Pareto-efficiency and endogenous fertility: a simple model

This article is devoted to the study of the Pareto-efficiency of the competitive equilibrium for a simple overlapping generations economy with endogenous fertility. For CES utility and production functions, it is proved that the economic properties of the economy are closely related to the two elasticitiesof substitution. First, the competitive equilibrium exists and is unique if the sum of the two elasticities is not smaller than one. Secondly, a set of parameters is provided such that the equilibrium is both in under-accumulation and inefficient. Thirdly, a sufficient condition is proved that ensures that an equilibrium converging in under-accumulation is Pareto-efficient: the sum of the two elasticities must not be greater than two.endogenous fertility ; Pareto-efficiency

A notion of sufficient input

In this paper, we study a notion of sufficient input, i.e. input that allows to produce at least one unit of output when the other inputs are fixed at any positive level. We show that such an input allows to produce any positive amount of production. The main property of sufficient inputs is as follows. A input is sufficient if and only if the unit cost goes to zero when its price goes to zero.

On Efficient Child Making

This paper is devoted to the study of the Pareto-efficiency of the competitive equilibrium for an overlapping generations economy with endogenous fertility. Pareto-efficiency needs a reformulation when fertility is endogenous. Then it is proved that a competitive equilibrium that converges in over-accumulation is non-Pareto-efficient. However, we provide an example in which a competitive equilibrium that converges in under-accumulation is non-Pareto-efficient. Finally, we give a general condition that ensures the Pareto-efficiency of the competitive equilibrium.endogenous fertility, Pareto-efficiency

How to Finance the Security of the International Trade ? A Global Public Good Approach

The aim of this article is to identify the modalities of financing international trade security. Our analysis is more specifically oriented by the issue of financing the developing countries which must make a considerable effort to attain the required level, whereas the developed countries have already largely invested in trade security since the events of 11th September 2001. We first characterise security in the context of a global public good, before studying the financing conditions and the discriminating criteria of the supply of the global public good security. We then presents a critical analysis of the various possible sources and instruments for financing the global public good security and propose different financing scenarios, each one based on a specific allocation of responsibilities among the players in security. We conclude by considering the role of the international institutions as project managers of the financing and implementation of the security of international trade.international, financing, global public goods, international trade, security

Cash-in-advance constraints, bubbles and monetary policy

In this paper, we study the equilibrium dynamics of an overlapping generations model with capital, money and cash-in-advance constraints. At each period, the economy can experience two different regimes: either the cash-inadvance constraint is binding and money is a dominated asset, or the constraint is strictly satisfied and money has the same return as capital. When the second regime occurs, we say that the economy experiences a temporary bubble. We show the existence of temporary bubbles, and we prove that cyclical equilibria may exist. In these equilibria, the economy experiences some periods without bubbles and some periods with bubbles. We also show that monetary creation can be used in order to eliminate temporary bubbles.overlapping generations model; bubbles; cash-in-advance constraint; monetary policy

Scale-up in laminar and transient regimes of a multi-stage stirrer, a CFD approach

A multi-stage industrial agitator system adapted to the mixing of a mixture whose viscosity varies during the process has been characterized by using CFD. In the entire study the mixture is supposed to have a Newtonian behavior even though it is rarely the case. It is shown that the well-adapted propeller is able to e7ciently blend high viscous media provided the Reynolds number is not too low. A scale-up study of the agitated system has also been carried out by respecting the classical scale-up rules such as the geometrical similarity and the conservation of the power per volume in the particular case of viscous media. Using an Eulerian approach, the hydrodynamics of three di9erent scales with geometrical similarity have been numerically characterized by the energy curve (power number versus Reynolds number) and by the Metzner and Otto constant in which both are required for scale-up procedure. Experimental power measurements have been carried out at the smaller scale so that simulations have been partially validated. New hydrodynamic criteria have also been introduced in order to quantify the =ows in the case of a multi-stage stirrer running at low Reynolds number. It has been shown how this hydrodynamic di9ers dramatically from one scale to another when scale-up at constant energy per volume is applied. From the CFD results, recommendations about the widely used scale-up rules have been suggested and modi>cations of stirring geometry have been proposed in order to reduce the =ow pattern variations during scale-up. ? 2002 Elsevier Science Ltd. All rights reserved

Verifying nondeterministic probabilistic channel systems against ω\omega-regular linear-time properties

Lossy channel systems (LCSs) are systems of finite state automata that communicate via unreliable unbounded fifo channels. In order to circumvent the undecidability of model checking for nondeterministic LCSs, probabilistic models have been introduced, where it can be decided whether a linear-time property holds almost surely. However, such fully probabilistic systems are not a faithful model of nondeterministic protocols. We study a hybrid model for LCSs where losses of messages are seen as faults occurring with some given probability, and where the internal behavior of the system remains nondeterministic. Thus the semantics is in terms of infinite-state Markov decision processes. The purpose of this article is to discuss the decidability of linear-time properties formalized by formulas of linear temporal logic (LTL). Our focus is on the qualitative setting where one asks, e.g., whether a LTL-formula holds almost surely or with zero probability (in case the formula describes the bad behaviors). Surprisingly, it turns out that -- in contrast to finite-state Markov decision processes -- the satisfaction relation for LTL formulas depends on the chosen type of schedulers that resolve the nondeterminism. While all variants of the qualitative LTL model checking problem for the full class of history-dependent schedulers are undecidable, the same questions for finite-memory scheduler can be solved algorithmically. However, the restriction to reachability properties and special kinds of recurrent reachability properties yields decidable verification problems for the full class of schedulers, which -- for this restricted class of properties -- are as powerful as finite-memory schedulers, or even a subclass of them.Comment: 39 page