Lie algebra configuration pairing

We give an algebraic construction of the topological graph-tree configuration pairing of Sinha and Walter beginning with the classical presentation of Lie coalgebras via coefficients of words in the associative Lie polynomial. Our work moves from associative algebras to preLie algebras to graph complexes, justifying the use of graph generators for Lie coalgebras by iteratively expanding the set of generators until the set of relations collapses to two simple local expressions. Our focus is on new computational methods allowed by this framework and the efficiency of the graph presentation in proofs and calculus involving free Lie algebras and coalgebras. This outlines a new way of understanding and calculating with Lie algebras arising from the graph presentation of Lie coalgebras.Comment: 21 pages; uses xypic; ver 4. added subsection 3.4 outlining another computational algorithm arising from configuration pairing with graph

Growth and the Ageing Joneses

We incorporate Keeping-up-with-the-Joneses (KUJ) preferences into the Blanchard-Yaari(BY) framework and develop, using an AK technology, a model of balanced growth. In this context we investigate status preference, demographic, and pension policy shocks. We find that a higher degree of KUJ lowers economic growth, while, in contrast, a decrease in the fertility and mortality rates increase it. In the second part of the paper we extend the model by incorporating a Pay-as-you-go (PAYG) pension system with a statutory retirement date. This introduces a life-cycle in human wealth earnings and implies that the growth rate is higher under PAYG. We also consider the implications of an increase in the retirement date under both defined benefit and defined contribution schemes.relative consumption, OLG, endogenous growth, pension reform

Keeping up with the Ageing Joneses

In this paper we consider the implications of relative consumption externalities in the Blanchard-Yaari overlapping generations framework. Unlike most of the macroeconomic literature that studies this question, the differences between agents, and, thus, in their relative position, persist in equilibrium. We show in our fixed employment model that consumption externalities lower consumption and the capital stock in long-run equilibrium, a result in sharp contrast to the recent findings of Liu and Turnovsky (2005). In addition, we solve for the intertemporal path of the economy to investigate its response to demographic shocks, specifically, to permanent changes in the birth and death rates.Relative consumption, Overlapping generations, Demographic shocks

Growth and the Ageing Joneses

We incorporate Keeping-up-with-the-Joneses (KUJ) preferences into the Blanchard-Yaari (BY) framework and develop, using an AK technology, a model of balanced growth. In this context we investigate status preference, demographic, and pension policy shocks. We find that a higher degree of KUJ lowers economic growth, while, in contrast, a decrease in the fertility and mortality rates increase it. In the second part of the paper we extend the model by incorporating a Pay-as-you-go (PAYG) pension system with a statutory retirement date. This introduces a life-cycle in human wealth earnings and implies that the growth rate is higher under PAYG. We also consider the implications of an increase in the retirement date under both defined benefit and defined contribution schemes.Relative consumption, OLG, Endogenous growth, Pension reform