Negishi-Solow Efficiency Wages, Unemployment Insurance and Dynamic Deterministic Indeterminacy

This paper introduces efficiency wages designed to provide workers with incentives to make appropriate effort levels, and involuntary unemployment, along the pioneering lines of Negishi (1979), Solow (1979), Shapiro and Stiglitz (1984), in a dynamic model involving heterogeneous agents and financial constraints as in Woodford (1986) and Grandmont, Pintus and de Vilder (GPV, 1998). Effort varies continuously while there is unemployment insurance funded out of taxation of labour incomes. Increasing unemployment insurance is beneficial to employment along the deterministic stationary state, and can even in some cases lead to a Pareto welfare improvement for all agents, through general equilibrium effects, by generating higher individual real labour incomes, hence larger consumptions of employed and unemployed workers, and thus a higher production. On the other hand, the local (in)determinacy properties of the stationary state are opposite to those obtained in the competitive specification of the model (GPV, 1998) : local determinacy (indeterminacy) occurs for elasticities of capitalefficient labour substitution lower (larger) than a quite small bound. Increasing unemployment insurance is more likely to lead to local indeterminacy and thus to generate dynamic inefficiencies due to the corresponding expectations coordination failures.Efficiency wages, involuntary unemployment, unemployment insurance, effort incentives, local indeterminacy, capital-labour substitution, local bifurcations.

On the motion of an elastic solid inside of an incompressible viscous fluid

The motion of an elastic solid inside of an incompressible viscous fluid is ubiquitous in nature. Mathematically, such motion is described by a PDE system that couples the parabolic and hyperbolic phases, the latter inducing a loss of regularity which has left the basic question of existence open until now. In this paper, we prove the existence and uniqueness of such motions (locally in time), when the elastic solid is the linear Kirchhoff elastic material. The solution is found using a topological fixed-point theorem that requires the analysis of a linear problem consisting of the coupling between the time-dependent Navier-Stokes equations set in Lagrangian variables and the linear equations of elastodynamics, for which we prove the existence of a unique weak solution. We then establish the regularity of the weak solution; this regularity is obtained in function spaces that scale in a hyperbolic fashion in both the fluid and solid phases. Our functional framework is optimal, and provides the a priori estimates necessary for us to employ our fixed-point procedure.Comment: 72 pages, to appear in Archive for Rational Mechanics and Analysi

Stability estimates for a Robin coefficient in the two-dimensional Stokes system

In this paper, we consider the Stokes equations and we are concerned with the inverse problem of identifying a Robin coefficient on some non accessible part of the boundary from available data on the other part of the boundary. We first study the identifiability of the Robin coefficient and then we establish a stability estimate of logarithm type thanks to a Carleman inequality due to A. L. Bukhgeim and under the assumption that the velocity of a given reference solution stays far from 0 on a part of the boundary where Robin conditions are prescribed

Environmental effects on constructed wetland microbial diversity and function in the context of wastewater management

Microbial communities play a crucial role in ecosystems, yet we know little about how microbial diversity influences ecosystem functioning. An important gap in our understanding is how environmental change affects microbial Biodiversity-Ecosystem Function relationships (BEF). These complex interactions between microbial biodiversity and ecosystem function can influence major biogeochemical processes, such as the nitrogen cycle in wetland ecosystems, which play an important role in managing wastewater. To address the effect of biodiversity on function, my study investigates the BEF relationships between microbial diversity and the function in terms of ammonia removal from wastewater at the Arcata Wastewater Treatment Facility (AWTF) both spatially and temporally. The AWTF uses several natural treatment systems consisting of Oxidation Ponds and constructed wetlands for secondary wastewater treatment. These natural treatment systems provide a unique opportunity to study microbial community BEF relationships because they are interconnected by the flow of nutrients in the wastewater and are exposed to seasonal changes. First, I conducted a field study where I sampled the AWTF natural treatment system from Autumn to Spring. Based on classical BEF studies, I expected a positive relationship between microbial biodiversity and ecosystem function, but also anticipated a potential effect of seasonal and spatial factors in strengthening or weakening the relationship. Instead, I found a significant negative BEF relationship between microbial community richness and ammonia removal. Ammonia concentration significantly decreased through the wastewater purification system, yet microbial diversity was unrelated to the different locations in the wastewater treatment system. In turn, seasonality significantly affected the microbial community diversity where richness was lower during Spring. Following the field study, I conducted a microcosm experiment to determine the direct effect of an environmental change in terms of dissolved oxygen (DO) concentration on biodiversity and ecosystem function. The DO concentration had a positive relationship with evenness and a negative relationship with richness. In addition to the DO relationships, I observed a negative correlation between evenness and nitrification which reflects the BEF relationship findings from the field study. Because the lower evenness values are associated with more ammonia removal, these results further support that ammonia removal capabilities of the AWTF are most efficient when fewer species dominate the microbial communities in the natural treatment system, regardless of oxygen levels and other environmental factors. By expanding our search for more microbial community BEF relationship scenarios we can further unravel how richness and evenness influence ecosystem processes in natural and humanized systems

Expectations Driven Nonlinear Business Cycles

The first part of the paper is a brief introduction to the concepts and methods used in recent endogenous business cycles models. Endogenous deterministic and stochastic fluctuations are bound to occur, under increasingly plausible assumptions, in models with individual optimization, market clearing and self-fulfilling expectations when there are capital market imperfections. The phenomenon is most likely to be observed, in a nonlinear framework, when some eigenvalue(s) of the system have a modulus close to 1 (unit roots). It is argued that endogenous business cycles models have become more and more credible alternatives to describe observed fluctuations in our economies. The second part of the paper reviews recent studies suggesting that self-fulfilling expectations are often dynamically unstable when learning is taken into account. The phenomenon is most likely to occur when expectations matter significantly, which might explain why actual economic time series display higher volatilities in markets for capital investment, inventories, durable goods, financial assets and stocks. It is suggested that on account of the important nonlinearities involved in learning, actual learning dynamics may generate highly complex, even chaotic, trajectories

On the interaction between quasilinear elastodynamics and the Navier-Stokes equations

The interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations, coupled to one another along the moving material interface through the continuity of the velocity and traction vectors. We prove the existence and uniqueness (locally in time) of strong solutions in Sobolev spaces for quasilinear elastodynamics coupled to the incompressible Navier-Stokes equations along a moving interface. Unlike our approach for the case of linear elastodynamics, we cannot employ a fixed-point argument on the nonlinear system itself, and are instead forced to regularize it by a particular parabolic artificial viscosity term. We proceed to show that with this specific regularization, we obtain a time interval of existence which is independent of the artificial viscosity; together with a priori estimates, we identify the global solution (in both phases), as well as the interface motion, as a weak limit in srong norms of our sequence of regularized problems.Comment: 43 pages, to appear in Archive for Rational Mechanics and Analysi

Transformations of the Commodity Space, Behavioral Heterogeneity and the Aggregation Problem

The aggregation problem in demand analysis and exchange equilibrium is studied by putting restrictions on the shape of the distribution of the agents’ characteristics. This is done by exploiting the finite dimensional linear structure induced on demand functions by affine transformations of the commodity space (or household equivalence scales). Increasing the degree of behavioral heterogeneity in the household sector or more specifically, making the conditional distributions in each equivalence class of demand functions fiat enough, has an important regularizing influence on aggregate budget shares: market demand has a negative dominant diagonal Jacobian matrix, aggregate excess demand has the gross substitutability property, on a large set of prices. These facts have strong consequences for the unicity and stability of equilibrium as well as for the prevalence of the weak axiom of revealed preference in the aggregate in a private ownership Walrasian exchange model