Measuring Nash Equilibrium Consumption Externalities

We estimate Nash equilibrium consumption externalities in household petrol budget shares. The reaction curves are obtained from an AIDS with petrol consumption externality. Using a continuous set of ten year cross sections from FES (1991-2000), we analyse the externality generated by households living in Newcastle area (UK). In each year, income decile cohorts are created. Panel techniques are used after pooling cross section estimates have been discussed. Using non nested procedures, two restricted models are compared: the cohort specific externality effect and the single popular case. The single popular is the model accepted by the data.Household Economics; Nath Equilibirum; Externalities; Cross-Sectional Models; Models with Panel Data hazard; non-responsiveness; resource allocation

History of the foundation of the School of Anatomy and Surgery

In the year 1676, Grand Master Fra Niccolo' Cottoner introduced the teaching of Anatomy in the Holy Infirmary of the Order. The decree, laying the foundation for the teaching of Anatomy and Surgery in Our Islands, read as follows: Diecadem Gran Maestro di haver instituto a proprie spese nella Sacra Infermeria lo studio di Chirurgia et Anatomia, deputando un Medico fisico, perche' facci detta lettione non solemente alli barberotti di essa, ma a qualsiasi altro, che vorra' attendere a detti professioni; intendendo lasciar stabilito lo studio, se riuscira' di profitto sopra le vendite della sua fondatione perche' in avvenire si deputi sempre a d'affetto un Maestro di gli conduminji di Gran Maestri Suo successori. Il che fu da tutto il Venerabile Consiglio non solamente approvato, ma sommamente commendato il zelo di sua per l'introduzione di cose tanto necessario et importante'. A condition laid down in the Cottoner foundation, was that the occupant of the Chair of Anatomy and Surgery had to be a physician, besides being a surgeon. This decree was dated 19th December 1676.peer-reviewe

Universality and time-scale invariance for the shape of planar L\'evy processes

For a broad class of planar Markov processes, viz. L\'evy processes satisfying certain conditions (valid \textit{eg} in the case of Brownian motion and L\'evy flights), we establish an exact, universal formula describing the shape of the convex hull of sample paths. We show indeed that the average number of edges joining paths' points separated by a time-lapse $\Delta \tau \in \left[\Delta \tau _1, \Delta \tau_2\right]$ is equal to $2\ln \left(\Delta \tau_2 / \Delta \tau_1 \right)$, regardless of the specific distribution of the process's increments and regardless of its total duration $T$. The formula also exhibits invariance when the time scale is multiplied by any constant. Apart from its theoretical importance, our result provides new insights regarding the shape of two-dimensional objects modelled by stochastic processes' sample paths (\textit{eg} polymer chains): in particular for a total time (or parameter) duration $T$, the average number of edges on the convex hull ("cut off" to discard edges joining points separated by a time-lapse shorter than some $\Delta \tau < T$) will be given by $2 \ln \left(\frac{T}{\Delta \tau}\right)$. Thus it will only grow logarithmically, rather than at some higher pace.Comment: 8 pages, 3 figures, accepted in PR

From Markovian to non-Markovian persistence exponents

We establish an exact formula relating the survival probability for certain L\'evy flights (viz. asymmetric $\alpha$-stable processes where $\alpha = 1/2$) with the survival probability for the order statistics of the running maxima of two independent Brownian particles. This formula allows us to show that the persistence exponent $\delta$ in the latter, non Markovian case is simply related to the persistence exponent $\theta$ in the former, Markovian case via: $\delta=\theta/2$. Thus, our formula reveals a link between two recently explored families of anomalous exponents: one exhibiting continuous deviations from Sparre-Andersen universality in a Markovian context, and one describing the slow kinetics of the non Markovian process corresponding to the difference between two independent Brownian maxima.Comment: Accepted in EP

Convex hull of n planar Brownian paths: an exact formula for the average number of edges

We establish an exact formula for the average number of edges appearing on the boundary of the global convex hull of n independent Brownian paths in the plane. This requires the introduction of a counting criterion which amounts to "cutting off" edges that are, in a specific sense, small. The main argument consists in a mapping between planar Brownian convex hulls and configurations of constrained, independent linear Brownian motions. This new formula is confirmed by retrieving an existing exact result on the average perimeter of the boundary of Brownian convex hulls in the plane.Comment: 14 pages, 8 figures, submitted to JPA. (Typo corrected in equation (14).

Efficient Allocations, Equilibria and Stability in Scarf's Economy

Scarf's economy has been a vehicle in understanding stability properties in exchange economies. The full set of market equilibria and Pareto optimal allocations for this economy has not been analysed. This paper aims to do that. Firstly, we examine the Pareto optima and we find three different classes. Only Class I exhausts the aggregate endowments of all the goods. Class II and III involve throwing away partially or totally one good in order to achieve Pareto efficiency. Secondly, we explore the price and endowment distribution combinations which sustain the different Pareto Optima as market equilibria. A Pareto optimum which involves throwing away the whole endowment of one of the goods is globally stable.Exchange economy, Complements, Stability