Economic Dynamics: Methods and Models - 1st Edition - ISBN: 9780444854193, 9780444601223

Economic Dynamics: Methods and Models

1st Edition

Authors: G Gandolfo
eBook ISBN: 9780444601223
Imprint: North Holland
Published Date: 1st September 1983
Page Count: 571
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Description

Economic Dynamics: Methods and Models aims to give a simple but comprehensive treatment of mathematical methods used in economic dynamics and show how they are utilized to build and to analyze dynamic models. The text also focuses on methods, and every mathematical technique introduced is followed by its application to selected models. The book is divided into three different parts. Part I: Different Equations discusses general principles; first-order, second-order, higher-order equations; simultaneous systems; and their economic applications. Part II: Differential Equations also discusses the same areas as those in Part I, but instead features differential equations, as what the section name suggests. Part III: More Advanced Material covers comparative statistics and the comparative principle; stability of equilibrium and Liapunov's second method; and linear mixed differential and difference equations, as well as its other related topics. The text is recommended for mathematicians and economists who have an idea on advanced mathematics and would like to know more about its applications in economics.

Table of Contents


Contents

Preface to the second edition

Preface to the first edition

Introduction

Part I Difference equations (linear and with constant coefficients)

Chapter 1 General Principles

Chapter 2 First-order equations

Chapter 3 Some Economic Applications of First Order Equations

§ 1 The cobweb theorem

§2 The dynamics of multipliers

§ 3 A formalization of Harrod's model

§4 A simple dynamic model of income inflation

Chapter 4 Second-order equations

Chapter 5 Some economic applications of second-order equations

§ 1 Samuelson's multiplier-accelerator model

§2 Hicks' trade cycle model

§3 Metzler's inventory cycle model

§4 Expectations and cobweb theorem (Goodwin)

§5 Monetary factors and multiplier-accelerator interaction (Smyth)

Chapter 6 Higher-order equations

Chapter 7 Some economic applications of higher-order equations

§ 1 Distributed lags and multiplier-accelerator interaction (Hicks)

§2 Expectations and inventory cycles (Metzler)

Chapter 8 Simultaneous systems

§ 1 First-order systems in normal form

§ 2 Stability conditions

§3 Particular solution. Determination of the arbitrary constants

§4 General systems

Chapter 9 Some economic applications of simultaneous systems

§ 1 Multiplier effects in an open economy

§2 Capital stock adjustment and extrapolative expectations

§3 Smithies' model

Part II Differential equations (linear and with constant coefficients)

Chapter 1 General principles

Chapter 2 First-order equations

Chapter 3 Some economic applications of first-order equations

§ 1 Stability of supply and demand equilibrium

§2 A re-formulation of the cobweb theorem

§3 Domar's model

§4 The neoclassical aggregate growth model (Solow)

§5 Money and growth in the neoclassical aggregate model (Stein)

Chapter 4 Second-order equations

Chapter 5 Some economic applications of second-order equations

§ 1 Phillips' stabilization model for a closed economy

§2 A model of foreign exchange speculation under floating exchange rates

Chapter 6 Higher-order equations

Chapter 7 Some economic applications of higher-order equations

§ 1 Phillips' integral stabilization policy

§2 Expectations and inventory adjustment

Chapter 8 Simultaneous systems

§ 1 First-order systems in normal form

§2 Stability conditions

§3 Particular solution. Determination of the arbitrary constants

§4 General systems

Chapter 9 Some economic applications of simultaneous systems

§ 1 Stability of Walrasian general equilibrium of exchange

§2 Leontief 's dynamic model

§3 The stability of a barter international equilibrium (Marshall-Kemp)

§4 A digression on 'arrow diagrams'

§5 Flexible exchange rates and the level of national income (Laursen and Metzler)

§6 Full employment and balance of payments equilibrium under fixed and flexible exchange rates: the 'assignment problem'

§7 A two-sector growth model (Shinkai)

§8 Rational and adaptive expectations in deterministic models (Evans and Yarrow)

Part III More advanced material

Chapter 1 Comparative statics and the correspondence principle

§ 1 Introduction

§2 The method of comparative statics

§3 Comparative statics and maximizing behaviour: an example from traditional demand theory

§4 Comparative statics and the dynamic stability of equilibrium: the 'correspondence principle'

§5 Extrema and dynamic stability: an application to the theory of the firm

§6 Elements of comparative dynamics

§7 Some economic applications of the correspondence principle

7.1 The 'complete' Keynesian model

7.2 The foreign trade multiplier under flexible exchange rates

Chapter 2 The stability of equilibrium and Liapunov 's 'second method'

§ 1 The concept of stability

§2 Liapunov's 'second method': general concepts

§3 The fundamental theorems

§4 Some economic applications

4.1 Global stability of Walrasian general equilibrium (Arrow et al.)

4.2 Rules of thumb in business management (Baumol and Quandt)

4.3.Price adjustment and oligopoly under product differentiation (Okuguchi)

Chapter 3 Other topics in differential and difference equations

§ 1 Introduction

§2 Exact equations of the first order and of the first degree

§3 Linear equations of the first order with variable coefficients

§4 The Bernoulli 'equation

§5 Elements of the qualitative theory of non-linear differential equations

5.1 Single equations

5.2 Systems of two simultaneous equations

5.3 The Lotka-Volterra equations 448

§6 Elements of the qualitative theory of non-linear difference equations

§7 Some economic applications

7.1 The neoclassical aggregate growth model again (Solow)

7.2 Embodied technical progress and 'vintage' models (Solow-Bergstrom)

7.3 A cyclical model by Goodwin

7.4 Goodwin's growth cycle

7.5 Uzawa's two-sector model of economic growth

7.6 A multi-sector extension of the neoclassical growth model and the 'Hahn problem' (Burmeister et al.)

7.7 The stability of Kaldor's 1957 growth model (Champernowne)

Chapter 4 Linear mixed differential-difference equations

§1 General concepts

§2 The method of solution and the stability conditions

§3 Some economic applications

3.1 Kalecki's (1935) model

3.2 A formalization of the classical price-specie-flow mechanism of balance of payments adjustment

Bibliography

Author index

Subject index

Details

No. of pages:
571
Language:
English
Copyright:
© North Holland 1971
Published:
Imprint:
North Holland
eBook ISBN:
9780444601223

About the Author

G Gandolfo