Extended theory about the allocation of time: Description and application to the increase in the retirement age policies

This paper revises mainstream economic models which include time use in an explicit and endogenous manner, suggesting a extended theory which escape from the main problem existing in the literature. In order to do it, we start by presenting in section 2 the mainstream time use models in economics, showing their main features. Once this is done, we introduce the reader in the main problems this kind of well established models imply, within section 3, being the most highlighted the problem of joint production. Subsequently, we propose an extended theory which solves the problem of joint production; this is extensively described in section 4. Last, but not least, we apply this model to offer a time use analysis of the effect of a policy which increases the retirement age in a life-cycle perspective for a representative individual.

Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1+1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c=1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.