Matrices with dominant diagonal blocks and economic theory

In this paper we shall define matrices with quasi-strictly-dominant diagonal blocks or quasi-dominant diagonal blocks on the basis of general matrix norms including the spectral norm. Several theorems on such matrices are derived and a simple numerical example and economic models are considered to apply our theorems.     

经济学中一般均衡存在性问题理论述评

本文对经济学中一般均衡理论进行了概述。文中主要介绍了Arrow—Debreu经济模型、均衡存在性定理、存在性涸题在无穷维商品空间上的扩展以及相关工作。     

Constructive and computable Hahn–Banach theorems for the (second) fundamental theorem of welfare economics

The Hahn–Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using non-constructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn–Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented economics intrinsically computational.     

A theory of time preferences over risky outcomes

This paper provides two representation theorems for time preferences. They both cover as special cases a variety of time preference models considered in the experimental and theoretical literatures on intertemporal choice. In particular, similarity relations on time and outcomes, exponential, quasi-hyperbolic and hyperbolic discounting are special cases of the theorems. This approach identifies certain factors that are common to time preference structures which look so different.The paper builds on the recent work by Masatlioglu and Ok [Masatlioglu, Y., Ok, E., 2008. A theory of (relative) discounting. Journal of Economic Theory, in press] on Euclidean bundles and obtains similar representation theorems for the case of compact, separable and connected spaces of bundles. My work allows for the inclusion of the case in which bundles are lotteries.     

Characterization of stationary preferences in a continuous time framework

We characterize preference relations on continuous time consumption paths which admit an exponential discounting representation. We provide two theorems as such, one in the cardinal framework and another in the ordinal framework. Our characterizations parallel the known characterizations in discrete time framework. In the cardinal framework, we adopt the axioms of Epstein (1983), which characterize a stationary preference relation in discrete time, and obtain the exponential discounting model as a special case of the discounting model proposed by Uzawa (1968). In the ordinal framework, we adopt the axioms of Bleichrodt et al. (2008) which were proposed to generalize Koopmans’ classical characterization of stationary preferences.     

Retailer’s Optimal Cycle Times in the EOQ Model with Imperfect Quality and a Permissible Credit Period

This paper modifies two assumptions of the classical EOQ model to reflect the real-life situations. First, the classical EOQ model assumes that all units produced or purchased are of good quality. Second, the payment of an order is made on the receipt of items by the inventory system. So, we incorporate both Goyal [Journal of the Operational Research Society 36: 335–338 (1985)] and Salameh and Jaber [International Journal of Production Economics 64: 59–64 (2000)] to develop a production/inventory model of the retailer to allow items with imperfect quality under permissible delay in payments. In addition, the objective function is modeled as an expected total annual profit maximization problem. Then, two theorems are developed to efficiently determine the optimal cycle time and the optimal order quantity for the retailer. Numerical examples are given to illustrate these theorems. Finally, we deduce some previously published results of other researchers as special cases.     

Implementation of solutions to the problem of fair division when preferences are single-peaked

We consider the problem of fairly allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. We address the issue of (Nash)-implementability of solutions to this problem. As the lack of monotonicity of preferences often causes solutions to violate no veto power, the classic Maskin-type theorems cannot be invoked. Instead, we show that more powerful theorems due to Danilov-Yamato and Sjöström can help settle implementation questions for most of the central fairness concepts, generally in the positive.     

On two market equilibrium theorems

Two theorems are presented which have as corollaries known market equilibrium theorems. The first theorem is for correspondences defined on sets which are compact and convex and the second theorem is for correspondences defined on the unit sphere. The proofs of both theorems rely upon one lemma.     

Coalitional manipulations in a bankruptcy problem

In a bankruptcy problem framework we consider rules immune to possible manipulations by the creditors involved in the problem via merging or splitting of their individual claims. The paper provides characterization theorems for the non manipulable rules, the no advantageous merging parametric rules and the no advantageous splitting parametric rules. Received: 24 February 1998 / accepted: 9 March 1999     

Alternative housing concepts and the benefits of public housing programs

Almost all previous studies analyzing the benefits and consumption effects of public housing programs have used aggregation theorems to construct composite goods “housing” and “all other goods.” In this paper we show that, if it is more realistically assumed that households have preferences defined on housing characteristics, benefits estimated using the composite approach are upward biased. Some empirical work suggests that the bias is large. We therefore strongly advise to take into account the composition of the bundle of housing attributes provided under a public housing program when evaluating the program's economic effects.     

关于逆函数的性质与定理

本文给出了逆函数的定义,介绍了它的性质,并证明了关于逆函数的几个定理。     

Arbitrage concepts under trading restrictions in discrete-time financial markets

In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker than classical absence of arbitrage opportunities. We center our analysis on this characterization of market viability and derive versions of the fundamental theorems of asset pricing based on portfolio optimization arguments. By considering specifically a discrete-time setup, we simplify existing results and proofs that rely on semimartingale theory, thus allowing for a clear understanding of the foundational economic concepts involved. We exemplify these concepts, as well as some unexpected situations, in the context of one-period factor models with arbitrage opportunities under borrowing constraints.     

IEEE 802.11s and the Philosophers' problem

IEEE 802.11s is the task group in the IEEE that is in the process of standardizing wireless mesh networks. A hot topic in this standardization effort concerns the need for additional medium access functionality beyond the basic IEEE 802.11 carrier sense multiple access with collision avoidance (CSMA/CA). In this paper, we discuss the connection between CSMA/CA and Dijkstra's classical Philosophers' problem, and its implications for the debate inside IEEE 802.11s. In an alternative view of this paper, we state some new mathematical models, theorems and conjectures related to the Philosophers' problem.     

Measuring the set of blocking coalitions in infinite dimensional economies

The classical core-Walras equivalence is investigated via the measurement of the set of blocking coalitions. In the framework of continuum economies with an infinite dimensional space of commodities, we find the measure of the set of coalitions that block a non-competitive Pareto optimal allocation. Then, from the relation between coalitions of a continuum economy with a finite number of types and fuzzy coalitions of an economy with finitely many agents, the previous results are translated as results on the measure of blocking fuzzy coalitions. Both results imply classically formulated core-Walras equivalence theorems. Finally, the measure of blocking "social communication structures" is determined.     

Entropy concentration and the empirical coding game

We give a characterization of maximum entropy/minimum relative entropy inference by providing two 'strong entropy concentration' theorems. These theorems unify and generalize Jaynes'concentration phenomenon' and Van Campenhout and Cover's 'conditional limit theorem'. The theorems characterize exactly in what sense a prior distribution Q conditioned on a given constraint and the distribution      minimizing D(P  ‖  Q ) over all P satisfying the constraint are 'close' to each other. We then apply our theorems to establish the relationship between entropy concentration and a game-theoretic characterization of maximum entropy inference of Topsøe and others.     

Monotone evolution of resource allocations

We prove several existence theorems for solutions of multivalued differential equations whose trajectories (a) remain in a subset defined by scarcity constraints, and (b) are monotone with respect to a preordering; we give applications to the problem of allocation of scarce resources.     

A Critical Review of Homo Economicus from Five Approaches

Neoclassical economics is based on and structured around the notion of homo economicus. The theory of consumer choice, the theory of the firm, industrial organization, and welfare theorems all require the assumption that agents act in accordance with the scheme of individualistic rational optimization. In this context, our contribution is threefold. First, we delimit the notion of homo economicus according to five characteristics or dimensions. Second, we critically review this anthropological scheme from five distinct approaches, namely, behavioral economics, institutional economics, political economy, economic anthropology, and ecological economics. Third, we conclude that the scheme of homo economicus is clearly inadequate and deficient. However, despite its inadequacies, it remains one of the fundamental pillars of the neoclassical paradigm in economics, which allows us to discuss why we have not yet overcome this paradigm.     

Asymptotics for Autocovariances and Integrated Periodograms for Linear Processes Observed at Lower Frequencies

One of the most frequently used class of processes in time series analysis is the one of linear processes. For many statistical quantities, among them sample autocovariances and sample autocorrelations, central limit theorems are available in the literature. We investigate classical linear processes under a nonstandard observation pattern; namely, we assume that we are only able to observe the linear process at a lower frequency. It is shown that such observation pattern destroys the linear structure of the observations and leads to substantially different asymptotic results for standard statistical quantities. Central limit theorems are given for sample autocovariances and sample autocorrelations as well as more general integrated periodograms and ratio statistics. Moreover, for specific autoregressive processes, the possibilities to estimate the parameters of the underlying autoregression from lower frequency observations are addressed. Finally, we suggest for autoregressions of order 2 a valid bootstrap procedure. A small simulation study demonstrates the performance of the bootstrap proposal for finite sample size.     

比喻在电路定理中的应用

电路定理是电路理论的重要组成部分。采用行之有效的教学方法帮助学生理解定理内容,是我们迫切要解决的问题。比喻教学法就是一种很好的教学方法。本文以电路中比较常用的三个定理为例,说明比喻在电路定理中的应用。     

Returns to Scale and Scale Elasticity in Farrell,Russell and Additive Models

This research extends the Farrell-based returns to scale methodology into Russell and Additive models in three ways with the focus of relationships between interior points and projected points. First, we present and prove four theorems that identify the scale nature. Second, we compare these results with the scale elasticity results. Third, we present techniques for estimating upper and lower bounds for the scale elasticities.