Dual Equilibrium Research Articles

Configurational‐force‐based structural updates and adaptive remeshing strategies

AbstractThe application of configurational forces in h ‐adaptive strategies for fracture mechanics and inelasticity is investigated. Starting from a global Clausius‐Planck inequality, dual equilibrium conditions are derived by means of a Coleman‐type exploitation method. The remaining reduced dissipation inequality is used for the derivation of evolution equations for the internal variables. In fracture mechanics, crack loading conditions as well as a normality rule for the crack propagation are obtained. In the discrete setting, the crack propagation is governed by a configurational‐force‐driven update of the geometry model. The material balance equation is used to set up a h ‐adaptive refinement indicator. A relative global criterion is defined used for the decision on mesh refinement. In addition, a criterion on the element level is evaluated controlling the local refinement procedure. The capability of the proposed procedures is demonstrated by means of numerical examples. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Excited-State Equilibration over 30 Å in a Platinum(II) Quinolinolate−Bridge−Platinum(II) Porphyrin Complex

Long-range triplet excited-state equilibration occurs over a nanometric distance between platinum(II) 8-quinolinolate (3Ptq2 = 1.87 eV) and platinum(II) tetraphenylporphyrin (3PtTPP = 1.89 eV). The equilibrium is mediated by a fluorene-thiophene-fluorene bridge (3FTF = 1.92 eV) and is characterized by a double-exponential decay (tau1 = 39 +/- 4 ps; tau2 = 351 +/- 15 ps) that suggests the participation of three separate excited states: 3Ptq2, 3FTF, and 3PtTPP, respectively. Numerical simulation of the dual equilibrium allowed for estimation of the individual rate constants for each of the reversible steps (kET = 3.9 x 10(9)-4.1 x 10(10) s(-1)). As a result of rapid triplet-state equilibration, almost 50% of the excited-state energy is directed from the PtTPP chromophore toward Ptq2, in spite of a small endothermic barrier (0.03 eV).

Goodwill hunting and profit sharing: Decision-making in a newspaper chain

A generalised equilibrium solution to the stochastic two-echelon newsvendor problem is achievable when formulated in the context of some cooperation and coordination between the primal (retailer) and dual (manufacturer) operators. We build on previous work detailing this equilibrium solution and apply it to the newspaper business. The solution incorporates changes in variability encountered due to promotional activity which extends the efficient frontier. We also consider consequences for profit and goodwill costs of identifying an equilibrium solution when additional income is generated from a source outside of the supply chain, such as advertising. We generalise to the supply chain network where there is some knowledge of demand or supply distributions further up or down the supply chain. We find that the primal–dual formulation and equilibrium solution apply to interactions between components of supply chain networks and illustrate with the transition to the direct distribution of newspapers.

Land and the transition from a dual to a modern economy

Tenurial contracts in agriculture can be an initial source of wealth accumulation for dynasties of poor, credit-constrained individuals. The income from such contracts can be invested in education of offspring, who then can find work in the formal manufacturing sector. This process allows the economy to develop into a modern economy with a large manufacturing sector. An excessive number of poor individuals competing for scarce land, however, drives up the rental price of land, which then slows the process of accumulation and forces the economy to converge to a less efficient dual equilibrium. In such cases, a policy of land redistribution coupled with a temporary education subsidy may be needed to push the economy to a modern equilibrium.

Structural optimization by simultaneous equilibration of spatial and material forces

SUMMARY In this contribution, a dual equilibrium methodology is applied to the shape optimization of trusses. The spatial co-ordinates as well as the material (i.e. initial) co-ordinates of the joints are taken as unknowns in the potential energy of the structure whereby the connectivity isxed. The conjugated variables, i.e. spatial forces and material forces, are equilibrated. Whereas equilibration of the spatial forces is equivalent tonding the optimal joint displacements, equilibration of the material forces yields the optimal initial joint positions. The two sets of equilibrium equations are derived and solved in a completely coupled manner. With a proper linearization and a Newton-Raphson scheme, shape optimization of the truss can be achieved within a few iterations. This is demonstrated by two numerical examples. Copyright ? 2005 John Wiley & Sons, Ltd.

Intra-Industry Trade in Intermediate Goods and Final Goods in a General Equilibrium Setting

This article develops a dual general equilibrium model to analyze the effects of intra-industry trade in both intermediate goods and final goods on the productivity in the final good production. Intra-industry trade in intermediate goods determines an increase in the number of intermediate good varieties available in the final good production, and intra-industry trade in final goods determines a reduction in the number of adaptations of an intermediate good to the final good production. Thereby, the productivity in the final good production increases. Different shares of intra-industry trade in intermediate goods and final goods in a general equilibrium setting implies that Jones' “magnification effect” and both the Rybczynski theorem and the Stolper-Samuelson theorem are not valid.

Characterizations of Solutions for Vector Equilibrium Problems

In this paper, we characterize the solutions of vector equilibrium problems as well as dual vector equilibrium problems. We establish also vector optimization problem formulations of set-valued maps for vector equilibrium problems and dual vector equilibrium problems, which include vector variational inequality problems and vector complementarity problems. The set-valued maps involved in our formulations depend on the data of the vector equilibrium problems, but not on their solution sets. We prove also that the solution sets of our vector optimization problems of set-valued maps contain or coincide with the solution sets of the vector equilibrium problems.

The shadow price of foreign exchange with minimum wages

This note derives the shadow price of foreign exchange in a small open economy with minimum wage unemployment under tariffs, quotas and voluntary export restraints. The analysis is conducted in a dual general equilibrium framework with many goods and factors.

A Note on Equilibrium Problems with Properly Quasimonotone Bifunctions

In this paper, we consider some well–known equilibrium problems and their duals in a topological Hausdorff vector space X for a bifunction F defined on \kk,where K is a convex subset of X. Some necessary conditions are investigated, proving different results depending on the behaviour of F on the diagonal set. The concept of proper quasimonotonicity for bifunctions is defined, and the relationship with generalized monotonicity is investigated. The main result proves that the condition of proper quasimonotonicity is sharp in order to solve the dual equilibrium problem on every convex set.

Pasinetti and dual equilibria in a post Keynesian model of growth and institutional distribution

In this paper we extend the post Keynesian theory of growth and distribution to a corporate economy. We show that the rate of profits and the distribution between profits and wages are influenced by the behavioural parameters of shareholders and firms, such as the degree of indifference between dividends and capital gains and the retention ratio, and by long-lasting stock market imperfections. What has been obtained in previous analyses such as O'Connell (1985, 1995) are special cases of these results. The conditions for the existence of what are known in the literature as Pasinetti and dual equilibria are also investigated.

Competitive Dynamics and the Introduction of New Products: The Motion Picture Timing Game

The extremely short life cycle and the rapid decay in revenues after opening coupled with the rapid and frequent introduction of new competitive products makes the timing of new product introductions in the motion picture industry critical, particularly during the high-revenue Christmas and summer seasons. Each studio wants to capture as much of the season as possible by opening early in the season. At the same time, each wants to avoid head-to-head competition. The authors model competition between two motion pictures in a share attraction framework and conduct an equilibrium analysis of the product introduction timing game in a finite season. The following three different equilibrium configurations emerge: (1) a single equilibrium with both movies opening simultaneously at the beginning of the season, (2) a single equilibrium with one movie opening at the beginning of the season and one delaying, and (3) dual equilibria, with either movie delaying opening. A key factor is the product life cycle, which can be captured well with a two-parameter exponential decline. The authors relate the life-cycle parameters to these possibilities with the general result that the weaker movie may be forced to delay opening. These results are related to case studies of the opening of recently released movies. A statistical analysis of the 1990 summer season in North America provides support for the conclusions and suggests that current release timing decisions can be improved. The authors discuss the rationale of “avoiding the competition” in the general context of product introduction timing.

Cooperation, job security, and wages in a dual labor market equilibrium

By introducing cooperation among individuals working within a firm, this paper constructs a model generating a dualistic competitive equilibrium with differentials in wages and job security in an industry with product demand uncertainty. Primary firms offer high job security to promote cooperation and achieve high productivity. Secondary firms merely take advantage of ability to adjust employment. Wage differentials arise because cooperation is more productive among members of the same social group and thus different groups of workers face different labor demand. In contrast to the Arrow-Debreu economy, firms making long-term decisions and those making short-term decisions coexist in the equilibrium.

Interactions Among Gypsy Moths, White‐footed Mice, and Acorns

Low—density populations of gypsy moth, Lymantria dispar, were studied over a 10—yr period in Massachusetts. Increases in gypsy moth density were associated with declines in density of the white—footed mouse, Peromyscus leucopus, a principal predator. Furthermore, changes in density of P. leucopus populations were positively correlated with the density of acorn crops, a dominant winter food source for these mice. To demonstrate these effects we used a novel bootstrap regression method that adjusts for spatial and temporal autocorrelation in the time series data. The findings are compatible with a dual equilibrium model of gypsy moth population dynamics, in which low densities are regulated by mice and high densities are regulated by other factors, notably a virus disease.

How to Select a Dual Nash Equilibrium

The paper analyzes situations, generalizing the duopoly problem, where two identical players are allowed with two control variables each, all of them linked through two non-strategic private constraints. Four dual equilibria are then obtained when each agent selects one leading variable to optimize and adjusts the other, and these equilibria are compared in a meta-game. For a simplified class of continuous games with linear constraints, it is shown that one symmetric dual equilibrium dominates the others and is the only perfect equilibrium of the metagame. The latter result holds locally for all quasi-concave utility functions and globally for all homogeneous ones, always keeping linear constraints. However, it is no longer valid in discrete games where the implicit constraints are not linear. Journal of Economic Literature Classification Numbers: C72, D43.

Positively Sloping Marginal Revenue, CES Utility and Subsistence Requirements

The possibility that marginal revenue may possess a positive slope has long been recognized as important. In her classic The Economics of Imperfect Competition, Joan Robinson [14] accorded considerable significance to the possibility and investigated it at length. Despite Robinson's insights, upward sloping marginal revenue functions remained largely a curiosity, widely regarded as an overly stringent perversity unlikely to occur in reality. Considerable doubt was cast on this view when in 1980 A. A. Walters [20] reported the presence of positively sloping marginal revenue in the pricing policies of the Port of Singapore. The case for upward sloping marginal revenue was furthered by Formby, Layson and Smith's [8] straightforward demonstration that upward sloping marginal revenue schedules are very easily produced and can never be ruled out because simple parallel shifts in strictly convex demand and/ or rotations always transform demand schedules with downward sloping marginal revenue into ones with positively sloping schedules.' This strongly suggests that no theoretically reasonable restrictions can be placed on the behavior of marginal revenue because to do so would rule out such simple transformations as parallel shifts or rotations in demand. Such restrictions would be too stringent to be acceptable. Upward sloping marginal revenue has found important application in such diverse topics as catastrophe theory [3], third-degree price discrimination [13], dual equilibria and monopolistic competition [11], specific taxes and quality [2] and international trade [7].2 The significance of non-monotonic marginal revenue functions is further underscored by the fact that the presence of upward sloping marginal revenue significantly affects the sign of comparative static results (for example, see [18, 260; 15; 16; 2]). A shortcoming of previous analyses lies in the fact that they draw conclusions from consideration of slope, level and curvature of the demand schedule alone. The behavior of marginal revenue derived directly from the more fundamental basis of utility theory has not been examined. This paper takes up this question, employing Wold's theorem to analyze marginal revenue

On Seigniorage, Operating Rules, and Dual Equilibria

On Seigniorage, Operating Rules, and Dual Equilibria

The flexible rolling schedule for infinite-horizon optimality in generation expansion planning

Prevailing approaches for reducing end effects in finite-horizon generation expansion planning (i.e. truncated, static post-horizon, salvage value, dual equilibrium, and rolling schedule) are compared, and the computationally efficient flexible rolling schedule introduced. The flexible rolling schedule is a general system-specific heuristic approximation for infinite-horizon optimal solutions. The significance of the baseload construction rate for infinite-horizon optimality is identified.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

EXTIRPATING ERROR CONTAMINATION CONCERNING THE POST-KEYNESIAN ANTI-PASINETTI EQUILIBRIUM

the capitalist-rentier's saving propensity). James Meade (1963) and Samuelson-Modigliani (1966) pointed out that in this 2-caste model, when the worker-caste's saving propensity became sufficiently large, the Pasinetti equilibrium just described ceases to obtain and is succeeded by a dual equilibrium in which only the workers' saving propensity has an effect on the interest rate and the distribution of income, the rentier's saving propensity becoming asymptotically of zero importance. Because Pasinetti (and Kaldor) are known to be trenchant critics of neoclassical marginalism, and because Meade, Samuelson, and Modigliani have been known to explore neoclassical models, there has grown up the dubious tradition of dubbing the Pasinetti equilibrium a macro-post-Keynesian distribution paradigm, while the dual equilibrium (non-optimally dubbed the anti-Pasinetti equilibrium) is sometimes thought to be peculiarly connected with the kind of neoclassical marginalism paradigm that Piero Sraffa (1960) proposed to subject to a careful critique. Speaking for no-one other than Samuelson, I wish to dissociate myself from such identifications. Moving far from the Clark and Cobb-Douglas marginal products in the form of smooth partial derivatives, we can envisage a discrete-activities Sraffian technology where output is producible out of labor and itself by alternative competing techniques. We then expect that high enough workers' propensity to save will be able to alter the balanced-growth equilibrium configuration in the anti-Pasinetti way, causing the competitive riskless profit rate to come to fall short of the Kaldor-Kalecki-Pasinetti ratio, (natural growth rate)/(rentier saving propensity).

Econometrics and the Design of Economic Reform

The concept of Economic Reform is described as a planned shift from one, Pareto inefficient, but quasi-stable, equilibrium (or 'trap') to a new Pareto superior equilibrium which is, or is designed to become, stable too. The concept is applied to recent 'shock' stabilization programs, with special reference to Israel, where the economy was credibly shifted from a 3-digit inflationary process with considerable inertia, to relative price stability with higher real growth, at only small adjustment costs, by means of a 'heterodox' plan. This two-pronged stabilization program consisted of a substantial correction of budget and external account 'fundamentals' together with a synchronized, wage-price-exchange rate freeze. The idea is theoretically rationalized within a simple dual equilibrium inflation model, for which some econometric estimates are also given.

A price endogenous computable planning model for a dual economy

This paper examines the nature of linkages between growth, employment and functional distribution of income in a dual economy. The analysis is carried out in terms of a dual economy general equilibrium model which is implicitly based on a social accounting matrix (SAM) type of information system. The parameter values and the structure of the model are based on Iranian data and the selection of policy packages is inspired by those undertaken in Iran during the 1970s. The model sheds some light on the consequences of the policies by quantifying their potential impact on the sectoral growth of output, levels of employment and functional distribution of income in the rural and urban areas.