Uniqueness of Equilibrium in the Multi-Country Ricardo Model

We present two arguments, one based on index theory, demonstrating that the multi-country Ricardo model has a unique competitive equilibrium if the aggregate demand functions exhibit gross substitutability. The result is somewhat surprising because the assumption of gross substitutability is sufficient for uniqueness in a model of exchange but not, in general, when production is included in the model.Ricardo model, Gross substitutes, Uniqueness

Fire Retardancy in 2001

Fire is a world-wide problem which claims lives and causes significant loss of property. Some of the problems are discussed and the solution delineated. This peer-reviewed volume is designed to be as the state-of-the-art. This chapter provides a perspective for current work

Horizontal Product Differentiation in Auctions and Multilateral Negotiations

We experimentally compare first-price auctions and multilateral negotiations after introducing horizontal product differentiation into a standard procurement setting. The two institutions yield the buyer the same surplus, a difference from prior findings with homogeneous products that results from differentiation’s influence on the sellers’ pricing behavior. In particular, we find that introducing product differentiation intensifies price competition among the sellers in some treatments, and has no effect in others, which contrasts with the conventional wisdom that product differentiation softens competition.

Building Citywide Systems for Quality: A Guide and Case Studies for Afterschool Leaders

This guide is intended to help cities strengthen and sustain quality afterschool programs by using an emerging practice known as a quality improvement system (QIS). The guide explains how to start building a QIS or how to further develop existing efforts and features case studies of six communities' QIS

Application of Coloured Noise as a Driving Force in the Stochastic Differential Equations

In this chapter we explore the application of coloured noise as a driving force to a set of stochastic differential equations(SDEs). These stochastic differential equations are sometimes called Random flight models as in A. W. Heemink (1990). They are used for prediction of the dispersion of pollutants in atmosphere or in shallow waters e.g Lake, Rivers etc. Usually the advection and diffusion of pollutants in shallow waters use the well known partial differential equations called Advection diffusion equations(ADEs)R.W.Barber et al. (2005). These are consistent with the stochastic differential equations which are driven by Wiener processes as in P.E. Kloeden et al. (2003). The stochastic differential equations which are driven by Wiener processes are called particle models. When the Kolmogorov’s forward partial differential equations(Fokker-Planck equation) is interpreted as an advection diffusion equation, the associated set of stochastic differential equations called particle model are derived and are exactly consistent with the advection-diffusion equation as in A. W. Heemink (1990); W. M. Charles et al. (2009). Still, neither the advection-diffusion equation nor the related traditional particle model accurately takes into account the short term spreading behaviour of particles. This is due to the fact that the driving forces are Wiener processes and these have independent increments as in A. W. Heemink (1990); H.B. Fischer et al. (1979). To improve the behaviour of the model shortly after the deployment of contaminants, a particle model forced by a coloured noise process is developed in this chapter. The use of coloured noise as a driving force unlike Brownian motion, enables to us to take into account the short-term correlated turbulent fluid flow velocity of the particles. Furthermore, it is shown that for long-term simulations of the dispersion of particles, both the particle due to Brownian motion and the particle model due to coloured noise are consistent with the advection-diffusion equation. Keywords: Brownian motion, stochastic differential equations, traditional particle models, coloured noise force, advection-diffusion equation, Fokker-Planck equation

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