The Stability of a Macroeconomic System with Quantity Constraints

ISBN-13: 9783540119920 / Angielski / Miękka / 1983 / 172 str.

P. Van Den Heuvel

Spis treści

1. Introduction.- 1.1. Scope.- 1.2. Relevant economic notions.- 1.3. Walras Equilibria.- 1.3.1. Definitions and background.- 1.3.2. Existence and uniqueness.- 1.4. Non-Walrasian Equilibria.- 1.4.1. Definitions.- 1.4.2. Background and some literature.- 1.4.3. The logic of Non-Walrasian Equilibria.- 1.4.4. Existence and uniqueness.- 1.5. Dynamics and Stability.- 1.5.1. Walras Equilibria.- 1.5.2. Non-Walrasian Equilibria.- 1.6. Outline.- 2. Mathematical Results in Optimization and Stability.- 2.1. Introduction and notation.- 2.2. Some concepts in analysis and optimization.- 2.3. Definitions and properties concerning stability.- 2.3.1. Differential systems.- 2.3.2. Stability properties of autonomous differential systems.- 2.3.3. Liapunov functions.- 2.4. Stability of piecewise differentiable systems.- 2.4.1. General results.- 2.4.2. Continuous systems.- 2.4.3. Discontinuous systems.- 3. Static Model.- 3.1. Introduction.- 3.2. Description of the basic model.- 3.3. Voluntary trades.- 3.4. Properties of demand and supply functions.- 3.5. Non-Walrasian Equilibrium states.- 3.5.1. Definition and several types of Non-Walrasian Equilibrium states.- 3.5.2. Existence and uniqueness results.- 3.5.3. Differentiability of transaction with respect to the parameters.- 3.6. Locations in the parameter space.- 3.7. Extensions.- Appendix: Proofs with respect to Sections 3.2-3.4.- 4. Dynamic Model.- 4.1. Introduction.- 4.2. Formulation of a dynamic system.- 4.2.1. Adjustments of stocks.- 4.2.2. Adjustments of prices.- 4.2.3. A differential system describing the dynamic model.- 4.3. Analysis of the adjustment functions.- 4.3.1. Adjustments of stocks.- 4.3.2. Adjustments of prices.- 4.3.3. The differentiability of the system.- 4.4. Walras Equilibria in the dynamic model.- 4.5. Locations in the parameter space.- 4.6. The BGM-model.- 4.7. Extensions.- 5. Stability Properties of the Different Types of Equilibria.- 5.1. Possible types of equilibria in the dynamic model.- 5.2. Walras Equilibria in IR2.- 5.2.1. Introduction.- 5.2.2. Linearization of regimes and right-hand sides.- 5.2.3. Stability of the subsystems.- 5.2.4. Stability of the total system.- 5.2.5. An alternative approach.- 5.3. Stability of other equilibria in IR2.- 5.3.1. Introduction.- 5.3.2. An assumption concerning the signs of the derivatives of the excess demand functions.- 5.3.3. Inflation equilibria.- 5.3.4. Keynesian equilibria.- 5.4. Walras Equilibria in IR3.- 5.4.1. Introduction.- 5.4.2. Linearization of regimes and right-hand sides.- 5.4.3. Discontinuity of the right-hand sides.- 5.4.4. Mathematical description of the linearized system.- 5.4.5. Stability of the subsystems.- 5.4.6. Stability of the total system.- 5.4.7. A heuristic approach.- 5.5. Stability of other equilibria in IR3.- 5.5.1. Introduction.- 5.5.2. An assumption concerning the signs of the derivatives of the excess demand functions.- 5.5.3. Inflation equilibria.- 5.5.4. Keynesian equilibria.- 6. Conclusions.- 6.1. General concluding remarks.- 6.2. Conclusions concerning stability.- 6.2.1. Some general stability results.- 6.2.2. The weight factors.- 6.2.3. Consequences of the addition of an inventory.- 6.2.4. Specifications of excess demand functions.- 6.3. Epilogue.- List of Symbols.- List of Assumptions.- References.