Random walk on a randomly oriented honeycomb lattice

We study the recurrence behaviour of random walks on partially oriented honeycomb lattices. The vertical edges are undirected while the orientation of the horizontal edges is random: depending on their distribution, we prove a.s. transience in some cases, and a.s. recurrence in other ones. The results extend those obtained for the partially oriented square grid lattices (Campanino and Petritis (2003), Campanino and Petritis (2014)).Comment: 21 pages, 1 figure; revised 'motivation' section and abstract; added conclusion; minor correction

Sublinear and continuous order-preserving functions for noncomplete preorders

We characterize the existence of a nonnegative, sublinear and continuous order-preserving function for a not necessarily complete preorder on a real convex cone in an arbitrary topological real vector space. As a corollary of the main result, we present necessary and sufficient conditions for the existence of such an order-preserving function for a complete preorder.Comment: 8 page

Stability of the unique continuation for the wave operator via Tataru inequality and applications

In this paper we study the stability of the unique continuation in the case of the wave equation with variable coefficients independent of time. We prove a logarithmic estimate in a arbitrary domain of ${\mathbb R}^{n+1}$, where all the parameters are calculated explicitly in terms of the $C^1$-norm of the coefficients and on the other geometric properties of the problem. We use the Carleman-type estimate proved by Tataru in 1995 and an iteration for locals stability. We apply the result to the case of a wave equation with data on a cylinder an we get a stable estimate for any positive time, also after the first conjugate point for the geodesics of the metric related to the variable coefficients.Comment: The version v1 of this preprint is an extended version that contains more details than the "journal version", that is, the version v2, of the pape

On the Role of Progressive Taxation in a Ramsey Model with Heterogeneous Households

The aim of this paper is to study the role of progressive tax rules on the allocations of steady state and the stability properties in a Ramsey economy with heterogeneous households and borrowing constraints. Since labor supply in elastic, considering different tax rates on capital and labor incomes is relevant. The steady state analysis allows us to highlight the existence of different types of stationary equilibria. While patient agents always hold capital, impatient ones have or not positive savings, depending on the leval of real interest rate. Furthermore, it is not always optimal for all households to have a positive labor supply. Studying the comparative statics and local dynamics, we focus on the steady state with a segmented population : patient households own the whole stock of capital, while the impatient ones are workers. Varying the population sizes and the tax rates, we underline the crucial role of fiscal progressivity and endogenous labor. Moreover, in contrast to many contributions, we prove that progressive tax rules can promote expectation-driven fluctuations and endogenous cycles which means that progressivity can be inopportune to stabilize macroeconomic volatility.Progressive taxation, heterogeneous agents, borrowing constraint, endogenous labor supply, steady state allocation, macroeconomic stability.

Weak continuity of preferences with nontransitive indifference

We characterize weak continuity of an interval order on a topological space by using the concept of a scale in a topological space.Weakly continuous interval order; continuous numerical representation

A generalization of Rader's utility representation theorem

Rader's utility representation theorem guarantees the existence of an upper semicontinuous utility function for any upper semicontinuous total preorder on a second countable topological space. In this paper we present a generalization of Rader's theorem to not necessarily total preorders that are weakly upper semicontinuous.Weakly upper semicontinuous preorder; utility function

Can heterogeneous preferences stabilize endogenous fluctuations ?

While most of the literature concerned with indeterminacy and endogenous cycles is based on the questionable assumption of a representative consumer, some recent works have investigated the role of heterogeneous agents on dynamics. This paper adds a contribution to the debate, highlighting the effects of heterogeneity in consumers' preferences within an overlapping generations economy with capital accumulation, endogenous labor supply and consumption in both periods. Using a mean-preserving approach to heterogeneity, we show that increasing the dispersion of propensities to save turns out to stabilize the macroeconomic volatility, by reducing the range of parameters compatible with indeterminacy and ruling out expectations-driven fluctuations under a sufficiently large heterogeneity.Endogenous fluctuations, heterogeneous preferences, mean-preserving dispersion, overlapping generations.

Can Heterogeneous Preferences Stabilize Endogenous Fluctuations?

While most of the literature concerned with indeterminacy and endogenous cycles is based on the restrictive assumption of a representative consumer,some recent contributions have investigated the role of heterogeneous agents in dynamics. This paper adds to this latter strand of the literature by highlighting the effects of heterogeneity in consumers' preferences within an overlapping generations economy with capital accumulation, endogenous labor supply and consumption in both periods. Using a mean-preserving approach to heterogeneity, we show that increasing the dispersion of propensity to save decreases macroeconomic volatility, by narrowing down the range of parameter values compatible with indeterminacy and ruling out expectations-driven fluctuations under a sufficiently large heterogeneity.Endogenous fluctuations; heterogeneouspreferences; mean-preserving dispersion; overlapping generations.

On Rational Exuberance

In his seminal contribution, Tirole (1985) shows that an overlapping generations economy may monotonically converges to a steady state with a positive rational bubble, characterized by the dynamically efficient golden rule. The issue we address is whether this monotonic convergence to an efficient long-run equilibrium may fail, while the economy experiences persistent endogenous fluctuations around the golden rule. Our explanation leads on the features of the credit market. We consider a simple overlapping generations model with three assets : money, capital and a pure bubble (bonds). Collateral matters because increasing his portfolio in capital and bubble, the household reduces the share of his consumption paid by cash. From a positive point of view, we show that the bubbly steady state can be locally indeterminate under arbitrarily small credit market imperfections and, thereby, persistent expectation-driven fluctuations of equilibria with (rational) bubbles can arise. From a normative point of view, monetary policies that are not too expansive, are recommended in order to rule out the occurence of sunspot fluctuations and enhance the welfare evaluated at the steady state.Bubbles, collaterals, indeterminacy, cash-in-advance constraint, overlapping generations.