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.

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.

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.

Comparative Statics of Asset Prices: the effect of other assets' risk

Currently, financial economics is unable to predict changes in asset prices with respect to changes in the underlying risk factors, even when an asset's dividend is independent of a given factor. This paper takes steps towards addressing this issue by highlighting a crucial component of wealth effects on asset prices hitherto ignored by the literature. Changes in wealth do not only alter an agents risk aversion, but also her perceived 'riskiness' of a security. The latter enhances significantly the extent to which market- clearing leads to endogenously-generated correlation across asset prices, over and above that induced by correlation between payoffs, giving the appearance of 'contagion.'

On equilibrium prices in continuous time

We combine general equilibrium theory and théorie générale of stochastic processes to derive structural results about equilibrium state prices.

On local analysis of oscillations of a non-ideal and non-linear mechanical model

It is of major importance to consider non-ideal energy sources in engineering problems. They act on an oscillating system and at the same time experience a reciprocal action from the system. Here, a non-ideal system is studied. In this system, the interaction between source energy and motion is accomplished through a special kind of friction. Results about the stability and instability of the equilibrium point of this system are obtained. Moreover, its bifurcation curves are determined. Hopf bifurcations are found in the set of parameters of the oscillating system.

Spectroscopic study and local coordination of polyphosphate colloidal systems

The interaction between metaphosphate chains and the metal ions Ca2+ and Eu3+ has been studied in water by Eu3+ luminescence, infrared absorption, and P-31 NMR spectroscopy. Two main families of sites could be identified for the metal ions in the aqueous polyphosphate colloidal systems: (1) cagelike sites provided by the polyphosphate chain and (2) a family which arises following saturation of cagelike sites. Occupation of this second family leads to supramolecular interactions between polyphosphate chains and the consequent destabilization of the colloidal system. In the polyphosphate-Ca2+ system, this destabilization appears as a coacervation process. Equilibrium existing between colloidal species as a function of the compositions could be reasoned based on the spectroscopic measurements. The determination of coordination numbers and the correlation of the results with the observation of coacervates show that Eu3+ luminescence properties can be used to probe in a unique way the coacervation process.

A NOTE ON THE UNIQUENESS OF SOLUTIONS FOR THE YAMABE PROBLEM

Using recent results on the compactness of the space of solutions of the Yamabe problem, we show that in conformal classes of metrics near the class of a nondegenerate solution which is unique (up to scaling) the Yamabe problem has a unique solution as well. This provides examples of a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.

Local Structure of Hydrogen-Bonded Liquids

Ordinary yet unique, water is the substance on which life is based. Water seems, at first sight, to be a very simple molecule, consisting of two hydrogen atoms attached to one oxygen. Its small size belies the complexity of its action and its numerous anomalies, central to a broad class of important phenomena, ranging from global current circulation, terrestrial water and CO2 cycles to corrosion and wetting. The explanation of this complex behavior comes from water's unique ability to form extensive three-dimensional networks of hydrogen-bonds, whose nature and structures, in spite of a great deal of efforts involving a plethora of experimental and theoretical techniques, still lacks a complete scientific understanding. This thesis is devoted to the study of the local structure of hydrogen-bonded liquids, with a particular emphasis on water, taking advantage of a combination of core-level spectroscopies and density functional theory spectra calculations. X-ray absorption, in particular, is found to be sensitive to the local hydrogen-bond environment, thus offering a very promising tool for spectroscopic identification of specific structural configurations in water, alcohols and aqueous solutions. More specifically, the characteristic spectroscopic signature of the broken hydrogen-bond at the hydrogen side is used to analyze the structure of bulk water, leading to the finding that most molecules are arranged in two hydrogen-bond configurations, in contrast to the picture provided by molecular dynamics simulations. At the liquid-vapor interface, an interplay of surface sensitive measurements and theoretical calculations enables us to distinguish a new interfacial species in equilibrium with the gas. In a similar approach the cluster form of the excess proton in highly concentrated acid solutions and the different coordination of methanol at the vacuum interface and in the bulk can also be clearly identified. Finally the ability of core-level spectroscopies, aided by sophisticated density functional theory calculations, to directly probe the valence electronic structure of a system is used to observe the nature of the interaction between water molecules and solvated ions in solution. Water around transition metal ions is found to interact with the solute via orbital mixing with the metal d-orbitals. The hydrogen-bond between water molecules is explained in terms of electrostatic interactions enhanced by charge rehybridization in which charge transfer between connecting molecules is shown to be fundamental.

Stability, viscous dissipation and local thermal non-equilibrium in fluid saturated porous media

In this thesis, the field of study related to the stability analysis of fluid saturated porous media is investigated. In particular the contribution of the viscous heating to the onset of convective instability in the flow through ducts is analysed. In order to evaluate the contribution of the viscous dissipation, different geometries, different models describing the balance equations and different boundary conditions are used. Moreover, the local thermal non-equilibrium model is used to study the evolution of the temperature differences between the fluid and the solid matrix in a thermal boundary layer problem. On studying the onset of instability, different techniques for eigenvalue problems has been used. Analytical solutions, asymptotic analyses and numerical solutions by means of original and commercial codes are carried out.