Duality on Banach spaces and a Borel parametrized version of Zippin's theorem

Let SB be the standard coding for separable Banach spaces as subspaces of $C(\Delta)$. In these notes, we show that if $\mathbb{B} \subset \text{SB}$ is a Borel subset of spaces with separable dual, then the assignment $X \mapsto X^*$ can be realized by a Borel function $\mathbb{B}\to \text{SB}$. Moreover, this assignment can be done in such a way that the functional evaluation is still well defined (Theorem $1$). Also, we prove a Borel parametrized version of Zippin's theorem, i.e., we prove that there exists $Z \in \text{SB}$ and a Borel function that assigns for each $X \in \mathbb{B}$ an isomorphic copy of $X$ inside of $Z$ (Theorem $5$)

Growth, Fiscal Policy and the Informal Sector in a Small Open Economy

We discuss the implications of informality on growth and fiscal policy by considering an informal sector based on low tech firms, in an open economy model of endogenous growth, where labour supply is elastic and increasing returns arise from public spending. We allow for both labour and capital to allocate between sectors and examine the dynamic and policy issues that arise in an economy, where long run outcomes are still dominated by formal activities, but long macroeconomic transitions arise as a result of informal microeconomic activities, which take advantage of both government taxation and limited fiscalization.Endogenous Growth Theory; Optimal Fiscal Policy; Informal Sector; Public Capital

Self-Enforcing Climate Change Treaties: A Generalized Differential Game Approach with Applications

Based on recent proposals on non cooperative dynamic games for analysing climate negotiation outcomes, such as Dutta and Radner (2004, 2006a), we generalize a specific framework for modelling differential games of this type and describe the set of conditions for the existence of closed loop dynamics and its relation to adaptive evolutionary dynamics. We then show that the Dutta and Radner (2004, 2006a) discrete time dynamic setup is a specific case of that generalization and describe the dynamics both analytically and numerically for closed loop feedback and perfect state patterns. Our discussion is completed with the introduction of a cooperative differential framework for welfare analysis purposes, within our non cooperative proposal for climate negotiations.Differential Game Theory, Environmental Economics, Evolutionary Dynamics, Climate Change Treaties