Does the existence of secondary markets for durable goods affect price and allocation on primary markets? We study competitive equilibria for durable goods where the possibility of future trade on secondary markets does not affect consumer behaviour in the primary market, provided consumers are exponential discounters. If consumers are hyperbolic discounters, however, secondary markets are no l...

Recently David Laibson and others have argued in favor of using hyperbolic discount functions. The purpose of this paper is to investigate whether conventional wisdom, based on the standard model with exponential discounting, also holds in the case where consumers have hyperbolic discount functions. In other words do hyperbolic preferences matter for practical policy evaluation? Within the fram...

We introduce the (2+1)-spacetimes with compact space of genus g ≥ 0 and r gravitating particles which arise by Minkowskian suspensions of flat or hyperbolic cone surfaces, by distinguished deformations of hyperbolic suspensions and by patchworking of suspensions. Similarly to the matter-free case, these spacetimes have nice properties with respect to the canonical Cosmological Time Function. Wh...

If G is a finitely presented group, then H2 (∞) (G,A) vanishes for all injective Banach spaces iff the regularized homological area function satisfies the linear isoperimetric inequality. This contrasts with the known result that G is word hyperbolic iff the homological area function satisfies the linear isoperimetric inequality. A closed 3-manifold group G is hyperbolic iff H2 (∞) (G,A) vanish...

Subgroup growth is an important new area of group theory. It attempts to quantify the number of finite index subgroups of a group, as a function of their index. In this paper, we will provide new, strong lower bounds on the subgroup growth of a variety of different groups. This will include the fundamental groups of all finite-volume hyperbolic 3-manifolds. By using the correspondence between s...

In this article, a generalized (G′/G)-expansion method is used to find exact travelling wave solutions of the Burgers equation and the Korteweg-de Vries (KdV) equation with variable coefficients. As a result, hyperbolic, trigonometric, and rational function solutions with parameters are obtained. When these parameters are taking special values, the solitary wave solutions are derived from the h...