Olivier F. Morand

Bio: Olivier F. Morand is an academic researcher from University of Connecticut. The author has contributed to research in topics: Monotone polygon & Lipschitz continuity. The author has an hindex of 10, co-authored 26 publications receiving 362 citations.

Endogenous Fertility, Income Distribution, and Growth

Abstract: This article analyzes the interaction between growth and fertility via income distribution in a model in which fertility decisions are motivated by old-age support It provides an explanation of the demographic transition of an economy from a stage of increasing fertility and low growth to a stage of low fertility, high human capital investments, and high growth

Economic growth, longevity and the epidemiological transition.

Abstract: This paper integrates investments in health to a standard growth model where physical and human capital investments are the combined engines of growth. It shows the existence of two distinct health regimes separated by an “epidemiological transition.’’ The various patterns of this transition identified in the epidemiological literature can be mapped into the model. The model also leads to the important hypothesis that the epidemiological transition may induce an economy to switch to a modern growth regime.

A Qualitative Approach to Markovian Equilibrium in Infinite Horizon Economies with Capital

Abstract: Using lattice programming and order theoretic fixpoint theory, we develop a powerful class of monotone iterative methods that provide a qualitative theory of Markovian equilibrium for a large class of infinite horizon economies with capital. The class of economies is large and includes situations where the second welfare theorem fails as in models with public policy, valued fiat money, various forms of market imperfections (e.g., monopolistic competition), production externalities, and various other nonconvexities in the production sets. The methods can be easily adapted to construct symmetric Markov equilibrium in models with many agents and market incompleteness. As our methods are constructive, we prove they have important implications for characterizing the structure of numerical approximations to extremal Markovian equilibrium within the class. Of independent interest is our new approach to characterizing dynamic complementarities. We apply recent generalized envelope theorems found in the literature on nonsmooth analysis to characterize equilibrium value functions in our dynamic programming setting. Our fixed point algorithms are sharp, and are able to distinguish sufficient conditions under which Markovian equilibrium form a complete lattice of Lipschitz continuous, uniformily continuous and semi-continuous monotone functions as well as unique differentiable equilibrium. We develop a new collection of partial orders that allow us to conduct extensive monotone comparative dynamics on the space of economies. We conclude with a discussion of how the methods can be extended to economies with ordinal (as opposed to cardinal) forms of complementary.

SET-Valued Analysis

Abstract: “Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas. Multivalued analysis is a remarkable mixture of many different parts of mathematics such as point-set topology, measure theory and nonlinear functional analysis. It is also closely related to “Nonsmooth Analysis” (Chapter 5) and in fact one of the main motivations behind the development of the theory, was in order to provide necessary analytical tools for the study of problems in nonsmooth analysis. It is not a coincidence that the development of the two fields coincide chronologically and follow parallel paths. Today multivalued analysis is a mature mathematical field with its own methods, techniques and applications that range from social and economic sciences to biological sciences and engineering. There is no doubt that a modern treatise on “Nonlinear Functional Analysis” can not afford the luxury of ignoring multivalued analysis. The omission of the theory of multifunctions will drastically limit the possible applications.

Fixed Point Theory

Abstract: Formally we have arrived at the middle of the book. So you may need a pause for recovering, a pause which we want to fill up by some fixed point theorems supplementing those which you already met or which you will meet in later chapters. The first group of results centres around Banach’s fixed point theorem. The latter is certainly a nice result since it contains only one simple condition on the map F, since it is so easy to prove and since it nevertheless allows a variety of applications. Therefore it is not astonishing that many mathematicians have been attracted by the question to which extent the conditions on F and the space Ω can be changed so that one still gets the existence of a unique or of at least one fixed point. The number of results produced this way is still finite, but of a statistical magnitude, suggesting at a first glance that only a random sample can be covered by a chapter or even a book of the present size. Fortunately (or unfortunately?) most of the modifications have not found applications up to now, so that there is no reason to write a cookery book about conditions but to write at least a short outline of some ideas indicating that this field can be as interesting as other chapters. A systematic account of more recent ideas and examples in fixed point theory should however be written by one of the true experts. Strange as it is, such a book does not seem to exist though so many people are puzzling out so many results.

Inequality and Growth: Why Differential Fertility Matters

Abstract: We develop a new theoretical link between inequality and growth. In our model, fertility and education decisions are interdependent. Poor parents decide to have many children and invest little in education. A mean-preserving spread in the income distribution increases the fertility differential between the rich and the poor, which implies thatmore weight gets placed on families who provide little education. Consequently, an increase in inequality lowers average education and, therefore, growth. We find that this fertility-differential effect accounts for most of the empirical relationship between inequality and growth.

Inequality and Growth: Why Differential Fertility Matters

Abstract: We argue that inequality and growth are linked through differential fertility and the accumulation of human capital. We build an overlapping-generations model in which dynasties differ in their initial endowment with human capital. Growth, the income-distribution, and fertility are endogenous. Due to a quantiy-quality tradeoff, families with less human capital decide to have more children and invest less in education. When initial inequality is high, large fertility differentials lower the growth rate of average human capital, since poor families who invest little in education make up a large fraction of the population in the next generation. A calibrated model shows that this fertility-differential effect is quantitatively important. We also provide empirical evidence to confirm the links between inequality, differential fertility and growth suggested by the model.