Local concavifiability of preferences and determinacy of equilibrium

In this paper we consider strictly convex monotone continuous complete preorderings on R+n that are locally representable by a concave utility function. By Alexandroff 's (1939) theorem, this function is twice dífferentiable almost everywhere. We show that if the bordered hessian determinant of a concave utility representation vanishes on a null set. Then demand is countably rectifiable, that is, except for a null set of bundles, it is a countable union of c1 manifolds. This property of consumer demand is enough to guarantee that the equilibrium prices of apure exchange economy will be locally unique, for almost every endowment. We give an example of an economy satisfying these conditions but not the Katzner (1968) - Debreu (1970, 1972) smoothness conditions.

Az egyensúlyi ráták unicitása és a bérráta pozitivitása a Neumann-modell általánosításaiban (Uniqueness of equilibrium rates and the positive value of the wage rate in generalizations from the Neumann model)

Cikkünk arról a paradox jelenségről szól, hogy a fogyasztást explicit módon megjelenítő Neumann-modell egyensúlyi megoldásaiban a munkabért meghatározó létszükségleti termékek ára esetenként nulla lehet, és emiatt a reálbér egyensúlyi értéke is nulla lesz. Ez a jelenség mindig bekövetkezik az olyan dekomponálható gazdaságok esetén, amelyekben eltérő növekedési és profitrátájú, alternatív egyensúlyi megoldások léteznek. A jelenség sokkal áttekinthetőbb formában tárgyalható a modell Leontief-eljárásra épülő egyszerűbb változatában is, amit ki is használunk. Megmutatjuk, hogy a legnagyobbnál alacsonyabb szintű növekedési tényezőjű megoldások közgazdasági szempontból értelmetlenek, és így érdektelenek. Ezzel voltaképpen egyrészt azt mutatjuk meg, hogy Neumann kiváló intuíciója jól működött, amikor ragaszkodott modellje egyértelmű megoldásához, másrészt pedig azt is, hogy ehhez nincs szükség a gazdaság dekomponálhatóságának feltételezésére. A vizsgált téma szorosan kapcsolódik az általános profitráta meghatározásának - Sraffa által modern formába öntött - Ricardo-féle elemzéséhez, illetve a neoklasszikus növekedéselmélet nevezetes bér-profit, illetve felhalmozás-fogyasztás átváltási határgörbéihez, ami jelzi a téma elméleti és elmélettörténeti érdekességét is. / === / In the Marx-Neumann version of the Neumann model introduced by Morishima, the use of commodities is split between production and consumption, and wages are determined as the cost of necessary consumption. In such a version it may occur that the equilibrium prices of all goods necessary for consumption are zero, so that the equilibrium wage rate becomes zero too. In fact such a paradoxical case will always arise when the economy is decomposable and the equilibrium not unique in terms of growth and interest rate. It can be shown that a zero equilibrium wage rate will appear in all equilibrium solutions where growth and interest rate are less than maximal. This is another proof of Neumann's genius and intuition, for he arrived at the uniqueness of equilibrium via an assumption that implied that the economy was indecomposable, a condition relaxed later by Kemeny, Morgenstern and Thompson. This situation occurs also in similar models based on Leontief technology and such versions of the Marx-Neumann model make the roots of the problem more apparent. Analysis of them also yields an interesting corollary to Ricardo's corn rate of profit: the real cause of the awkwardness is bad specification of the model: luxury commodities are introduced without there being a final demand for them, and production of them becomes a waste of resources. Bad model specification shows up as a consumption coefficient incompatible with the given technology in the more general model with joint production and technological choice. For the paradoxical situation implies the level of consumption could be raised and/or the intensity of labour diminished without lowering the equilibrium rate of the growth and interest. This entails wasteful use of resources and indicates again that the equilibrium conditions are improperly specified. It is shown that the conditions for equilibrium can and should be redefined for the Marx-Neumann model without assuming an indecomposable economy, in a way that ensures the existence of an equilibrium unique in terms of the growth and interest rate coupled with a positive value for the wage rate, so confirming Neumann's intuition. The proposed solution relates closely to findings of Bromek in a paper correcting Morishima's generalization of wage/profit and consumption/investment frontiers.

On uniqueness of equilibrium in the Kyle Model

A longstanding unresolved question is whether the one-period Kyle Model of an informed trader and a noisily informed market maker has an equilibrium that is different from the closed-form solution derived by Kyle (1985). This note advances what is known about this open problem.

Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies

In applied work in macroeconomics and finance, nonoptimal infinite horizon economies are often studied in the the state space is unbounded. Important examples of such economies are single vector growth models with production externalities, valued fiat money, monopolistic competition, and/or distortionary government taxation. Although sufficient conditions for existence and uniqueness of Markovian equilibrium are well known for the compact state space case, no similar sufficient conditions exist for unbounded growth. This paper provides such a set of sufficient conditions, and also present a computational algorithm that will prove asymptotically consistent when computing Markovian equilibrium.

Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns

Two new concepts for molecular solids, 'local similarity' and 'boundary-preserving isometry', are defined mathematically and a theorem which relates these concepts is formulated. 'Locally similar' solids possess an identical short-range structure and a 'boundary-preserving isometry' is a new mathematical operation on a finite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a 'boundary-preserving isometry' in a given solid has infinitely many 'locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are first introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld refinement. Further ab initio packing calculations on other molecules reveal that 'local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The 'boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

Existence and uniqueness of a fixed-point for local contractions

This paper proves the existence and uniqueness of a fixed-point for local contractions without assuming the family of contraction coefficients to be uniformly bounded away from 1. More importantly it shows how this fixed-point result can apply to study existence and uniqueness of solutions to some recursive equations that arise in economic dynamics.

Global and local implications of biotechnology and climate change for future food supplies

The development of improved technology for agricultural production and its diffusion to farmers is a process requiring investment and time. A large number of studies of this process have been undertaken. The findings of these studies have been incorporated into a quantitative policy model projecting supplies of commodities (in terms of area and crop yields), equilibrium prices, and international trade volumes to the year 2020. These projections show that a “global food crisis,” as would be manifested in high commodity prices, is unlikely to occur. The same projections show, however, that in many countries, “local food crisis,” as manifested in low agricultural incomes and associated low food consumption in the presence of low food prices, will occur. Simulations show that delays in the diffusion of modern biotechnology research capabilities to developing countries will exacerbate local food crises. Similarly, global climate change will also exacerbate these crises, accentuating the importance of bringing strengthened research capabilities to developing countries.

Towards local cultures of sustainability : facilitating community created environment education centres through design

Ecological sustainability has been proposed to address the problem of human impacts increasingly degrading planetary resources and ecosystems, threatening biodiversity, eco-services and human survival. Ecological sustainability is an imperative, with Australia having one of the highest eco-footprints per person worldwide. While significant progress has been made via implementation of ecologically sustainable design in urban communities, relatively little has been undertaken in small, disparate regional communities in Australia. Regional communities are disadvantaged by rural economic decline associated with structural change and inequities of resource transfer. The ecologically sustainable solution is holistic, so all settlements need to be globally wise, richly biodiverse yet locally specific. As a regional solution to this global problem, this research offers the practical means by which a small regional community can contribute. It focuses on the design and implementation of a community centre and the fostering of transformative community learning through an integrated ‘learning community’ awareness of ecologically sustainable best practice. Lessons learned are documented by the participant researcher who as a designer, facilitator, local resident and social narrator has been deeply connected with the Tweed-Caldera region over a period since 1980. The collective action of the local community of Chillingham has been diligently recorded over a decade of design and development. Over this period, several positive elements emerged in terms of improvements to the natural and built environment, greater social cohesion and co-operative learning along with a shift towards a greener local economy. Behavioural changes in the community were noted as residents strived to embrace ecological ideals and reduce fossil fuel dependency. They found attractive local solutions to sourcing of food and using local employment opportunities to up skill their residents via transformative learning as a community in transition. Finally, the catalytic impact of external partnering has also been documented. How well the region as a whole has achieved its ecologically sustainable objectives is measured in terms of the delivered success of private and public partnering with the community, the creation of a community centre cum environment education centre, the restoration of local heritage buildings, the repair of riparian forests and improved water conditions in local river systems, better roads and road safety, local skills and knowledge transfer, support of local food and local/regional growers markets to attract tourists via the integrated trails network. In aggregate, each and every element contributes to a measure of eco-positive development for the built environment, its social organisation and its economy that has guided the local community to find its own pathway to sustainability. Within the Tweed-Caldera bioregion in northern New South Wales, there has been a lack of strategic planning, ecologically sustainable knowledge and facilities in isolated communities that could support the development of a local sustained green economy, provide a hub for socio-cultural activities and ecology based education. The first challenge in this research was to model a whole systems approach to eco-positive development in Chillingham, NSW, a small community where Nature and humanity know no specific boundary. The net result was the creation of a community environment education centre featuring best-affordable ecological practice and regionally distinctive, educational building form from a disused heritage building (cow bale). This development, implemented over a decade, resonated with the later regional wide programs that were linked in the Caldera region by the common purpose of extending the reach of local and state government assistance to regional NSW in economic transition coupled with sustainability. The lessons learned from these linked projects reveal that subsequent programs have been significantly easier to initiate, manage, develop and deliver results. In particular, pursuing collaborative networks with all levels of government and external private partners has been economically effective. Each community’s uniqueness has been celebrated and through drawing out these distinctions, has highlighted local vision, strategic planning, sense of belonging and connection of people with place. This step has significantly reduced the level of friction between communities that comes from natural competition for the finite pool of funds. Following the pilot Tweed-Caldera study, several other NSW regional communities are now undertaking a Community Economic Transition Program based on the processes, trials and positive experiences witnessed in the Tweed-Caldera region where it has been demonstrated that regional community transition programs can provide an opportunity to plan and implement effective long term strategies for sustainability, empowering communities to participate in eco-governance. This thesis includes the design and development of a framework for community created environment education centres to provide an equal access place for community to participate to meet their essential needs locally. An environment centre that facilitates community transition based on easily accessible environmental education, skills and infrastructure is necessary to develop local cultures of sustainability. This research draws upon the literatures of ecologically sustainable development, environmental education and community development in the context of regional community transition towards ‘strong sustainability’. The research approach adapted is best described as a four stage collaborative action research cycle where the participant researcher (me) has a significant involvement in the process to foster local cultures of sustainability by empowering its citizens to act locally and in doing so, become more self reliant and socially resilient. This research also draws upon the many fine working exemplars, such as the resilience of the Cuban people, the transition town initiative in Totnes, U.K. and the models of Australian Community Gardens, such as CERES (Melbourne) and Northey Street (Brisbane). The objectives of this study are to research and evaluate exemplars of ecologically sustainable environment education centres, to facilitate the design and development of an environment education centre created by a small regional community as an ecologically sustainable learning environment; to facilitate a framework for community transition based on environmental education, skills and infrastructure necessary to develop local cultures of sustainability. The research was undertaken as action research in the Tweed Caldera in Northern NSW. This involved the author as participant researcher, designer and volunteer in two interconnected initiatives: the Chillingham Community Centre development and the Caldera Economic Transition Program (CETP). Both initiatives involved a series of design-led participatory community workshops that were externally facilitated with the support of government agency partnerships, steering committees and local volunteers. Together the Caldera research programs involved communities participating in developing their own strategic planning process and outcomes. The Chillingham Community Centre was developed as a sustainable community centre/hub using a participatory design process. The Caldera Economic Transition Program (CETP) prioritised Caldera region projects: the Caldera farmer’s market; community gardens and community kitchens; community renewable energy systems and an integrated trails network. The significant findings were: the CETP projects were capable of moving towards an eco-positive design benchmark through transformative learning. Community transition to sustainability programs need to be underpinned by sustainability and environmental education based frameworks and practical on ground experience in local needs based projects through transformative learning. The actioned projects were successfully undertaken through community participation and teamwork. Ecological footprint surveys were undertaken to guide and assess the ongoing community transition process, however the paucity of responses needs to be revisited. The concept of ecologically sustainable development has been adopted internationally, however existing design and planning strategies do not assure future generations continued access to healthy natural life support systems. Sustainable design research has usually been urban focussed, with little attention paid to regional communities. This study seeks to redress this paucity through the design of ecologically sustainable (deep green) learning environments for small regional communities. Through a design-led process of environmental education, this study investigates how regional communities can be facilitated to model the principles of eco-positive development to support transition to local cultures of sustainability. This research shows how community transition processes and projects can incorporate sustainable community development as transformative learning through design. Regional community transition programs can provide an opportunity to plan long term strategies for sustainability, empowering people to participate in eco-governance. A framework is developed for a community created environment education centre to provide an equal access place for the local community to participate in implementing ways to meet their essential needs locally. A community environment education centre that facilitates community transition based on holistic environmental education, skills and infrastructure is necessary to develop local cultures of sustainability.

On the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamics

This investigation deals with certain generalizations of the classical uniqueness theorem for the second boundary-initial value problem in the linearized dynamical theory of not necessarily homogeneous nor isotropic elastic solids. First, the regularity assumptions underlying the foregoing theorem are relaxed by admitting stress fields with suitably restricted finite jump discontinuities. Such singularities are familiar from known solutions to dynamical elasticity problems involving discontinuous surface tractions or non-matching boundary and initial conditions. The proof of the appropriate uniqueness theorem given here rests on a generalization of the usual energy identity to the class of singular elastodynamic fields under consideration.

Following this extension of the conventional uniqueness theorem, we turn to a further relaxation of the customary smoothness hypotheses and allow the displacement field to be differentiable merely in a generalized sense, thereby admitting stress fields with square-integrable unbounded local singularities, such as those encountered in the presence of focusing of elastic waves. A statement of the traction problem applicable in these pathological circumstances necessitates the introduction of "weak solutions'' to the field equations that are accompanied by correspondingly weakened boundary and initial conditions. A uniqueness theorem pertaining to this weak formulation is then proved through an adaptation of an argument used by O. Ladyzhenskaya in connection with the first boundary-initial value problem for a second-order hyperbolic equation in a single dependent variable. Moreover, the second uniqueness theorem thus obtained contains, as a special case, a slight modification of the previously established uniqueness theorem covering solutions that exhibit only finite stress-discontinuities.

Entanglement negativity in the harmonic chain out of equilibrium

We study the entanglement in a chain of harmonic oscillators driven out of equilibrium by preparing the two sides of the system at different temperatures, and subsequently joining them together. The steady state is constructed explicitly and the logarithmic negativity is calculated between two adjacent segments of the chain. We find that, for low temperatures, the steady-state entanglement is a sum of contributions pertaining to left-and right-moving excitations emitted from the two reservoirs. In turn, the steady-state entanglement is a simple average of the Gibbs-state values and thus its scaling can be obtained from conformal field theory. A similar averaging behaviour is observed during the entire time evolution. As a particular case, we also discuss a local quench where both sides of the chain are initialized in their respective ground states.

Thermal transport in out-of-equilibrium quantum harmonic chains

We address the problem of heat transport in a chain of coupled quantum harmonic oscillators, exposed to the influences of local environments of various nature, stressing the effects that the specific nature of the environment has on the phenomenology of the transport process. We study in detail the behavior of thermodynamically relevant quantities such as heat currents and mean energies of the oscillators, establishing rigorous analytical conditions for the existence of a steady state, whose features we analyze carefully. In particular, we assess the conditions that should be faced to recover trends reminiscent of the classical Fourier law of heat conduction and highlight how such a possibility depends on the environment linked to our system.

An approach to determine the local boundary of small disturbance voltage stability region in a cut-set power space:基于微扰的割集电压稳定域局部边界求解方法

A new approach to determine the local boundary of voltage stability region in a cut-set power space (CVSR) is presented. Power flow tracing is first used to determine the generator-load pair most sensitive to each branch in the interface. The generator-load pairs are then used to realize accurate small disturbances by controlling the branch power flow in increasing and decreasing directions to obtain new equilibrium points around the initial equilibrium point. And, continuous power flow is used starting from such new points to get the corresponding critical points around the initial critical point on the CVSR boundary. Then a hyperplane cross the initial critical point can be calculated by solving a set of linear algebraic equations. Finally, the presented method is validated by some systems, including New England 39-bus system, IEEE 118-bus system, and EPRI-1000 bus system. It can be revealed that the method is computationally more efficient and has less approximation error. It provides a useful approach for power system online voltage stability monitoring and assessment. This work is supported by National Natural Science Foundation of China (No. 50707019), Special Fund of the National Basic Research Program of China (No. 2009CB219701), Foundation for the Author of National Excellent Doctoral Dissertation of PR China (No. 200439), Tianjin Municipal Science and Technology Development Program (No. 09JCZDJC25000), National Major Project of Scientific and Technical Supporting Programs of China During the 11th Five-year Plan Period (No. 2006BAJ03A06). ©2009 State Grid Electric Power Research Institute Press.

Evaluation of dynamic pass-through of carbon prices into electricity prices – a cointegrated VECM analysis

This paper addresses the impact of the CO2 opportunity cost on the wholesale electricity price in the context of the Iberian electricity market (MIBEL), namely on the Portuguese system, for the period corresponding to the Phase II of the European Union Emission Trading Scheme (EU ETS). In the econometric analysis a vector error correction model (VECM) is specified to estimate both long–run equilibrium relations and short–run interactions between the electricity price and the fuel (natural gas and coal) and carbon prices. The model is estimated using daily spot market prices and the four commodities prices are jointly modelled as endogenous variables. Moreover, a set of exogenous variables is incorporated in order to account for the electricity demand conditions (temperature) and the electricity generation mix (quantity of electricity traded according the technology used). The outcomes for the Portuguese electricity system suggest that the dynamic pass–through of carbon prices into electricity prices is strongly significant and a long–run elasticity was estimated (equilibrium relation) that is aligned with studies that have been conducted for other markets.