Description
The concept of general equilibrium, one of the central components of economic theory, explains the behavior of supply, demand, and prices by showing that supply and demand exist in balance through pricing mechanisms. The mathematical tools and properties for this theory have developed over time to accommodate and incorporate developments in economic theory, from multiple markets and economic agents to theories of production.
Yves Balasko offers an extensive, up-to-date look at the standard theory of general equilibrium, to which he has been a major contributor. This book explains how the equilibrium manifold approach can be usefully applied to the general equilibrium model, from basic consumer theory and exchange economies to models with private ownership of production. Balasko examines properties of the standard general equilibrium model that are beyond traditional existence and optimality. He applies the theory of smooth manifolds and mappings to the multiplicity of equilibrium solutions and related discontinuities of market prices. The economic concepts and differential topology methods presented in this book are accessible, clear, and relevant, and no prior knowledge of economic theory is necessary.
General Equilibrium Theory of Value offers a comprehensive foundation for the most current models of economic theory and is ideally suited for graduate economics students, advanced undergraduates in mathematics, and resea
Chapter
CHAPTER 3: DEMAND FUNCTIONS
3.2 CONSTRAINED UTILITY MAXIMIZATION
3.3 THE INDIVIDUAL DEMAND FUNCTION
3.4 PROPERTIES OF DEMAND FUNCTIONS IN D
3.5 DEMAND-BASED CONSUMER THEORY
CHAPTER 4: THE EXCHANGE MODEL
4.2 THE SETS ..., ... , AND ... OF m-TUPLES OF DEMAND FUNCTIONS DEFINING THE EXCHANGE MODEL
4.5 THE EQUILIBRIUM MANIFOLD AND THE NATURAL PROJECTION
4.6 THE SMOOTH EQUILIBRIUM MANIFOLD
4.7 SMOOTHNESS OF THE NATURAL PROJECTION
4.8 CRITICAL AND REGULAR POINTS AND VALUES
CHAPTER 5: THE EQUILIBRIUM MANIFOLD
5.2 GLOBAL PROPERTIES AND THEIR INTEREST
5.3 THE NO-TRADE EQUILIBRIA
5.4 THE FIBERS OF THE EQUILIBRIUM MANIFOLD
5.5 THE EQUILIBRIUM MANIFOLD AS A COLLECTION OF LINEAR FIBERS PARAMETERIZED BY THE NO-TRADE EQUILIBRIA
5.6 A PICTURE OF THE EQUILIBRIUM MANIFOLD
5.7 DIFFEOMORPHISM WITH ...
CHAPTER 6: APPLICATIONS OF THE GLOBAL COORDINATE SYSTEM
6.2 COORDINATE SYSTEM (A)
6.3 COORDINATE SYSTEM (B)
6.4 FORMULAS OF THE NATURAL PROJECTION
6.5 THE JACOBIAN MATRIX OF AGGREGATE EXCESS DEMAND
CHAPTER 7: THE BROAD PICTURE
7.3 SMOOTH SELECTION AT A REGULAR EQUILIBRIUM
7.4 THE EQUILIBRIUM MANIFOLD OVER REGULAR ECONOMIES
7.5 GENERICITY OF REGULAR ECONOMIES
7.6 THE DEGREES OF THE NATURAL PROJECTION
CHAPTER 8: THE FINE PICTURE
8.2 AGGREGATE DEMAND AT A NO-TRADE EQUILIBRIUM
8.3 REGULARITY OF THE NO-TRADE EQUILIBRIA
8.4 THE SET OF EQUILIBRIUM ALLOCATIONS
8.5 ECONOMIES WITH A UNIQUE EQUILIBRIUM
8.6 DEGREE OF THE NATURAL PROJECTION
8.7 THE SET OF REGULAR EQUILIBRIA
CHAPTER 9: PRODUCTION WITH DECREASING RETURNS
9.2 PRODUCTION SETS: DEFINITIONS
9.3 PRODUCTION SETS: MAIN PROPERTIES
9.4 THE FIRM’S OBJECTIVE FUNCTION
9.5 THE STRICT DECREASING RETURNS TO SCALE FIRM
9.6 THE NET SUPPLY FUNCTION AS A PRIMITIVE CONCEPT
CHAPTER 10: EQUILIBRIUM WITH DECREASING RETURNS
10.2 THE GENERAL EQUILIBRIUM MODEL WITH PRIVATE OWNERSHIP OF DECREASING RETURNS TO SCALE FIRMS
10.3 PRODUCTION ADJUSTED DEMAND FUNCTIONS
10.4 THE EQUIVALENT EXCHANGE MODEL
10.5 PROPERNESS OF THE NATURAL PROJECTION
CHAPTER 11: PRODUCTION WITH CONSTANT RETURNS
11.3 THE NET SUPPLY CORRESPONDENCE
11.5 NET SUPPLY CORRESPONDENCE OF A SMOOTH CONSTANT RETURNS TO SCALE FIRM
11.6 THE GRAPH OF THE NET SUPPLY CORRESPONDENCE
CHAPTER 12: EQUILIBRIUM WITH CONSTANT RETURNS
12.2 DECREASING AND CONSTANT RETURNS: GENERAL CASE
12.3 CONSTANT RETURNS: REDUCED FORM
12.4 EQUILIBRIA OF THE MODEL N
12.5 THE EQUILIBRIUM MANIFOLD APPROACH
12.6 THE EQUILIBRIUM MANIFOLD FOR THE MODEL N
12.7 THE NATURAL PROJECTION
12.8 REGULAR AND CRITICAL EQUILIBRIA
12.9 DEGREES OF THE NATURAL PROJECTION
12.10 REGULAR AND SINGULAR ECONOMIES
12.11 UNIQUENESS OF EQUILIBRIUM OVER …(T)
12.12 THE NATURAL PROJECTION AS A FINITE COVERING OF THE SET OF REGULAR ECONOMIES
12.13 VALUES OF THE NATURAL PROJECTION DEGREES
A.1 POINTS, VECTORS, INNER PRODUCT
A.3 SECOND-ORDER DERIVATIVES AND THE HESSIAN MATRIX OF A SMOOTH FUNCTION
APPENDIX B: POINT-SET TOPOLOGY
APPENDIX C: SMOOTH MANIFOLDS
C.1 THE IMPLICIT FUNCTION THEOREM
C.2 SMOOTH MANIFOLDS AND SUBMANIFOLDS
C.3 SMOOTH MAPPINGS, IMMERSIONS, AND SUBMERSIONS
APPENDIX D: SINGULARITIES OF SMOOTH MAPS
D.1 CRITICAL AND REGULAR POINTS
D.2 SINGULAR AND REGULAR VALUES
D.4 THE REGULAR VALUE THEOREM
D.5 THE CASE WHERE dimX = dimY
D.7 SURJECTIVITY OF MAPS WITH NON-ZERO MODULO 2 DEGREE
E.1 CONVEX AND STRICTLY CONVEX SETS
E.2 QUASI-CONCAVE FUNCTIONS
E.3 SMOOTH QUASI-CONCAVITY AND SECOND-ORDER DERIVATIVES
E.4 BORDERED HESSIAN OF A SMOOTHLY QUASI-CONCAVE FUNCTION
E.5 RECESSION CONE OF A CONVEX SET
F.1 DIMENSION OF SEMI-ALGEBRAIC SETS
General Equilibrium Theory of Value
：General Equilibrium Theory of Value
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