Advanced Microeconomic Theory

PREFACE

PART 1: ECONOMIC AGENTS

CHAPTER 1: CONSUMER THEORY

1.1 Primitive Notions

1.2 Preferences and Utility

1.2.1 Preference Relations

1.2.2 The Utility Function

1.3 The Consumer's Problem

1.4 Indirect Utility and Expenditure

1.4.1 The Indirect Utility Function

1.4.2 The Expenditure Function

1.4.3 Relations Between the Two

1.5 Properties of Consumer Demand

1.5.1 Relative Prices and Real Income

1.5.2 Income and Substitution Effects

1.5.3 Some Elasticity Relations

1.6 Exercises

CHAPTER 2: TOPICS IN CONSUMER THEORY

2.1 Duality: A Closer Look

2.1.1 Expenditure and Consumer Preferences

2.1.2 Convexity and Monotonicity

2.1.3 Indirect Utility and Consumer Preferences

2.2 Integrability

2.3 Revealed Preference

2.4 Uncertainty

2.4.1 Preferences

2.4.2 Von Neumann-Morgenstern Utility

2.4.3 Risk Aversion

2.5 Exercises

CHAPTER 3: THEORY OF THE FIRM

3.1 Primitive Notions

3.2 Production

3.2.1 Returns to Scale and Varying Proportions

3.3 Cost

3.4 Duality in Production

3.5 The Competitive Firm

3.5.1 Profit Maximisation

3.5.2 The Profit Function

3.6 Exercises

PART 2: MARKETS AND WELFARE

CHAPTER 4: PARTIAL EQUALIBRIUM

4.1 Perfect Competition

4.2 Imperfect Competition

4.2.1 Cournot Oligopoly

4.2.2 Bertrand Oligopoly

4.2.3 Monopolistic Competition

4.3 Equilibrium and Welfare

4.3.1 Price and Individual Welfare

4.3.2 Efficiency of the Competitive Outcome

4.3.3 Efficiency and Total Surplus Maximisation

4.4 Exercises

CHAPTER 5: GENERAL EQUALIBRIUM

5.1 Equilibrium in Exchange

5.2 Equilibrium in Competitive Market Systems

5.2.1 Existence of Equilibrium

5.2.2 Efficiency

5.3 Equilibrium in Production

5.3.1 Producers

5.3.2 Consumers

5.3.3 Equilibrium

5.3.4 Welfare

5.4 Contingent Plans

5.4.1 Time

5.4.2 Uncertainty

5.4.3 Walrasian Equilibrium with Contingent Commodities

5.5 Core and Equilibria

5.5.1 Replica Economies

5.6 Exercises

CHAPTER 6: SOCIAL CHOICE AND WELFARE

6.1 The Nature of the Problem

6.2 Social Choice and Arrow's Theorem

6.2.1 A Diagrammatic Proof

6.3 Measurability, Comparability, and Some Possibilities

6.3.1 The Rawlsian Form

6.3.2 The Utilitarian Form

6.3.3 Flexible Forms

6.4 Justice

6.5 Social Choice and the Gibbard-Satterthwaite Theorem

6.6 Exercises

PART 3: STRATEGIC BEHAVIOUR

CHAPTER 7: GAME THEORY

7.1 Strategic Decision Making

7.2 Strategic Form Games

7.2.1 Dominant Strategies

7.2.2 Nash Equilibrium

7.2.3 Incomplete Information

7.3 Extensive Form Games

7.3.1 Game Trees: A Diagrammatic Representation

7.3.2 An Informal Analysis of Take-Away

7.3.3 Extensive Form Game Strategies

7.3.4 Strategies and Payoffs

7.3.5 Games of Perfect Information and Backward Induction Strategies

7.3.6 Games of Imperfect Information and Subgame Perfect Equilibrium

7.3.7 Sequential Equilibrium

7.4 Exercises

CHAPTER 8: INFORMATION ECONOMICS 

8.1 Adverse Selection

8.1.1 Information and the Efficiency of Market Outcomes

8.1.2 Signalling

8.1.3 Screening

8.2 Moral Hazard and the Principal-Agent Problem

8.2.1 Symmetric Information

8.2.2 Asymmetric Information

8.3 Information and Market Performance

8.4 Exercises

CHAPTER 9: AUCTIONS AND MECHANISM DESIGN 

9.1 The Four Standard Auctions

9.2 The Independent Private Values Model

9.2.1 Bidding Behaviour in a First-Price, Sealed-Bid Auction

9.2.2 Bidding Behaviour in a Dutch Auction

9.2.3 Bidding Behaviour in a Second-Price, Sealed-Bid Auction

9.2.4 Bidding Behaviour in an English Auction

9.2.5 Revenue Comparisons

9.3 The Revenue Equivalence Theorem

9.3.1 Incentive-Compatible Direct Selling Mechanisms: A Characterisation

9.3.2 Efficiency

9.4 Designing a Revenue Maximising Mechanism

9.4.1 The Revelation Principle

9.4.2 Individual Rationality

9.4.3 An Optimal Selling Mechanism

9.4.4 A Closer Look at the Optimal Selling Mechanism

9.4.5 Efficiency, Symmetry, and Comparison to the Four Standard Auctions

9.5 Designing Allocatively Efficient Mechanisms

9.5.1 Quasi-Linear Utility and Private Values

9.5.2 Ex Post Pareto Efficiency

9.5.3 Direct Mechanisms, Incentive Comparability and the Revelation Principle

9.5.4 The Vickery-Clarke-Groves Mechanism

9.5.5 Achieving a Balanced Budget: Expected Externality Mechanisms

9.5.6 Property Rights, Outside Options, and Individual Rationality Contraints

9.5.7 The IR-VCG Mechanism: Sufficiency of Expected Surplus

9.6 Exercises

MATHEMATICAL APPENDICES

CHAPTER A1: SETS AND MAPPINGS

A1.1 Elements of Logic

A1.1.1 Necessity and Sufficiency

A1.1.2 Theorems and Proofs

A1.2 Elements of Set Theory

A1.2.1 Notation and Basic Concepts

A1.2.2 Convex Sets

A1.2.3 Relations and Functions

A1.3 A Little Topology

A1.3.1 Continuity

A1.3.2 Some Existence Theorems

A1.4 Real-Valued Functions

A1.4.1 Related Sets

A1.4.2 Concave Functions

A1.4.3 Quasiconcave Functions

A1.4.4 Convex and Quasiconvex Functions

A1.5 Exercises

CHAPTER A2: CALCULUS AND OPTIMISATION 

A2.1 Calculus

A2.1.1 Functions of a Single Variable

A2.1.2 Functions of Several Variables

A2.1.3 Homogeneous Functions

A2.2 Optimisation

A2.2.1 Real-Valued Functions of Several Variables

A2.2.2 Second-Order Conditions

A2.3 Constrained Optimisation

A2.3.1 Equality Constraints

A2.3.2 Lagrange's Method

A2.3.3 Geometric Interpretation

A2.3.4 Second-Order Conditions

A2.3.5 Inequality Constraints

A2.3.6 Kuhn-Tucker Conditions

A2.4 Optimality Theorems

A2.5 Separation Theorems

A2.6 Exercises

LIST OF THEOREMS

LIST OF DEFINITIONS

HINTS AND ANSWERS

REFERENCES

INDEX

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