Modem geometric methods combine the intuitiveness of spatial visualization with the rigor of analytical derivation. Classical analysis is shown to provide a foundation for the study of geometry while geometrical ideas lead to analytical concepts of intrinsic beauty. Arching over many subdisciplines of mathematics and branching out in applications to every quantitative science, these methods are, notes the Russian mathematician A.T. Fomenko, in tune with the Renais sance traditions. Economists and finance theorists are already familiar with some aspects of this synthetic tradition. Bifurcation and catastrophe theo ries have been used to analyze the instability of economic models. Differential topology provided useful techniques for deriving results in general equilibrium analysis. But they are less aware of the central role that Felix Klein and Sophus Lie gave to group theory in the study of geometrical systems. Lie went on to show that the special methods used in solving differential equations can be classified through the study of the invariance of these equations under a continuous group of transformations. Mathematicians and physicists later recognized the relation between Lie's work on differential equations and symme try and, combining the visions of Hamilton, Lie, Klein and Noether, embarked on a research program whose vitality is attested by the innumerable books and articles written by them as well as by biolo gists, chemists and philosophers.

Symmetry and Economic Invariance (second enhanced edition) explores how the symmetry and invariance of economic models can provide insights into their properties. Although the professional economist of today is adept at many of the mathematical techniques used in static and dynamic optimization models, group theory is still not among his or her repertoire of tools. The authors aim to show that group theoretic methods form a natural extension of the techniques commonly used in economics and that they can be easily mastered. Part I provides an introduction that minimizes prerequisites including prior knowledge of group theory. Part II discusses recent developments in the field.

Editor is well known. She is presidnet of the History of Economics Society and has completed a 12 year term as editor of the Eastern Economics Journal Work is controversial - challenges the relevance of mathematics in economics

Productivity of inputs is an important determinant of the competitiveness of firms in national and international markets. Productivity growth arises from deliberate decisions to innovate but the technological opportunities could be such that different inputs would have different rates of growth. Previous literature has mostly concentrated on labor productivity but empirical studies indicate that productivity of capital is also increasing. One of the objectives of this book is to examine the difference or bias in the productivity growth of the two inputs. In this book, application of this general approach to study of biased technical change is developed and new empirical results presented for both macroeconomies and microeconomic firms.

In modern economies a substantial proportion of resources is increasingly allocated to transaction costs. An improvement in the definition of transaction costs to include both the information role and efficiency role requires an integration of the approaches of positive economics and normative economics. In The Economics of Transaction Costs P.K.Rao provides a comprehensive analytical treatment of the subject and suggests a few directions for formal economic models.

This handbook offers a unique and original collection of analytical studies in Islamic economics and finance, and constitutes a humble addition to the literature on new economic thinking and global finance. The growing risks stemming from higher debt, slower growth, and limited room for policy maneuver raise concerns about the ability and propensity of modern economies to find effective solutions to chronic problems. It is important to understand the structural roots of inherent imbalance, persistence-in-error patterns, policy and governance failures, as well as moral and ethical failures. Admittedly, finance and economics have their own failures, with abstract theory bearing little relation with the real economy, uncertainties and vicissitudes of economic life. Economic research has certainly become more empirical despite, or perhaps because of, the lack of guidance from theory. The analytics of Islamic economics and finance may not differ from standard frameworks, methods, and techniques used in conventional economics, but may offer new perspectives on the making of financial crises, nature of credit cycles, roots of financial system instability, and determinants of income disparities. The focus is placed on the logical coherence of Islamic economics and finance, properties of Islamic capital markets, workings of Islamic banking, pricing of Islamic financial instruments, and limits of debt financing, fiscal stimulus and conventional monetary policies, inter alia. Readers with investment, regulatory, and academic interests will find the body of analytical evidence to span many areas of economic inquiry, refuting thereby the false argument that given its religious tenets, Islamic economics is intrinsically narrative, descriptive and not amenable to testable implications. Thus, the handbook may contribute toward a redefinition of a dismal science in search for an elusive balance between rationality, ethics and morality, and toward a remodeling of economies based on risk sharing and prosperity for all humanity

Symmetry and Economic Invariance: An Introduction explores how symmetry and invariance of economic models can provide insights into their properties. While the professional economist is nowadays adept at many of the mathematical techniques used in static and dynamic optimization models, group theory is still not among his or her repertoire of tools. The authors aim to show that group theoretic methods form a natural extension of the techniques commonly used in economics and that they can be easily mastered.