed point and the problem of the existence of impatience order can be reduced to the determination of suitable properties of semigroups G of increasing homeomorphisms of R onto R satisfying the conditions: (ii) if f has a fixed point p f and g has a fixed point p g , then p f > p g if and only if f • g > g • f . ...
... Let G t , t > 0 and H a , a ∈ R be the functions defined by (2). The weakened assumption on F says that all these functions are continuous and for every x ∈ I the functions t → G t (x) and a → H a (x) are Lebesgue measurable. ...
Define on the set \(G:=\mathbb R^+\times \mathbb R\) the operation \((t,a)*(s,b)=(ts,tb+a)\). \((G,*)\) is a non-commutative group with the neutral element (1, 0). We consider a non-commutative translation equation \(F(\eta ,F(\xi ,x))=F(\eta *\xi ,x)\), \(\eta , \xi \in G\), \(x\in I\), \(F(1,0)=\mathrm{id}\), where I is an open interval and \(F:G\times I\rightarrow I\) is a continuous mapping. This equation can be written in the form: \(F((t,a),F((s,b),x))=F((ts,tb+a),x)\), \( t,s \in \mathbb R^+\), \(x\in I\). For \(t=1\) the family \(\{F(t,a)\}\) defines an additive iteration group, however for \(a=0\) it defines a multiplicative iteration group. We show that if F(t, 0) for some \(t\ne 1\) has exactly one fixed point \(x_t\), \((F(t,0)-\mathrm{id})(x_t-\mathrm{id})\ge 0\) and for an \(a>0 \) \(F(1,a)>\mathrm {id}\), then there exists a unique homeomorphism \(\varphi :I\rightarrow \mathbb R\) such that \(F((s,b),x)=\varphi ^{-1}(s\varphi (x)+b)\) for \(s\in \mathbb R^+\) and \(b\in \mathbb R\).
... Centuries later, Ramsey (1926) provided the first formal axiomatic treatment of expected utility, which would later be refined by von Neumann and Morgenstern (1953) to form the now widely adopted foundations of decision theory. Following this development, an expansive body of research has explored how to account for other aspects of rationality, including uncertainty (Kreps and Porteus, 1978), time (Koopmans, 1960;Koopmans et al., 1964), and computation (Lewis, 1985;Richter and Wong, 1999;Rustem and Velupillai, 1990). ...
The reward hypothesis posits that, "all of what we mean by goals and purposes can be well thought of as maximization of the expected value of the cumulative sum of a received scalar signal (reward)." We aim to fully settle this hypothesis. This will not conclude with a simple affirmation or refutation, but rather specify completely the implicit requirements on goals and purposes under which the hypothesis holds.
... However, some of the decision-making processes may be complex, risky and uncertain and the benefits uncertain and potentially split between private individuals and the wider public. Economic approaches that can be used for decision-making under risk and uncertainty thus have much to offer here, including real options and discounting utility modelling techniques (Baucells & Heukamp 2012;Drury 1992;Janney & Dess 2004;Koopmans et al. 1964). ...
The discovery of antimicrobial agents for the treatment of infectious diseases was one of the most significant events of the 20th century. Notwithstanding their importance, acquired resistance has become increasingly evident and this pattern has followed the introduction of each new antimicrobial agent. Antimicrobial resistance (AMR) has not only led to unwarranted mortality rates, but it presents as a major economic burden to societies. The alarming worldwide escalation in AMR poses a serious threat to public health and can cause major disruption globally. Whilst there has been progress in understanding AMR in the scientific literature, there is a dearth of knowledge that considers AMR from an economic perspective, especially as it relates to resource‐based sectors. This paper uses two case studies to illustrate how an economic lens can improve understanding of the potential risks surrounding AMR and to identify the net welfare associated with specific interventions. We demonstrate the importance of economics when considering the impacts of AMR in the context of livestock and wastewater use in Australia and when quantifying the potential disruption to the economy. We also illustrate how economics can both highlight the magnitude of the risks from AMR but offer a way forward through cost‐effective policy options.
... The term on the right-hand side of (II) is an a posteriori error estimate for the approximate solution A n x 0 of the operator equation Ax = x to be in any domain which contains A n x 0 and the solution x . 39 Here the domain is h ; vi. Assume E is a Banach lattice. ...
We reconsider the theory of Thompson aggregators proposed by Marinacci and Montrucchio (Marinacci and Montrucchio, 2010). We prove the existence of a Least Fixed Point (LFP) solution to the Koopmans equation. It is a recursive utility function. Our proof turns on demonstrating the Koopmans operator is a Scott continuous function when its domain is an order bounded subset of a space of bounded functions defined on the commodity space. Kleene’s Fixed Point Theorem yields the construction of the LFP by an iterative procedure. We argue the LFP solution is the Koopmans equation’s principal solution. It is constructed by an iterative procedure requiring less information (according to an information ordering) than approximations for any other fixed point. Additional distinctions between the LFP and GFP (Greatest Fixed Point) are presented. A general selection criterion for multiple solutions for functional equations and recursive methods is proposed.
... The infinitesimal amount 1 2 r 0 (x) can be interpreted as the compensation required by the investor in order to satisfy his impatience in the time interval (0, ). More about the theory of investor's impatience can be found in Fisher [41, Chapter IV], Koopmans [75, p. 296] and Diamond et al. [34]. ...
We study the hedging and valuation of European and American claims on a non-traded asset Y, when a traded stock S is available for hedging, with S and Y following correlated geometric Brownian motions. This is an incomplete market, often called a basis risk model. The market agent's risk preferences are modelled using a so-called forward performance process (forward utility), which is a time-decreasing utility of exponential type. Moreover, the market agent (investor) does not know with certainty the values of the asset price drifts. This market setting with drift parameter uncertainty is the partial information scenario. We discuss the stochastic control problem obtained by setting up the hedging portfolio and derive the optimal hedging strategy. Furthermore, a (dual) forward indifference price representation of the claim and its PDE are obtained. With these results, the residual risk process representing the basis risk (hedging error), pay-off decompositions and asymptotic expansions of the indifference price in the European case are derived. We develop the analogous stochastic control and stopping problem with an American claim and obtain the corresponding forward indifference price valuation formula.
... Samuelson [69] introduced an exponential model of the subjective discount factor. This model was adjusted in [70]. ...
In general, the present value (PV) concept is ambiguous. Therefore, behavioural factors may influence on the PV evaluation. The main aim of our paper is to propose some method of soft computing PV evaluated under the impact of behavioural factors. The starting point for our discussion is the notion of the Behavioural PV (BPV) defined as an imprecisely real-valued function of distinguished variables which can be evaluated using objective financial knowledge or subjective behavioural premises. In our paper, a BPV is supplemented with a forecast of the asset price closest to changes. Such BPV is called the oriented BPV (O-BPV). We propose to evaluate an O-BPV by oriented fuzzy numbers which are more useful for portfolio analysis than fuzzy numbers. This fact determines the significance of the research described in this article. O-BPV may be applied as input signal for systems supporting invest-making. We consider here six cases of O-BPV: overvalued asset with the prediction of a rise in its price, overvalued asset with the prediction of a fall in its price, undervalued asset with the prediction of a rise in its price, undervalued asset with the prediction of a fall in its price, fully valued asset with the prediction of a rise in its rice and fully valued asset with the prediction of a fall in its rice. All our considerations are illustrated by numerical examples. Presented examples show the way in which we transform superposition of objective market knowledge and subjective investment opinion into simple return rate.
... The infinitesimal amount 1 2 r 0 (x) can be interpreted as the compensation required by the investor in order to satisfy his impatience in the time interval (0, ). More about the theory of investor's impatience can be found in Fisher [41, Chapter IV], Koopmans [75, p. 296] and Diamond et al. [34]. ...
We study the hedging and valuation of European and American claims on a non-traded asset $Y$, when a traded stock $S$ is available for hedging, with $S$ and $Y$ following correlated geometric Brownian motions. This is an incomplete market, often called a basis risk model. The market agent's risk preferences are modelled using a so-called forward performance process (forward utility), which is a time-decreasing utility of exponential type. Moreover, the market agent (investor) does not know with certainty the values of the asset price drifts. This market setting with drift parameter uncertainty is the partial information scenario. We discuss the stochastic control problem obtained by setting up the hedging portfolio and derive the optimal hedging strategy. Furthermore, a (dual) forward indifference price representation of the claim and its PDE are obtained. With these results, the residual risk process representing the basis risk (hedging error), pay-off decompositions and asymptotic expansions of the indifference price in the European case are derived. We develop the analogous stochastic control and stopping problem with an American claim and obtain the corresponding forward indifference price valuation formula.
... All postulates are concerned with only one ordering, namely that guiding decisions to be taken in the present." - Koopmans et al. (1964) Halevy (2015) has observed in a simplified setting 3 that any two of the three properties in Definition 1 implies the third. Inspection of the definitions shows that this observation holds in general. ...
Recent work on collective intertemporal choice suggests that non-dictatorial social preferences are generically time inconsistent. We argue that this claim conflates time consistency with two distinct properties of preferences: stationarity and time invariance. While time invariance and stationarity together imply time consistency, the converse does not hold. Although non-dictatorial social preferences cannot be stationary, they may be time consistent if time invariance is abandoned. If individuals are discounted utilitarians, revealed preference provides no guidance on whether social preferences should be time consistent or time invariant. Nevertheless, we argue that time invariant social preferences are often normatively and descriptively problematic.
... Translation Scale Invariance axiom in Asheim (2010) and , respectively. 11 Heal (2005, p. 1115) refers to (0 u) as the postponement of u. Koopmans et al. (1964) refer to (c u) as the postponement of u with "insertion" c. 12 That is, for each t, s t+1 − s t = u t+1 − v t+1 . ...
This paper presents an infinite-horizon version of intergenerational utilitarianism. By studying discounted utilitarianism as the discount factor tends to one, we obtain a new welfare criterion: limit-discounted utilitarianism (LDU). We show that LDU meets the standard assumptions of efficiency, equity, and interpersonal comparability, but allows us to compare more pairs of utility streams than commonly used utilitarian criteria, including the overtaking criterion and the catching-up criterion. We also introduce a principle of compensation for postponements of utility streams and use it to characterize the LDU criterion on a restricted domain.
... The classic contributions on the subject areKoopmans (1960),Koopmans et al. (1964) andDiamond (1965).2 Hammond equity has several variations which have been discussed in the literature. ...
Today enormous data storage capacities and computational power in the e-big data era have created unforeseen opportunities for big data hoarding corporations to reap hidden benefits from individuals' information sharing, which occurs bit by bit in small tranches over time. Behavioral economics describes human decision-making fallibility over time but has—to this day—not covered the problem of individuals' decision to share information about themselves in tranches on social media and big data administrators being able to reap a benefit from putting data together over time and reflecting the individual's information in relation to big data of others. The decision-making fallibility inherent in individuals having problems understanding the impact of their current information sharing in the future is introduced as hyper-hyperbolic discounting decision-making predicament.
This paper investigates fair (i.e., envy-free and efficient) allocations in an overlapping generations economy without production and with two-period lived agents. We show that there is a conflict between no-envy and efficiency when all generations have identical preferences. This conflict crucially depends on the size of the given young age consumption of the initial old generation relative to the young age consumption at the golden-rule. We then show that there exist non-stationary preferences for which such a conflict does not arise, regardless of the young age consumption of the initial old generation.
JEL Classifications: D60, D63, D70
We extend the standard Bellman's theory of dynamic programming and the theory of recursive contracts with forward-looking constraints of Marcet and Marimon (2019) to encompass non-differentiability of the value function associated with non-unique solutions or multipliers. The envelope theorem provides the link between the Bellman equation and the Euler equations, but it may fail to do so if the value function is non-differentiable. We introduce an envelope selection condition which restores this link. In standard single-agent dynamic programming, ignoring the envelope selection condition may result in inconsistent multipliers, but not in non-optimal outcomes. In recursive contracts it can result in inconsistent promises and non-optimal outcomes. Planner problems with recursive preferences are a special case of recursive contracts and, therefore, solutions can be dynamically inconsistent if they are not unique. A recursive method of solving dynamic optimization problems with non-differentiable value function involves expanding the co-state and imposing the envelope selection condition.
Today enormous data storage capacities and computational power in the e-big data era have created unforeseen opportunities for big data hoarding corporations to reap hidden benefits from individuals' information sharing, which occurs bit by bit in small tranches over time. Behavioral economics describes human decision-making fallibility over time but has—to this day—not covered the problem of individuals' decision to share information about themselves in tranches on social media and big data administrators being able to reap a benefit from putting data together over time and reflecting the individual's information in relation to big data of others. The decision-making fallibility inherent in individuals having problems understanding the impact of their current information sharing in the future is introduced as hyper-hyperbolic discounting decision-making predicament.
Discounting plays a central role in decisions about global environmental change that affect the well-being of future generations. Discounting the future more heavily tilts decisions toward the present, making it less likely that society will undertake actions to mitigate climate change or other global environmental change. This article reviews the standard economics approach to discounting that emerges from solving for optimal savings and investment through time. Discounting depends on the pure rate of time preference and differences in consumption levels across time, giving rise to different marginal utilities of consumption. Discounting for problems like climate change that impact future generations involves an ethical dimension. This article includes discussions of ethical dimensions of discounting related to intragenerational and intergenerational equity and also covers behavioral economics, ecological economics, and mainstream economics approaches to discounting. The article closes with a review of the debates over discounting in climate change policy.
Expected final online publication date for the Annual Review of Environment and Resources, Volume 46 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
We consider a model of intertemporal choice where time is a continuum, the set of instantaneous outcomes (e.g., consumption bundles) is a topological space, and intertemporal plans (e.g., consumption streams) must be continuous functions of time. We assume that the agent can form preferences over plans defined on open time intervals. We axiomatically characterize the intertemporal preferences that admit a representation via discounted utility integrals. In this representation, the utility function is continuous and unique up to positive affine transformations, and the discount structure is represented by a unique Riemann–Stieltjes integral plus a unique linear functional measuring the long-run asymptotic utility.
This book focuses on the economics of smart meters and is one of the first to present comprehensive evidence on the impacts, cost-benefits and risks associated with smart metering. Throughout this volume, Jacopo Torriti integrates his findings from institutional cost-benefit analyses and smart metering trials in a range of European countries with key economic and social concepts and policy insights derived from almost ten years of research in this area. He explores the extent to which the benefits of smart meters outweigh the cost, and poses key questions including: which energy savings can be expected from the roll out of smart meters in households? Is Cost-Benefit Analysis an appropriate economic tool for assessing the impacts of smart metering rollouts? Can smart meters play a significant role in research on people's activities and the timing of energy demand? Torriti concludes by providing a much-needed survey of recent changes and expected future developments in this growing field. This book will be of great interest to students and scholars of energy policy and demand and smart metering infrastructure.
Sustainability management has originally and—to this day—primarily been focused on environmental aspects. Today, enormous data storage capacities and computational power in the e-big data era have created unforeseen opportunities for big data hoarding corporations to reap hidden benefits from an individual's information sharing, which occurs bit by bit over time. This article presents a novel angle of sustainability, which is concerned with sensitive data protection given by the recently detected trade-off predicament between privacy and information sharing in the digital big data age. When individual decision makers face the privacy versus information sharing predicament in their corporate leadership, dignity and utility considerations could influence risk management and sustainability operations. Yet, to this day, there has not been a clear connection between dignity and utility of privacy and information sharing as risk management and sustainability drivers. The chapter unravels the legal foundations of dignity in privacy but also the behavioral economics of utility in communication and information sharing in order to draw a case of dignity and utility to be integrated into contemporary corporate governance, risk management and sustainability considerations of e-innovation.
Existing work has shown that ambiguity averse agents dislike positive autocorrelation in their consumption profile. Remarkably, the same prediction can be generated by expected-utility models with endogenous discounting if one makes the common assumption of increasing marginal impatience. This paper disentangles the intertemporal predictions of ambiguity aversion from those of endogenous discounting by identifying a form of autocorrelation that is disliked by ambiguity averse agents only. The analysis is supplemented by two representation theorems. The first delivers a novel axiomatization of endogenous discounting without restricting beliefs to be expected utility. Leveraging our analysis of ambiguity aversion, the second result delivers a maxmin representation of beliefs.
We consider convex dynamic programs with general (bounded) recursive utilities. The Contraction Mapping Theorem fails when the utility aggregator does not obey any discounting property. This failure occurs even with traditional aggregators and certainty equivalent specifications. However, the Bellman operator admits a unique fixed point when an interior policy is feasible. This happens because utility values are unique at interior consumption plans and, when an interior perturbation is feasible, drops in utility values can be avoided.
What ethical criterion for intergenerational justice should be adopted, e.g., when faced with the task of managing the global environment? Koopmans ’ axiomatization of discounted utilitarianism is based on seemingly compelling conditions, yet this criterion leads to hard-to-justify outcomes. The present analysis considers a class of sustainable recursive social welfare functions within Koopmans ’ general framework. This class is axiomatized by means of a weak equity condition (“Hammond Equity for the Future”) and general existence is established. Any member of the class satisfies the key axioms of Chichilnisky’s ’s “sustainable preferences”. The analysis singles out one of Koopmans’ original separability conditions (his Postulate \(3'\)a), here called “Independent Present”, as particularly questionable from an ethical perspective.
The history of the axiomatic approach to the ranking of infinite streams starts with Koopmans (1960) characterization of the discounted utilitarian rule. This rule, however, meets Chichilnisky’s axiom of dictatorship of the present and puts future generations offside. Recently, Lauwers (2010a) and Zame (2007) have uncovered the impossibility to combine in a constructible way the requirements of equal treatment, sensitivity, and completeness. This contribution presents and discusses different axioms proposed to guide the ranking of infinite streams and the criteria they imply. The literature covered in this overview definitely points towards a set of meaningful alternatives to discounted utilitarianism.
The importance of the correct choice of discount rate for social (or indeed individual) investments hardly needs elaboration. In the social context, the discount rate is, at least in part, an expression of concerns about equity between the present and future generations and among future generations. I say, in part, because it also expresses both an expectation of the rates of return available to future generations in alternative uses of capital and an expectation of the growth of income of the representative individual.
Impatience refers to the preference for earlier rather than later consumption an idea which stems from Böhm-Bawerk (1912) and Fisher (1930), among others. Preference orderings that exhibit impatience are also described as being myopic or as embodying discounting. Because in many contexts the future has no natural termination date, an infinite horizon framework is most appropriate and convenient for the analysis of many problems in intertemporal economics. The open-endedness of the future raises several issues surrounding impatience (its presence, degree, and the precise form it takes) which do not arise in finite horizon models.
Three facets of subjective preferences have played central roles in economics. They are the qualitative structure of an agent’s preferences, numerical representations of preferences, and the use of numerical representations or utility functions in economic analysis. We consider various representations and their ties to qualitative preference structures.
This paper examines the constructive nature of a social welfare order that respects Hammond equity axiom and Weak Pareto axiom. It describes the domains (of the one period utilities) on which an explicit construction is possible. A social welfare order satisfying the Hammond equity and Weak Pareto admits an explicit construction if and only if the domain is a well-ordered set.
Das Sprichwort „lieber der Spatz in der Hand als die Taube auf dem Dach“ bedeutet, dass es besser ist, sich mit dem zu begnügen, was man bekommen kann, als etwas Unsicheres anzustreben. Psychologisch betrachtet kommt es dabei auf zwei Aspekte an: die zeitliche Dimension und die Unsicherheit. Nach der Wert-Erwartungs-Theorie setzt sich die Handlungsmotivation daraus zusammen, welcher Wert einem Ereignis zugeschrieben und wie hoch die Wahrscheinlichkeit eingeschätzt wird, dass es eintritt. Da der subjektive Wert einer Belohnung abnimmt, je weiter sie in der Zukunft liegt bzw. je unsicherer sie ist, neigen Menschen in der Regel zu einer Gegenwartspräferenz. Da Verluste für Menschen schwerer wiegen als Gewinne, werden Risiken eher gescheut, um Verluste zu vermeiden. Neben diesen allgemeinen Phänomenen spielen auch die Persönlichkeit (z. B. Extraversion) und situative Faktoren (z. B. Macht) eine Rolle dabei, ob eher der kleine, sichere Gewinn gewählt wird oder der große, unsichere.
Although economists recognized long ago that “time enters into all economic questions,” as William Stanley Jevons wrote, the ways they treated and modeled time varied substantially in the last century. While in the 1920s there was a distinctive Cambridge tradition against discounting utilities of future generations, to which Frank Ramsey subscribed, postwar neoclassical growth economists (of the “Ramsey-Cass-Koopmans model”) applied the discount factor either to the individual's or the social planner's decision making as a technical requirement of dynamic general equilibrium models. My goal in this article is to analyze the different communities and their interpretative practices regarding discounting: the Cambridge economists in the 1920s, some American mathematicians in the 1920s and 1930s, a group of economists working on economic dynamics from the 1930s to the 1950s, the founders of the optimal growth model and those bringing recursive methods to macroeconomics in the 1950s and 1960s, and, finally, those who reacted against this utilitarian approach to social planning problems. With this I hope to shed some historical light on how a practice that was condemned as ethically indefensible when applied to intergenerational comparisons became a technical requirement in dynamic models of either a consumer or a planner deciding the intertemporal allocation of resources.
The problem of economic growth was a major preoccupation of Joan Robinson. She was a major contributor to the post-Keynesian theory of economic growth that followed the publication of Harrod’s seminal dynamic model. She wrote extensively and critically on the foundations of neoclassical growth theory; her concern for logically sound argument lay behind her extensive writings questioning the validity of an aggregate capital concept and the corresponding notion of an aggregate production function. Her critique of neoclassical theory placed her at the forefront of the still raging ‘Cambridge controversy’ in capital theory. Joan Robinson’s work on capital and growth also showed a real concern that economic dynamics be studied as a process in real time. The dynamics of the stationary state might be a useful starting point, but the more serious concerns were the relationship between the short- and long-run periods in the process of accumulation and growth. She also stressed the importance of understanding the evolution of economies outside equilibrium positions.
Three facets of subjective preferences have played central roles in economics. They are the qualitative structure of an agent’s preferences, numerical representations of preferences, and the use of numerical representations or utility functions in economic analysis. We consider various representations and their ties to qualitative preference structures.
Der Interessenkonflikt zwischen den Eigentümern und den Managern der Unternehmung ist Gegenstand einer beträchtlichen Literatur (siehe etwa Cyert/March 1963, Gordon 1964, Williamson 1970, Berhold 1971, Ross 1973, Jensen/Meckling 1976). Es wird angenommen, daß der Manager, der seinen eigenen Nutzen maximiert, nicht allein an den Gewinnen, sondern an gewissen unproduktiven, seinen Komfort steigernden Ausgaben, an aufgeblähten Mitarbeiterstäben und Slack im Budget interessiert ist. Die Literatur bildet mögliches Managerverhalten in deskriptiven Modellen nach und diskutiert die Eignung von Kontrollmechanismen und Anreizen zur Steuerung des Verhaltens.
Cost-benefit and risk analysis studies that model tradeoffs between the present and the distant future by means of present value discounting have been criticized for according the future, and thus future generations, far too little importance. This paper presents an alternative means of modeling tradeoffs between different periods that accords the future far more importance than present value discounting, and that is no more difficult to apply.
This study is dedicated to Professor Trout Rader whose influence on my choice of career and research program was profound. I wish to express my deep appreciation for his contributions as a researcher and teacher as well as my gratitude for his guidance and friendship over the past twenty-three years.
Impatience refers to the preference for earlier rather than later consumption, an idea which stems from Böhm–Bawerk (1912) and Fisher (1930), among others. Preference orderings that exhibit impatience are also described as being myopic or as embodying discounting. Because in many contexts the future has no natural termination date, an infinite horizon framework is most appropriate and convenient for the analysis of many problems in intertemporal economics. The open-endedness of the future raises several issues surrounding impatience (its presence, degree, and the precise form it takes) which do not arise in finite horizon models.
The main objective of this article is to describe the most important features of business cycles in Portugal during the period 1958-1989. We compare these features with the empirical regularities of economic fluctuations in other OECD countries and with the predictions of two benchmark dynamic general equilibrium models.
The theory of optimal intertemporal allocation has been developed primarily for the case in which the objective function of the planner or representative agent can be written as \(U(c1, c2\ldots) \equiv {{{\sum}^\infty}_{t=1}} {{\delta}^{t-1}}w(c_{t})\) where c
t represents consumption at date t, w the period felicity function, and \(\delta\,\,\epsilon\) (o,1) a discount factor, representing the time preference of the agent.KeywordsUtility FunctionEuler EquationDiscount FactorCharacteristic RootOptimal ProgramThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
: Previous treatments of this approach brought topological considerations of the prospects space into the axioms. In this paper considerations of the topology of the prospect space itself are removed, the previous axioms are weakened an infinite number of sure prospects are allowed. On the basis of these axioms the existence of a measurable utility is established.
The impatience implications of several axiom sets assumed for preferences over an infinite future are explored. Sufficient conditions for the existence of a continuous utility function are presented. This analysis is done both for the product topology and the metric function equating the distance between two infinite streams to the maximal one-period difference between them.
Subjective Programming
- R J Aumann
AUMANN, R. J.: "Subjective Programming," to be published in Bryan and Shelly, eds. Human Judgments and Optimality, Wiley, New York, 1964.
Stationary Ordinal Utility and Impatience Econometrica Essays in Honor of Ragnar Frisch
- T C Koopmans
KOOPMANS, T. C.: "Stationary Ordinal Utility and Impatience," Econometrica Essays in Honor of Ragnar Frisch, Econometrica, April, 1960, pp. 287-309.
MORGENSTERN: Theory of Games and Economic Behavior Section 3 and appendix on "The Axiomatic Treatment of Utility
- Von Neumann
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VON NEUMANN, J., AND 0. MORGENSTERN: Theory of Games and Economic Behavior, Princeton University Press, 1947, Chapter 9, Section 3 and appendix on "The Axiomatic Treatment of Utility."
Measure Theory, van Nostrand
- P R Halmos
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