The Balassa–Samuelson effect in Romania – The role of regulated prices

Due to the Balassa–Samuelson effect, the candidate countries to the European Monetary Union face a possible conflict between the effects of tradable productivity increase on inflation and on the appreciation of the real exchange rate on one hand, and the Maastricht criteria regarding inflation and exchange rate stability on the other hand. A restrictive monetary policy could succeed in reaching inflation criteria, but only with the cost of slowing down real convergence. This paper deals with the Balassa–Samuelson effect in Romania. The main conclusion of the paper is that in the period 1998–2006 the average annual rate of inflation generated by the Balassa–Samuelson effect in Romania was on average 0.6% in the case of the classical model. Due to the existence of government-regulated prices (mostly non-tradable goods) accounting for as much as 21% of the CPI basket in Romania – the price of non-tradables has increased by less than in the case those prices were market prices. If we include these regulated prices in non-tradable, which is named by us extended model, the impact of Balassa–Samuelson on inflation could have been on average 2.46%. Therefore, the Balassa–Samuelson effect is expected to result into higher inflation with future price liberalization for non-tradables.     

An algorithm for the classical spatial price equilibrium problem

This paper proposes an algorithm for the solution of the classical Samuelson and Takayama and Judge model of spatial price equilibrium. Computational comparisons on randomly generated numerical examples suggest that this method is substantially more efficient and accurate and, at the same time, requires no more computer storage than an earlier algorithm.     

The incompatibility of individualism and ordinalism

A formal proof is offered of the fact that Individualism and Ordinalism imply the controversial condition A3 used by Kemp and Ng (1976) to show the non-existence of an individualistic social welfare function based only on ordinal preferences but objected to by Samuelson (1977) as unreasonable. Mayston's argument against our definition of ordinality is refuted; his notion of ‘true ordinality’ involves elements of cardinality and/or goes against individualism.     

均值-方差期望效用函数下的风险共担

借助Samuelson提出的风险汇合(Risk Adding)与风险分担(Risk Pooling)的概念,讨论了风险共担(Risk Sharing)机制产生的原理.在均值-方差效用函数下,给出了帕累托有效风险共担原则的具体形式,以及风险共担群体接纳新的个体,从而形成更大风险共担群体的条件.在此基础上,证明在均值-方差期望效用函数下,当考虑风险共担群体的形成条件以后,帕累托有效的风险共担原则等价于条件期望风险分配函数.从而在这一特殊效用函数下,建立了风险共担与风险分配函数之间的等价关系.     

The LeChatelier principle in a DEA model

This paper aims to relate the LeChatelier principle, first introduced into economics by Samuelson (1947), with the DEA approach through two propositions. These propositions allow for bridging the principle over a DEA model with and without the presence of non-discretionary inputs and enable one to make comparisons for the various efficiency measures under different conditions. The quasi-fixity of some inputs hinders a firm’s capacity from instantly and freely adjusting its input combination in order to minimize its production costs. The assumption that all inputs are discretionary tends to exaggerate managers’ ability to dispense resources and renders invalid information on the adjustment of the current input mix.     

The pricing of derivatives on assets with quadratic volatility

The basic model of financial economics is the Samuelson model of geometric Brownian motion because of the celebrated Black-Scholes formula for pricing the call option. The asset's volatility is a linear function of the asset value and the model guarantees positive asset prices. In this paper, it is shown that the pricing partial differential equation can be solved for level-dependent volatility which is a quadratic polynomial. If zero is attainable, both absorption and negative asset values are possible. Explicit formulae are derived for the call option: a generalization of the Black-Scholes formula for an asset whose volatiliy is affine, the formula for the Bachelier model with constant volatility, and new formulae in the case of quadratic volatility. The implied Black-Scholes volatilities of the Bachelier and the affine model are frowns, the quadratic specifications imply smiles.     

A Learning Place Called Earlham

Abstract

A Canticle for Leibowitz by Walter M. Miller, Jr. New York: Bantam Books, 313 pages, $2.25

The Science Fiction Stories of Walter M. Miller, Jr., with introduction by David Samuelson. Boston: Gregg Press, 374 pages, $15.     

Bi-f-harmonic map equations on singly warped product manifolds

Bi-f-harmonic maps are the critical points of bi-f-energy functional. This class of maps tends to integrate bi-harmonic maps and f-harmonic maps. In this paper, we show that bi-f-harmonic maps are not only an extension of f-harmonic maps but also an extension of bi-harmonic maps, and that there should exist many examples of proper bi-f-harmonic maps.In order to find some concrete examples of proper bi-f-harmonic maps, we study the basic properties of bi-f-harmonic maps from two directions which are conformal maps between the same dimensional manifolds and some special maps from or into a warped product manifold.     

On variable discounting in dynamic programming: applications to resource extraction and other economic models

This paper generalizes the classical discounted utility model introduced in Samuelson (Rev. Econ. Stud. 4:155–161, 1937) by replacing a constant discount rate with a function. The existence of recursive utilities and their constructions are based on Matkowski’s extension of the Banach Contraction Principle. The derived utilities go beyond the class of recursive utilities studied in the literature and enable a discussion on subtle issues concerning time preferences in the theory of finance, economics or psychology. Moreover, our main results are applied to the theory of optimal economic growth related with resource extraction models with unbounded utility function of consumption.     

The economics of forestry and a set-valued turnpike of the classical type

In recent work, the authors set classical turnpike theory in the context of the economics of forestry, as developed by Mitra and Wan, and presented two far-reaching results. In this paper, we present a conceptual generalization that takes this theory and configures it around a set in the space of forest configurations rather than around the golden-rule forest configuration. Our set-valued analysis hinges on periodicity and yields the earlier results as corollaries under a non-interiority condition on the felicity function that shrinks the set to the point. The question that we pose, and answer, has obvious relevance to more general contexts and, in particular, to turnpike theory as developed by Samuelson, Gale, McKenzie, and their followers.     

New bijective links on planar maps via orientations

This article presents new bijections on planar maps. At first a bijection is established between bipolar orientations on planar maps and specific “transversal structures” on triangulations of the 4-gon with no separating 3-cycle, which are called irreducible triangulations. This bijection specializes to a bijection between rooted non-separable maps and rooted irreducible triangulations. This yields in turn a bijection between rooted loopless maps and rooted triangulations, based on the observation that loopless maps and triangulations are decomposed in a similar way into components that are respectively non-separable maps and irreducible triangulations. This gives another bijective proof (after Wormald’s construction published in 1980) of the fact that rooted loopless maps with n edges are equinumerous to rooted triangulations with n inner vertices.     

Transversal wave maps and transversal exponential wave maps

Transversal wave maps and wave maps are different. There are wave maps which are not transversal wave maps, and vice versa. However, if f is a wave map under certain circumstance, then f is a transversal wave map. We show that if f is a transversal exponential wave map, then the associated energy–momentum is transversally conserved. We finally obtain the relationship among transversal wave maps, transversal exponential wave maps and certain second order symmetric tensors.     

关于三商映射

三商映射是完备映射和开映射的共同推广。本文综述三商映射的理论，论术这三商映射，开映射，紧覆盖映射，诱导完备映之间的一些转换关系，提出了几个供进一步研究的问题。     

C-bifurcations and period-adding in one-dimensional piecewise-smooth maps

This paper examines the behaviour of piecewise-smooth, continuous, one-dimensional maps that have been derived in the literature as normal forms for grazing and sliding bifurcations. These maps are linear for negative values of the parameter and non-linear for positive values of the parameter. Both C¹ and C² maps of this form are considered. These maps display both period-adding and period-doubling behaviour. For maps with a squared or 3/2 term the stability and existence conditions of fixed points and period-2 orbits in the vicinity of the border-collision are found analytically. These agree with the Feigin classification proposed by di Bernardo et al. [Chaos Solitons and Fractals 10 (1999) 1881]. The period-adding behaviour is examined in these maps, where analytical solutions for the boundaries of periodic solutions are found. Implicit equations for the boundaries of periodic windows for varying power term are also found and plotted. Thus, it is proved that period-adding scenarios are generic in maps of this form.     

THE GAUSS MAP OF TIMELIKE SURFACES IN R_1~n

ＴＨＥＧＡＵＳＳＭＡＰＯＦＴＩＭＥＬＩＫＥＳＵＲＦＡＣＥＳＩＮＲ_１~ｎ￥ＨＯＮＧＪＩＡＮＱＩＡＯＡｂｓｔｒａｃｔ：Ｇａｕｓｓｍａｐｓｏｆｏｒｉｅｎｔｅｄｔｉｍｅｌｉｋｅ２－ｓｕｒｆａｃｅｓｉｎａｒｅｃｈａｒａｃｔｅｒｉｚｅｄ，ａｎｄｉｔｉｓｓｈｏｗｎ...     

Banach空间中多类1-集-压缩映象的逼近定理和不动点定理

本文证明了 Ｋｙ Ｆａｎ定理［１］对定义在 Ｂａｎａｃｈ空间中含有内点的有界闭凸子集上的１－集－压缩映象正确．１－集－压缩映象类包含凝聚映象、非扩张映象、半压缩映象、局部几乎非扩张映象和其它映象．作为定理的应用,得到了一些非自映象在许多众知边界条件下的不动点定理,改进和推广了许多作者的最近结果．     

Regular combinatorial maps

The classical approach to maps is by cell decomposition of a surface. A combinatorial map is a graph-theoretic generalization of a map on a surface. Besides maps on orientable and non-orientable surfaces, combinatorial maps include tessellations, hypermaps, higher dimensional analogues of maps, and certain toroidal complexes of Coxeter, Shephard, and Grünbaum. In a previous paper the incidence structure, diagram, and underlying topological space of a combinatorial map were investigated. This paper treats highly symmetric combinatorial maps. With regularity defined in terms of the automorphism group, necessary and sufficient conditions for a combinatorial map to be regular are given both graph- and group-theoretically. A classification of regular combinatorial maps on closed simply connected manifolds generalizes the well-known classification of metrically regular polytopes. On any closed manifold with nonzero Euler characteristic there are at most finitely many regular combinatorial maps. However, it is shown that, for nearly any diagram D, there are infinitely many regular combinatorial maps with diagram D. A necessary and sufficient condition for the regularity of rank 3 combinatorial maps is given in terms of Coxeter groups. This condition reveals the difficulty in classifying the regular maps on surfaces. In light of this difficulty an algorithm for generating a large class of regular combinatorial maps that are obtained as cyclic coverings of a given regular combinatorial map is given.     

Biharmonic Maps from Tori into a 2-Sphere

Biharmonic maps are generalizations of harmonic maps. A well-known result on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere(whatever the metrics chosen) in the homotopy class of maps of Brower degree±1. It would be interesting to know if there exists any biharmonic map in that homotopy class of maps. The authors obtain some classifications on biharmonic maps from a torus into a sphere, where the torus is provided with a flat or a class of non-flat metrics whilst the sphere is provided with the standard metric. The results in this paper show that there exists no proper biharmonic maps of degree±1 in a large family of maps from a torus into a sphere.     

Natural congruences and isomorphism theorems for directed complete partially ordered sets

Directed complete partially ordered sets (dcpos, for short) play an important role in domain theory. The aim of this paper is to characterise natural congruences of dcpos. We also show that the kernels of dcpo maps, that is, directed join-preserving maps between dcpos are not necessarily natural dcpo congruences. Then we characterise dcpo maps whose kernels are natural dcpo congruences. Finally, we prove the Decomposition and Isomorphism Theorems for dcpo maps.