A note on the separability principle in economies with single-peaked

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and continuity (with respect to the social endowment). We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of continuity. Furthermore, we prove that Pareto optimality, equal division lower bound, and separability imply no-envy. Using this result, we strengthen one of Chun's (2001) characterizations of the uniform rule by showing that the uniform rule is the only rule satisfying Pareto optimality, equal división lower bound, separability, and either continuity or duplication-invariance.

Minimal truncations of supersingular p-divisible groups

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

Traverso's isogeny conjecture for p-divisible groups

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

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

Power laws and scaling of rain events and dry spells in the Catalonia region

We analyze the statistics of rain-event sizes, rain-event durations, and dry-spell durations in a network of 20 rain gauges scattered in an area situated close to the NW Mediterranean coast. Power-law distributions emerge clearly for the dryspell durations, with an exponent around 1.50 ± 0.05, although for event sizes and durations the power-law ranges are rather limited, in some cases. Deviations from power-law behavior are attributed to finite-size effects. A scaling analysis helps to elucidate the situation, providing support for the existence of scale invariance in these distributions. It is remarkable that rain data of not very high resolution yield findings in agreement with self-organized critical phenomena.

Financial Repression in a Natural Experiment: Loan Allocation and the Change in the Usury Laws in 1714

If financial deepening aids economic growth, then financial repression should be harmful. We use a natural experiment – the change in the English usury laws in 1714 – to analyze the effects of interest rate restrictions. We use a sample of individual loan transactions to demonstrate how the reduction of the legal maximum rate of interest affected the supply and demand for credit. Average loan size and minimum loan size increased strongly, and access to credit worsened for those with little ‘social capital.’ While we have no direct evidence that loans were misallocated, the discontinuity in loan receipts makes this highly likely. We conclude that financial repression can undermine the positive effects of financial deepening.

Restless bandits, partial conservation laws and indexability

We show that if performance measures in a stochastic scheduling problem satisfy a set of so-called partial conservation laws (PCL), which extend previously studied generalized conservation laws (GCL), then the problem is solved optimally by a priority-index policy for an appropriate range of linear performance objectives, where the optimal indices are computed by a one-pass adaptive-greedy algorithm, based on Klimov's. We further apply this framework to investigate the indexability property of restless bandits introduced by Whittle, obtaining the following results: (1) we identify a class of restless bandits (PCL-indexable) which are indexable; membership in this class is tested through a single run of the adaptive-greedy algorithm, which also computes the Whittle indices when the test is positive; this provides a tractable sufficient condition for indexability; (2) we further indentify the class of GCL-indexable bandits, which includes classical bandits, having the property that they are indexable under any linear reward objective. The analysis is based on the so-called achievable region method, as the results follow fromnew linear programming formulations for the problems investigated.

The effect of divorce laws on divorce rates in Europe

This paper analyzes a panel of 18 European countries spanning from 1950 to 2003 toexamine the extent to which the legal reforms leading to easier divorce that took placeduring the second half of the 20th century have contributed to the increase in divorce rates across Europe. We use a quasi-experimental set-up and exploit the different timing of the reforms in divorce laws across countries. We account for unobserved country-specificfactors by introducing country fixed effects, and we include country-specific trends tocontrol for time-varying factors at the country level that may be correlated with divorcerates and divorce laws, such as changing social norms or slow moving demographictrends. We find that the reforms were followed by significant increases in divorce rates.Overall, we estimate that the introduction of no-fault, unilateral divorce increased thedivorce rate by about 1, a sizeable effect given the average rate of 4.2 divorces per 1,000married people in 2002.

Interest rate restrictions in a natural experiment: loan allocation and the change in the usury laws in 1714

This article studies the effects of interest rate restrictions on loan allocation. The British governmenttightened the usury laws in 1714, reducing the maximum permissible interest rate from 6% to5%. A sample of individual loan transactions reveals that average loan size and minimum loan sizeincreased strongly, while access to credit worsened for those with little social capital. Collateralisedcredits, which had accounted for a declining share of total lending, returned to their former role ofprominence. Our results suggest that the usury laws distorted credit markets significantly; we findno evidence that they offered a form of Pareto-improving social insurance.

Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws

The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors. Concerning the kinetics, it is shown that the extended volume evolves with time according to αex = [exp(κCt′)]m+1, where t′ is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters

Infinitely many periodic orbits for the rhomboidal five-body problem

We prove the existence of infinitely many symmetric periodic orbits for a regularized rhomboidal five-body problem with four small masses placed at the vertices of a rhombus centered in the fifth mass. The main tool for proving the existence of such periodic orbits is the analytic continuation method of Poincaré together with the symmetries of the problem. © 2006 American Institute of Physics.

Speed limit laws in America: economics, politics and geography

The regulation of speed limits in the US had been centralized at the federal level since 1974, until decisions were devolved to the states in 1995. However, the centralization debate has reemerged in recent years. Here, we conduct the first econometric analysis of the determinants of speed limit laws. By using economic, geographic and political variables, our results suggest that geography -which affects private mobility needs and preferences- is the main factor influencing speed limit laws. We also highlight the role played by political ideology, with Republican constituencies being associated with higher speed limits. Furthermore, we identify the presence of regional and time dependence effects. By contrast, poor road safety outcomes do not impede the enactment of high speed limits. Overall, we present the first evidence of the role played by geographical, ideological and regional characteristics, which provide us with a better understanding of the formulation of speed limit policies.