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

Optimal Cycles and Social Inequality: What Do We Learn from the Gini Index?

One of the plausible explanations for macroeconomic fluctuations relies on the occurrence of endogenous deterministic cycles. In the last three decades, most of the relevant literature has rested on the assumption of a representative agent but, recently, a few papers have investigated the role of consumers' heterogeneity on endogenous fluctuations. Our article aims at taking a step forward in order to give a more suitable interpretation. To keep things as simple as possible, we introduce heterogeneous households in a two-sector optimal growth model and we study how wealth heterogeneity affects the occurrence of endogenous cycles. In contrast to previous results, we relate the existence of such cycles to the most commonly used inequality measure, the Gini index, and analyze the impact of consumers' heterogeneity on this index.Endogenous cycles ; two-sector models ;heterogeneous agents ; Gini index

Time, Bifurcations and Economic Applications

In this paper,we show how to recover discrete-time models from their continuous-time versions through Euler discretizations. In the first part, we introduce general polynomial discretizations in backward and forward looking and we study the preservation of stability properties and local bifurcations under different discretizations. In the second part, we apply these results to popular growth models. We show how to reconcile the traditional Solow models in discrete and continuous time through a backward-looking discretization. Discrete-time models of endogenous saving, suchas Ramsey(1928), need hybrid discretizations of the continuous-time model because of the forward-looking nature of the Euler equation. The introduction of externalities allows us to illustrate the preservation of stability properties and local bifurcations.discretizations, bifurcations, growthmodels

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.

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.

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

Normal force controlled rheology applied to agar gelation

A wide range of thermoreversible gels are prepared by cooling down to ambient temperature hot aqueous polymer solutions. During the sol-gel transition, such materials may experience a volume contraction which is traditionally overlooked as rheological measurements are usually performed in geometries of constant volume. In this article, we revisit the formation of 1.5\% wt. agar gels through a series of benchmark rheological experiments performed with a plate-plate geometry. We demonstrate on that particular gel of polysaccharides that the contraction associated with the sol/gel transition cannot be neglected. Indeed, imposing a constant gap width during the gelation results in the strain hardening of the sample, as evidenced by the large negative normal force that develops. Such hardening leads to the slow drift in time of the gel elastic modulus $G'$ towards ever larger values, and thus to an erroneous estimate of $G'$. As an alternative, we show that imposing a constant normal force equals to zero during the gelation, instead of a constant gap width, suppresses the hardening as the decrease of the gap compensates for the sample contraction. Using normal force controlled rheology, we then investigate the impact of thermal history on 1.5\% wt. agar gels. We show that neither the value of the cooling rate, nor the introduction of a constant temperature stage during the cooling process influence the gel elastic properties. Instead, $G'$ only depends on the terminal temperature reached at the end of the cooling ramp, as confirmed by direct imaging of the gel microstructure by cryoelectron microscopy. The present work offers an extensive review of the technical difficulties associated with the rheology of hydrogels and paves the way for a systematic use of normal force controlled rheology to monitor non-isochoric processes.Comment: 19 pages, 15 figures - accepted for publication in Journal of Rheolog

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