This book presents the contributions of the 20th century to economic theory in a mathematical language and in historical sequence. General equilibrium is the focal point of the book; but also a number of macroeconomic models, especially with respect to the first half of the century, are considered. Dynamic models are extensively studied per se, and not merely as extensions of their static counterparts. The book with its extensive bibliography gives a broad view over the developments in mathematical economics and is therefore an invaluable source of information for researchers and students working in this field.

Increasing efficiency in generating national income and improving equity in its distribution among economic agents is at the forefront of priorities of most modern economies. This book presents a model which aims to maximize a symmetrical welfare function under certain constraints which consider both efficiency and equity, i.e. taxes and subsidies, implemented by a public authority. The model is numerically implemented and considers a set of economic agents with starting incomes that satisfy Pareto income law under various values of the alpha parameter. Also, the model implementations respect the social production function. Various experiments are presented which show how income inequality (measured by means of the Lorenz curve and, what I call, the Lorenz-Gini inequality index) and measures of poverty are sensibly reduced by redistributing national income without lowering efficiency in production. A case study, or application, of Italian personal income in 2008 is also presented.

To write everything about nothing, or to write nothing about everything: this is the problem. (Anonym, circa 1996-97) The first idea to write a book on M athematical Economics, more or less ordered in a historical sequence, occurred to me in 1995, when I was asked, by Istituto delta Enciclopedia Italiana, to write the entry "Storia dell'economia 1 2 matematica," for the collective work "Storia deI XX Secolo." I thought that it would be interesting to elaborate on the text presented to the editors, to turn it into a book aiming at giving a panorama of what, in my opinion, are the main 20th century contributions to mathematical eco nomics. Of course, only a narrow set of the contributions made by economic theorists could be included, both for space limitations and necessity, because 3 of the limited competence of any single author. For instance, I have paid very limited attention to what is now called Macroeconomics, and also to Game Theory, which actually has grown so much as to acquire scientific in dependence as a living branch of applied mathematics. For the same reason, I have also left completely untouched such fields as Mathematical Finance, Public Economics, Theory of Taxation, etc. I have always based my presentation on published material only, assuming that what is contained in working papers still waits to be confirmed, possibly in the first years of the 21th century."

This book presents a macroeconomic dynamic model a la Solow-Swan, including the market for labor, in a discrete time structure. The model is expanded to include expenditure on R&D and public expenditure on infrastructure. For each of the three models the results are shown in time series figures, which demonstrate that even small changes in the parameters produce responses in the time behavior of the main variables: from steady growth, to regular cycles, to chaotic-like time paths."