Increasing quasiconcave production and utility functions with diminishing returns to scale

In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator functions in production and consumer theory. In particular representation theorems for direct and indirect aggregator functions are obtained. These involve only small sets of generator functions. The study is carried out in the contemporary framework of abstract convexity and abstract concavity.

Can genetic algorithms explain experimental anomalies? An application to common property resources

It is common to find in experimental data persistent oscillations in the aggregate outcomes and high levels of heterogeneity in individual behavior. Furthermore, it is not unusual to find significant deviations from aggregate Nash equilibrium predictions. In this paper, we employ an evolutionary model with boundedly rational agents to explain these findings. We use data from common property resource experiments (Casari and Plott, 2003). Instead of positing individual-specific utility functions, we model decision makers as selfish and identical. Agent interaction is simulated using an individual learning genetic algorithm, where agents have constraints in their working memory, a limited ability to maximize, and experiment with new strategies. We show that the model replicates most of the patterns that can be found in common property resource experiments.

Rational sabotage in cooperative production

In this paper we consider a model of cooperative production in which rational agents have the possibility to engage in sabotage activities that decrease output. It is shown that sabotage depends on the interplay between the degree of congestion, the technology of sabotage, the number of agents the degree of meritocracy and the form of the sharing rule. In particular it is shown that, ceteries paribus, meritocratic systems give more incentives to sabotage than egalitarian systems. We address two questions: The degree of meritocracy that is compatible with absence of sabotage and the existence of a Nash equilibrium with and without sabotage.

Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

Testing of stair climbing point-of-choice prompts in Barcelona at an outdoor set of stairs and scalators on the Montjuïc site

Regular stair climbing has well-documented health dividends, such as increased fitness and strength, weight loss and reduced body fat, improved lipid profiles and reduced risk of osteoporosis. The general absence of barriers to participation makes stair climbing an ideal physical activity (PA) for health promotion. Studies in the US and the UK have consistently shown that interventions to increase the accumulation of lifestyle PA by climbing stairs rather than using the escalators are effective. However, there are no previous in Catalonia. This project tested one message for their ability to prompt travelers on the Montjuïc site to choose the stairs rather than the escalator when climbing up the Monjuïc hill. One standard message, " Take the stairs! 7 minutes of stair climbing a day protects your heart" provided a comparison with previous research done in the UK. Translated into Catalan and Spanish, it was presented on a poster positioned at the point of choice between the stairs and the escalator. The study used a quasi-experimental, interrupted time series design. Travelers, during several and specific hours on two days of the week, were coded for stair or escalator use, gender, age, ethnic status, presence of accompanying children or bags by one observer. Overall, the intervention resulted in a 81% increase in stair climbing. In the follow-up period without messages, stair climbing dropped out to baseline levels. This preliminary study showed a significant effect on stair use. However, caution is needed since results are based on a small sample and, only a low percentage of the sample took the stairs at baseline or the intervention phase . Future research on stair use in Catalonia should focus on using bigger samples, different sites (metro stations, airports, shopping centers, etc) , different messages and techniques to promote stair climbing.

The Social contract with endogenous sentiments

Moral values infuence individual behavior and social interactions. A specially signif- cant instance is the case of moral values concerning work e¤ort. Individuals determine what they take to be proper behaviour and judge the others, and themselves, accordingly. They increase their esteem -and self-esteem- for those who perform in excess of the standard and decrease their esteem for those who work less. These changes in self-esteem result from the self-regulatory emotions of guilt or pride extensively studied in Social Psychology. We examine the interactions between sentiments, individual behaviour and the social contract in a model of rational voting over redistribution where individual self-esteem and relative es-teem for others are endogenously determined. Individuals di¤er in their productivities. The desired extent of redistribution depends both on individual income and on individual attitudes toward others. We characterize the politico-economic equilibria in which sentiments, labor supply and redistribution are simultaneously determined. The model has two types of equilibria. In "cohesive" equilibria, all individuals conform to the standard of proper behav- iour, income inequality is low and social esteem is not biased toward any particular type. Under these conditions equilibrium redistribution increases in response to larger inequality. In a "clustered" equilibrium skilled workers work above the mean while unskilled workers work below. In such an equilibrium, income inequality is large and sentiments are biased in favor of the industrious. As inequality increases, this bias may eventually overtake the egoistic demand for greater taxation and equilibrium redistribution decreases. The type of equilibrium that emerges crucially depends on inequality. We contrast the predictions of the model with data on inequality, redistribution, work values and attitudes toward work and toward the poor for a set of OECD countries.

Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

A general construction of internal sheaves in algebraic set theory

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

Rational first integrals in the Darboux theory of integrability in Cn

"Vegeu el resum a l'inici del document del fitxer adjunt."

Avaluació de set materials representatius del programa didàctic aplicat a les Escoles Bressol Municipals de Mataró dins del projecte de formació del professorat 2006/07

ii. Desprès de finalitzar el primer any d’aplicació del projecte “La música a les Escoles Bressol Municipals de Mataró”, s’inicia la present recerca, en la que participen tots els grups que formen part del projecte, amb l’objectiu de valorar-ho i veure’n la continuïtat. Es detecta que els materials emprats en la proposta didàctica són l’element que ha esdevingut més exitós fins al moment. Definint-ne una mostra de set materials, es procedeix a determinar l’ús que les educadores els atorguen en relació a la proposta didàctica i a avaluar-los

Persistent bundles over a two dimensional compact set

"Vegeu el resum a l'inici del document del fitxer adjunt."

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.