Dynamic Economics: Optimization by the Lagrange Method

Dynamic Economics: Optimization by the Lagrange Method

Dynamic Economics: Optimization by the Lagrange Method

Dynamic Economics: Optimization by the Lagrange Method

Synopsis

This work provides a unified and simple treatment of dynamic economics using dynamic optimization as the main theme, and the method of Lagrange multipliers to solve dynamic economic problems. The author presents the optimization framework for dynamic economics in order that readers can understand the approach and use it as they see fit. Instead of using dynamic programming, the author chooses instead to use the method of Lagrange multipliers in the analysis of dynamic optimization because it is easier and more efficient than dynamic programming, and allows readers to understand the substance of dynamic economics better. The author treats a number of topics in economics, including economic growth, macroeconomics, microeconomics, finance and dynamic games. The book also teaches by examples, using concepts to solve simple problems; it then moves to general propositions.

Excerpt

Classical economic ideas, beginning with those recorded in Adam Smith Wealth of Nations (1776), have been refined, improved, and challenged. Two main ideas are that individuals pursue self-interests (or maximize utility and profits in a "rational" manner) and that markets can coordinate individual self- interests for the common good (or achieve a competitive equilibrium which is Pareto optimal) without government intervention. Observing the poverty of British workers in the 19th century, Karl Marx rejected these ideas. Witnessing the Great Depression in the 1930s Keynes wrote the General Theory (1936) and started a revolution against classical economics. Later the ideas of classical economics have been recovering from the Keynesian attack, to a large extent through the efforts of University of Chicago economists, beginning with Milton Freidman in the 1950s. Thus, the two main ideas of classical economics, the rationality of economic agents and the efficiency of markets, have gone through refinement and challenge. This book reports on the development of the economic ideas of self-interest and market equilibrium from the 1960s to the 1990s.

As the subtitle indicates, dynamic economic behavior is explained by assuming rationality of economic agents who optimize. Much of the book presents models in which markets are both clear and efficient. Both ideas are opposed to the main ideas of Keynes' General Theory. When I studied dynamic economics in the early 1970s, the idea of using optimization as the basis of dynamic economics was not as widely accepted as it is today. [See my Analysis and Control of Dynamic Economic Systems (1975, p. 22).] Today, some leading economists--including Robert Solow, who is the father of modern growth theory--do not believe that optimization together with market equilibrium is necessarily the way to model economic behavior. [See Solow article Perspective on Growth Theory, Journal of Economic Perspectives (1994, pp. 45-54) and his recent book A Critical Essay on Modern Macroeconomic Theory (MIT Press, 1995), coauthored with Frank Hahn.] Without taking a stand, I present in this book the optimization framework for . . .

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