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.

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.

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.

Demand for less skilled workers decreased dramatically in the US and in other developed countries over the past two decades. We argue that pervasive skill-biased technological change rather than increased trade with the developing world is the principal culprit. The pervasiveness of this technological change is important for two reasons. First, it is an immediate and testable implication of technological change. Second, under standard assumptions, the more pervasive the skill-biased technological change the greater the increase in the embodied supply of less skilled workers and the greater the depressing effect on their relative wages through world goods prices. In contrast, in the Heckscher-Ohlin model with small open economies, the skill-bias of local technological changes does not affect wages. Thus, pervasiveness deals with a major criticism of skill-biased technological change as a cause. Testing the implications of pervasive, skill-biased technological change we find strong supporting evidence. First, across the OECD, most industries have increased the proportion of skilled workers employed despite rising or stable relative wages. Second, increases in demand for skills were concentrated in the same manufacturing industries in different developed countries.

Theory of Technical Change and Economic Invariance: Application of Lie Groups presents the economic invariance problems observable behavior under general transformations such as taste change or technical change. This book covers a variety of topics in economic theory, ranging from the analysis of production functions to the general recoverability problem of optimal dynamic behavior. Organized into nine chapters, this book begins with an overview of the theory of observable behavior by analyzing the invariant relationships among economic variables. This text then examines the Lie group theory which provides one of the most efficient methods of studying invariance properties. Other chapters consider the analysis of exogenous technical change, a process partly due to dynamic market forces of supply and demand. This book discusses as well the topics closely related to parametric changes under Lie groups and related transformations. The final chapter deals with mathematical foundations of the theory of observable market behavior. This book is a valuable resource for economists.

In the second edition of this user-friendly book, Olivier de La Grandville provides a clear and original introduction to the theory of economic growth, its mechanisms and its challenges. The book has been fully updated to incorporate several important new results and proofs since the first edition. In addition to a progressive treatment of dynamic optimization, readers will find intuitive derivations of all central equations of the calculus of variations and of optimal control theory. It offers a new solution to the fundamental question: How much should a nation save and invest? La Grandville shows that the optimal savings rule he suggests not only corresponds to the maximization of future welfare flows for society, but also maximizes the value of society's activity, as well as the total remuneration of labour. The rule offers a fresh alternative to dire current predictions about an ever-increasing capital–output ratio and a decrease of the labour share in national income.

Since the very beginnings of economics as a science, which might be dated from Ibn Khaldun's "Introduction to History" (1377), the challenge of making societies escape from poverty and attain some degree of prosperity has always been, and can remain, a fundamental issue. This book presents research on each of these issues.