Impatience implication of weakly Paretian orders: Existence and genericity

We study order theoretic and topological implications for impatience of weakly Paretian, representable orders on infinite utility streams. As a departure from the traditional literature, we do not make any continuity assumptions in proving the existence of impatient points. Impatience is robust in the sense that there are uncountably many impatient points. A general statement about genericity of impatience cannot be made for representable, weakly Paretian orders. This is shown by means of an example. If we assume a stronger sensitivity condition, then genericity obtains.     

Dense families of low-complexity attainable sets of markets

The complexity of the attainable set of utility outcomes of a market (with finitely many traders) is defined as the least number of commodities involved in any market giving the same set. This notion is investigated both for the case of quasiconcave and concave utility functions. It is shown that, in either case, there is a dense collection of attainable sets, each having complexity at most n(n?1)/2.     

The Ideal Inflation‐Indexed Bond and Irving Fisher's Impatience Theory of Interest with Overlapping Generations*

Abstract Irving Fisher long advocated inflation‐indexed bonds. But with what index? I prove in the context of a multicommodity CAPM world that the best welfare‐improving bond pays the minimum money needed to achieve the same utility, and not the minimum needed to buy an ideal commodity bundle. Irving Fisher also developed and advocated the impatience theory of interest. But in OLG economies, the rate of interest is determined by population growth, not impatience. I reconcile this contradiction by proving that in stationary OLG economies with land, the interest rate at the unique steady state does depend on impatience. Indeed, the proposition that greater impatience creates higher interest rates holds more generally in OLG with land than in Fisher's two‐period model, because then income effects and substitution effects naturally work in the same direction.     

Some results on the existence of utility functions on path connected spaces

This paper concerns the existence of utility representations for preferences defined on a path connected space X. This includes any convex set. A classical result of Eilenberg (1941) proves the existence of utility representations when the consumption set is connected and separable. In an infinite dimensional space the above result may not be useful, because we lack, in general, the separability of the space. The non-separable spaces L^∞ and ca(K) are typical examples in mathematical economics. In this paper we show that a continuous preference relation ≽, on X has a continuous utility representation if and only if it is countably bounded, i.e., there is some countable subset F of X such that for all x in X there exist y and z in F with y≽x≽z. An easy corollary states that any continuous preference which has a best and a worst point has a continuous representation. We also obtain a convex continuous preference on a Banach lattice that has not a utility representation, because it is not countably bounded.     

Equilibria in a class of aggregative location games

Consider a multimarket oligopoly, where firms have a single license that allows them to supply exactly one market out of a given set of markets. How does the restriction to supply only one market influence the existence of equilibria in the game? To answer this question, we study a general class of aggregative location games where a strategy of a player is to choose simultaneously both a location out of a finite set and a non-negative quantity out of a compact interval. The utility of each player is assumed to depend solely on the chosen location, the chosen quantity, and the aggregated quantity of all other players on the chosen location. We show that each game in this class possesses a pure Nash equilibrium whenever the players’ utility functions satisfy the assumptions negative externality, decreasing marginal utility, continuity, and Location–Symmetry. We also provide examples exhibiting that, if one of the assumptions is violated, a pure Nash equilibrium may fail to exist.     

Generalized time-invariant overtaking

We present a new version of the overtaking criterion, which we call generalized time-invariant overtaking. The generalized time-invariant overtaking criterion (on the space of infinite utility streams) is defined by extending proliferating sequences of complete and transitive binary relations defined on finite dimensional spaces. The paper presents a general approach that can be specialized to at least two, extensively researched examples, the utilitarian and the leximin orderings on a finite dimensional Euclidean space.     

Smooth preferences and the regularity of equilibria

To study equilibria we describe an economy by its distribution of consumers' preferences and endowments. All preferences are smooth and weakly convex. Demand of an economy need not be single valued, but there is an open dense set of economies for which demand is a C¹-function in a neighborhood of the equilibrium prices. We call an economy regular if its excess demand is transversal to zero. A regular economy has locally unique equilibria. It is shown that regular economies form an open dense set on which the equilibrium price correspondence varies continuously and the number of equilibria is locally constant.     

A characterization and an impossibility of finite length anonymity for infinite generations

In the context of ranking infinite utility streams, the impartiality axiom of finite length anonymity requires the equal ranking of any two utility streams that are equal up to a finite length permutation ( Fleurbaey and Michel, 2003). We first characterize any finite length permutation as a composition of a fixed step permutation and an “almost” fixed step permutation. We then show that if a binary relation satisfies finite length anonymity, then it violates all the distributional axioms that are based on a segment-wise comparison. Examples of those axioms include the weak Pareto principle and the weak Pigou-Dalton principle.     

Generic properties of simple Bergson-Samuelson welfare functions

Methods of transversality theory are introduced to determine the generic properties of a simple non-collegial preference function σ, whose domain is the class of ordinal utility profiles on a smooth manifold W of policy alternatives. When the dimension of W is sufficiently large, it is shown that (i) the set of local optima of σ is generically empty, and (ii) the local cycle set of σ is generically dense.     

RISE OF THE FIDUCIARY STATE: A SURVEY OF SOVEREIGN WEALTH FUND RESEARCH

We survey the literature documenting the rise of sovereign wealth funds (SWFs), which, with assets under management of over $5.4 trillion at year‐end 2014, are a major force in global finance. Research papers have analyzed the evolution of SWFs from stabilization funds to stand‐alone wealth management funds; we both survey this research and show that more than 25 countries have launched or proposed new SWFs since January 2008. The most salient and controversial feature of SWFs is that they are state‐owned; we survey the existing literature on state ownership and discuss what this predicts about the efficiency and beneficence of government control of SWF assets. We discuss the documented importance of SWF funding sources (oil sales revenues versus excess reserves from export earnings) and survey the normative literature describing how SWFs should allocate funds. We then summarize the empirical literature studying how SWFs actually do allocate funds—across asset classes, geographically, and across industries. We document that most SWF equity investments in publicly traded firms involve cross‐border purchases of sizeable minority stakes (median around 20%) in target firms, with a strong preference for investments in the financial sector. Next, we assess empirical studies examining the impact of SWF stock investments on target firm financial and operating performance, and find universal support for a positive announcement period stock price increase of 1–3%. This, however, is significantly lower than the 5% abnormal return documented for stock purchases by comparable privately owned financial investors in recent studies, indicating a “sovereign wealth fund discount.” We conclude by summarizing the lessons of SWF research and pointing out unresolved issues.     

Inequality and catching-up under decreasing marginal impatience

This paper examines how endogenous time preference interacts with inequalities in economic development. We consider two distinct groups of households with intrinsic inequality (e.g., capitalists and workers), and show that (i) under decreasing marginal impatience (DMI), an unequal society may be preferable for poor households than an egalitarian one in which every household owns an equal share of asset; (ii) poor households tend to benefit more under DMI than CMI (constant marginal impatience) from positive shocks; (iii) inequality exhibits a sharp inverted-U shape as more people become rich, which should be good news for developing countries in catching up; and (iv) a tax on capital income reduces poor households’ income when the fraction of the rich is sufficiently small. We also examine immigration and discuss capital mobility.     

On continuous utility functions derived from demand functions

In the theory of revealed preference and in the approach to integrability theory of Hurwicz and Uzawa certain conditions are proposed implying the existence of a utility function generating the given demand function. This article presents a hypothesis which, under supposition of some well-known axioms of those models, is necessary and sufficient for the existence of a continuous utility function. This hypothesis implies the existence of a utility function u with the property that all of the boundary points of the set $\text{{x|u(x)≧α}}$ for every $\text{α?}\text{R}$ are lower boundary points, being fundamental for the continuity of the utility function.     

Continuous mean demand functions derived from non-convex preferences

In this paper we show that for a large subset of utility functions in the space of all C¹ utility functions and for all prices the mean demand of those consumers whose taste is represented by a given utility function in that subset is uniquely determined. This implies that for a large set of economies mean demand is a continuous function. Our analysis uses derivatives of first and of higher order. The result is essentially a consequence of the multijet transversality theorem.     

The structure of decision schemes with cardinal preferences

This paper replacesGibbard’s (Econometrica 45:665-681, 1977) assumption of strict ordinal preferences by themore natural assumption of cardinal preferences on the set pure social alternatives and we also admit indifferences among the alternatives. By following a similar line of reasoning to the Gibbard-Satterthwaite theoremin the deterministic framework, we first show that if a decision scheme satisfies strategy proofness and unanimity, then there is an underlying probabilistic neutrality result which generates an additive coalitional power function. This result is then used to prove that a decision scheme which satisfies strategy proofness and unanimity can be represented as a weak random dictatorship. A weak random dictatorship assigns each individual a chance to be a weak dictator. An individual has weak dictatorial power if the support of the social choice lottery is always a subset of his/her maximal utility set. In contrast to Gibbard’s complete characterization of randomdictatorship, we also demonstrate with an example that strategy proofness and unanimity are sufficient but not necessary conditions for a weak random dictatorship.     

Universal Pareto dominance and welfare for plausible utility functions

We study Pareto efficiency in a setting that involves two kinds of uncertainty: Uncertainty over the possible outcomes is modeled using lotteries whereas uncertainty over the agents’ preferences over lotteries is modeled using sets of plausible utility functions. A lottery is universally Pareto undominated if there is no other lottery that Pareto dominates it for all plausible utility functions. We show that, under fairly general conditions, a lottery is universally Pareto undominated iff it is Pareto efficient for some vector of plausible utility functions, which in turn is equivalent to affine welfare maximization for this vector. In contrast to previous work on linear utility functions, we use the significantly more general framework of skew-symmetric bilinear (SSB) utility functions as introduced by Fishburn (1982). Our main theorem generalizes a theorem by Carroll (2010) and implies the ordinal efficiency welfare theorem. We discuss three natural classes of plausible utility functions, which lead to three notions of ordinal efficiency, including stochastic dominance efficiency, and conclude with a detailed investigation of the geometric and computational properties of these notions.     

Are CEOs expected utility maximizers?

Are individuals expected utility maximizers? This question represents much more than academic curiosity. In a normative sense, at stake are the fundamental underpinnings of the bulk of the last half-century’s models of choice under uncertainty. From a positive perspective, the ubiquitous use of benefit-cost analysis across government agencies renders the expected utility maximization paradigm literally the only game in town. In this study, we advance the literature by exploring CEO’s preferences over small probability, high loss lotteries. Using undergraduate students as our experimental control group, we find that both our CEO and student subject pools exhibit frequent and large departures from expected utility theory. In addition, as the extreme payoffs become more likely CEOs exhibit greater aversion to risk. Our results suggest that use of the expected utility paradigm in decision making substantially underestimates society’s willingness to pay to reduce risk in small probability, high loss events.     

Time Schedule and Program Profile: TV News in Norway and Denmark

Two TV channels compete on programming with respect to both time schedule (continuous choice) and program profile (discrete choice), with a directional constraint concerning time schedule (viewers cannot watch TV before they get home). We show how the relative importance of program profile and time schedule, as perceived by the viewers, determines the equilibrium outcome. Furthermore, we find that there is a first-mover disadvantage in a sequential game where one channel sets its two choice variables before its rival does, and a first-mover advantage in a semise-quential game where the channels set time schedules sequentially and thereafter set program profiles simultaneously. The results are applied to the Norwegian and Danish markets for TV news, where number-two channels have challenged the incumbents.     

Revealed preference theory on the choice of lotteries

The choice behavior of a decision-maker is said to be consistent with expected utility maximization if there exists a utility function defined on the set of prizes such that the decision-maker chooses lotteries with the highest expected utility. We present a revealed preference characterization of choice behavior that is consistent with expected utility maximization. A necessary and sufficient condition for expected utility maximization is that there does not exist a way to compound lotteries such that the probability distribution over the final prizes generated by the chosen lotteries of each observation is equal to that generated by the rejected lotteries of each observation. Our result is quite general and can be applied to any compact set of prizes and any choice correspondence.