A linear model to determine the optimal policy for investment in social infrastructure is formulated and its solution is obtained using the Maximum Principle. The unique solution is characterized by a-bang-bang control, with only one interval of investment in social capital, and the endpoints of this interval can be numerically determined, given values for the parameters of the model. A generalization of the model which allows instantaneous jumps in the level of social capital is also analyzed, and the solution to the modified problem is shown to be a uniquely determined impulse control. The final extension of the model allows us to determine an upper bound for the optimal time horizon. / Science, Faculty of / Mathematics, Department of / Graduate

The dissertation suggests that geographical, institutional, religious and cultural links may be determinants of growth. We address a number of issues in this thesis. The starting point is naturally a study on growth, while the main focus is on the analysis of inequalities between countries with respect to their environment, and also on inequalities within countries.<p>The very first step of the study, presented in Chapter one, is to build such non-physical relations between countries. In this chapter, we present both the choices and methods used to model the institutional and cultural weights matrices. Chapter 1 also presents a comparative study between the different matrices built. The final aim of this chapter is to identify the differences between the geographical, institutional and cultural environment.<p>The following chapter incorporates these innovative new types of matrices in a study on growth. An externality growth model is therefore developed that takes proximities between entities into account, whether geographical, institutional or cultural. The purpose of the chapter is threefold. First, it compares the results obtained from spatial econometrics methods with classical regression, where observations of growth are considered as independent. Second, it examines whether the development of an externality model improves the quality of the estimation. Third, it investigates whether the institutional and cultural types of proximity make sense compared to the geographical one.<p>Chapter 3 narrows the analysis of countries’ dependency with regard to their neighborhood, whether geographical, institutional or religious, and a quintile regression approach allows us to check whether the countries' wealth level matters. Do the poorest countries react in the same way as richer ones regarding the wealth of their geographical, institutional and religious neighbors? The gross impact of neighboring wealth on a country’s wealth is then estimated, and some relative effects of the three matrices combined are also shown, as well as the robustness of the estimates.<p><p>Finally, Chapter 4 analyzes the dependence of poverty regarding neighborhood. The relative wealth and poverty of the neighborhood are examined as factors that can influence a country’s poverty level. The poverty index used is the proportion of people living on less than one or two dollars a day. The study only considers the developing countries as data for the developed countries on the proportion of this variable is near zero. Once again, the final aim is to check whether a country’s poverty is exacerbated by its geographical, institutional and religious neighborhood poverty or if it takes advantage of neighborhood wealth to manage its own poverty issues.<p> / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished