Locally Provided Public Schooling in Brazilian Municipalities

The objective of this paper is to assess the demand for public schooling in the Brazilian municipalities within a median voter framework. The quantile regression and spatial techniques proved to be useful to account for the spatial and marginal effects associated with educational services. The coefficients attached to the main variables – price, income and population – were significant and had the expected sign. The relatively high values for those parameters attest the status for these merit goods as “luxuries”. Last, but no least, the municipal school system in Brazil seems to present increasing returns to scale both, at the school and the municipality level.Public Schooling, Demand, Brazilian municipalities, Median voter

Economic Consequences of Low Fertility in Europe

This special issue of the European Journal of Population focuses on possible economic consequences of low fertility in Europe. This introduction reviews the history of falling fertility in Europe and the literature that explores its causes, its potential implications, and possible policy responses. It also summarizes the evolution of thinking about the relationship between population growth and economic development, with attention to recent work on the mechanisms through which fertility decline can spur economic growth if the necessary supporting conditions are met. The introduction also identifies some of the challenges of population aging that are associated with low fertility and suggests that there may be less reason for alarm than has been suggested by some observers. The papers that appear in this special issue are also summarized.Economic consequences, low fertility, Europe

Economic consequences of low fertility in Europe

This paper focuses on possible economic consequences of low fertility in Europe. It summarizes a selection of papers that were presented at a conference at the University of St. Gallen in April 2008. This introduction also reviews the history of falling fertility in Europe and the literature that explores its causes, its potential implications, and possible policy responses. It summarizes the evolution of thinking about the relationship between population growth and economic development, with attention to recent work on the mechanisms through which fertility decline can spur economic growth if the necessary supporting conditions are met. The paper also identifies some of the challenges of population aging that are associated with low fertility and suggests that there may be less reason for alarm than has been suggested by some observers. --

A new truncated MM-fractional derivative type unifying some fractional derivative types with classical properties

We introduce a truncated $M$-fractional derivative type for $\alpha$-differentiable functions that generalizes four other fractional derivatives types recently introduced by Khalil et al., Katugampola and Sousa et al., the so-called conformable fractional derivative, alternative fractional derivative, generalized alternative fractional derivative and $M$-fractional derivative, respectively. We denote this new differential operator by $_{i}\mathscr{D}_{M}^{\alpha,\beta }$, where the parameter $\alpha$, associated with the order of the derivative is such that $0 0$ and $M$ is the notation to designate that the function to be derived involves the truncated Mittag-Leffler function with one parameter. The definition of this truncated $M$-fractional derivative type satisfies the properties of the integer-order calculus. We also present, the respective fractional integral from which emerges, as a natural consequence, the result, which can be interpreted as an inverse property. Finally, we obtain the analytical solution of the $M$-fractional heat equation and present a graphical analysis.Comment: 16 pages, 3 figure