Does productive capital affect the order of resource exploitation?

The purpose of this paper is to show that in a general equilibrium framework it is never optimal to use high cost substitute after lower cost exhaustible resource even if it is possible to accumulate productive capital. Indeed if the high cost substitute is scarce it is always optimal to consume it simultaneously with a lower cost stock. Moreover it may be optimal to consume the high cost substitute before using a lower cost resource

Matrix representation of the time operator

In quantum mechanics the time operator $\Theta$ satisfies the commutation relation $[\Theta,H]=i$, and thus it may be thought of as being canonically conjugate to the Hamiltonian $H$. The time operator associated with a given Hamiltonian $H$ is not unique because one can replace $\Theta$ by $\Theta+ \Theta_{\rm hom}$, where $\Theta_{\rm hom}$ satisfies the homogeneous condition $[\Theta_{\rm hom},H]=0$. To study this nonuniqueness the matrix elements of $\Theta$ for the harmonic-oscillator Hamiltonian are calculated in the eigenstate basis. This calculation requires the summation of divergent series, and the summation is accomplished by using zeta-summation techniques. It is shown that by including appropriate homogeneous contributions, the matrix elements of $\Theta$ simplify dramatically. However, it is still not clear whether there is an optimally simple representation of the time operator.Comment: 13 pages, 3 figure

Mallarmé et la « valeur de bizarrerie » du poète comme ombre

L’obscurité est un des lieux communs majeurs entourant le nom Mallarmé,l’oeuvre et le poète. Si elle lui est souvent reprochée comme preuve de sonélitisme, Mallarmé en fait cependant le ressort de sa visibilité dans la communautélittéraire car elle lui confère une identité si particulière qu’elle en devientévidente et transmissible. C’est que l’obscurité a pour corollaire un autre lieucommun poétique, celui du lien privilégié de tout poète avec les ombres. Nousvoulons ainsi interroger la manière dont Mallarmé s’attèle à une fabrique del’ombre qui puisse répondre à la « crise de vers » scellée par la mort de Hugo, parune oeuvre toute d’obscurité et une fi gure de poète nimbée dans l’ombre commeune apparition toujours disparaissant

Funding for Universal Service Obligations in Electricity Sector : the case of green power development

The process of deregulation in network industries, in particular in the electric sector, raises the problem of Þnancing the Universal Service Obligations (USO) corresponding to the production, transport and distribution operations. In this paper, we study three ways of funding for an USO of production, especially the "green" electricity development: the Þnancing with cross-subsidies, the implementation of a fund (financing by a tax) and finally a voluntary funding system by direct subscriptions of consumers. We notably show that this last one Pareto dominates mostly, from a welfare point of view, the other scenarios.ELECTRICITY ; ENVIRONMENT ; REGULATION ; NETWORK ; UNIVERSAL SERVICE,