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.

On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants.

In this paper we examine the time T to reach a critical number K0 of infections during an outbreak in an epidemic model with infective and susceptible immigrants. The underlying process X, which was first introduced by Ridler-Rowe (1967), is related to recurrent diseases and it appears to be analytically intractable. We present an approximating model inspired from the use of extreme values, and we derive formulae for the Laplace-Stieltjes transform of T and its moments, which are evaluated by using an iterative procedure. Numerical examples are presented to illustrate the effects of the contact and removal rates on the expected values of T and the threshold K0, when the initial time instant corresponds to an invasion time. We also study the exact reproduction number Rexact,0 and the population transmission number Rp, which are random versions of the basic reproduction number R0.