Holdings: Modern microeconomics

Modern microeconomics:

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Bibliographic Details
Main Author:	Kumar, Brajesh (Author)
Format:	Book
Language:	English
Published:	Cranbrook, Kent, United Kingdom Global Professional Publ. 2009
Subjects:	Mikroökonomik Microeconomics Mikroökonomie
Online Access:	Inhaltsverzeichnis
Physical Description:	XIX, 323 S. graph. Darst. 24cm
ISBN:	9781906403300

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MARC


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adam_text	Contents PART-A Mathematics and Modern Economics 1. Fundamentals of Mathematics and Modern Economics .....................................................................3 1.1 Nature of Modern Economics .........................................................................................................3 Modern Economics and Economic Theory .........................................................................3 Assumptions and Properties Commonly Used Economics .................................................4 Analytical Framework of Modern Economics ....................................................................4 Methodology for Studying Modern Economics ..................................................................6 Roles, Generality, and Limitation of Economic Theory .....................................................7 Roles of Mathematics in Modern Economics .....................................................................8 Conversion between Economic and Mathematical Languages ...........................................9 Distinguish Necessary and Sufficient Conditions for Statements .......................................9 Language and Methods of Mathematics .........................................................................................9 1.2.1 Functions .............................................................................................................................9 1.2.2 Separating Hyperplane Theorem ......................................................................................11 1.2.3 Concave and Convex Functions ........................................................................................11 Optimization .....................................................................................................................12 The Envelope Theorem .....................................................................................................14 Point-to-Set Mappings ......................................................................................................15 Continuity of a Maximum .................................................................................................17 Fixed Point Theorems .......................................................................................................18 1.2 .2.4 .2.5 .2.6 .2.7 .2.8 PART - В Theory of Individual Decision Making 2. Theory of Consumer Behaviour ..........................................................................................................23 2.1 Introduction ...................................................................................................................................23 2.2 Consumption Set and Budget Constraint ......................................................................................23 XII Modern Microeconomics 2.2.1 Consumption Set ...............................................................................................................23 2.2.2 Budget Constraint .............................................................................................................24 2.3 Preferences and Utility ..................................................................................................................25 2.3.1 Preferences ........................................................................................................................25 2.3.2 The Utility Function ..........................................................................................................28 2.4 Utility Maximization and Optimal Choice ....................................................................................31 2.4.1 Consumer Behaviour: Utility Maximization .....................................................................31 2.4.2 Consumeris Optimal Choice .............................................................................................31 2.4.3 Consumeris First Order-Conditions ..................................................................................32 2.4.4 Sufficiency of Consumeris First-Order Conditions ..........................................................34 2.5 Indirect Utility, and Expenditure, and Money Metric Utility Functions .......................................37 2.5.1 The Indirect Utility Function ............................................................................................37 2.5.2 The Expenditure Function and Hicksian Demand ............................................................38 2.5.3 The Money Metric Utility Functions ................................................................................40 2.5.4 Some Important Identities .................................................................................................42 2.6 Duality Between Direct and Indirect Utility .................................................................................44 2.7 Properties of Consumer Demand ..................................................................................................46 2.7.1 Income Changes and Consumption Choice ......................................................................46 2.7.2 Price Changes and Consumption Choice ..........................................................................46 2.7.3 Income-Substitution Effect: The Slutsky Equation ...........................................................47 2.7.4 Continuity and Differentiability of Demand Functions .....................................................49 2.7.5 Inverse Demand Functions ...............................................................................................50 2.8 The Integrability Problem .............................................................................................................51 2.9 Revealed Preference .....................................................................................................................53 2.9.1 Axioms of Revealed Preferences ......................................................................................53 2.9.2 Characterization of Revealed Preference Maximization ..................................................54 2.10 Recoverability ...............................................................................................................................55 2.11 Topics in Demand Behaivour ........................................................................................................57 2.11.1 Endowments in the Budget Constraint ............................................................................57 2.11.2 Income-Leisure Choice Model .......................................................................................58 2.11.3 Homothetic Utility Functions ..........................................................................................58 2.11.4 Aggregating Across Goods .............................................................................................58 2.11.5 Aggregating Across Consumers ......................................................................................62 3. Theory of Production ...........................................................................................................................65 3.1 Introduction ...................................................................................................................................65 3.2 Production Technology .................................................................................................................65 3.2.1 Measurement of Inputs and Outputs .................................................................................65 3.2.2 Specification of Technology .............................................................................................66 3.2.3 Common Properties of Production Sets ............................................................................68 Preface ХИ! 3.2.4 Returns to Scale ................................................................................................................69 3.2.5 The Marginal Rate of Technical Substitution ...................................................................70 3.2.6 The Elasticity of Substitution ............................................................................................70 3.3 Profit Maximization ......................................................................................................................72 3.3.1 Producer Behaviour ..........................................................................................................72 3.3.2 Produceris Optimal Choice ...............................................................................................72 3.3.3 Produceris First-Order Conditions ....................................................................................73 3.3.4 Sufficiency of Produceris First-Order Condition ..............................................................74 3.3.5 Properties of Net Supply Functions ..................................................................................75 3.3.6 Weak Axiom of Profit Maximization ................................................................................76 3.3.7 Recoverability ...................................................................................................................77 3.4 Profit Function ..............................................................................................................................78 3.4.1 Properties of the Profit Function .......................................................................................78 3.4.2 Deriving Net Supply Functions from Profit Function .......................................................79 3.5 Cost Minimization ........................................................................................................................79 3.5.1 First-Order Conditions of Cost Minimization ...................................................................80 3.5.2 Sufficiency of First-Order Conditions for Cost Minimization ..........................................81 3.6 Cost Functions ..............................................................................................................................84 3.6.1 Properties of Cost Functions .............................................................................................84 3.6.2 Properties of Conditional Input Demand ..........................................................................85 3.6.3 Average and Marginal Costs .............................................................................................85 3.6.4 The Geometry of Costs .....................................................................................................87 3.6.5 Long-Run and Short-Run Cost Curves .............................................................................88 3.7 Duality in Production ....................................................................................................................89 3.7.1 Recovering a Production Set from a Cost Function ..........................................................89 3.7.2 Characterization of Cost Functions ...................................................................................91 3.7.3 The Integrability for Cost Functions .................................................................................92 4. Theory of Choices Under Uncertainty ................................................................................................95 4.1 Introduction ...................................................................................................................................95 4.2 Expected Utility Theory ................................................................................................................95 4.2.1 Lotteries ............................................................................................................................95 4.2.2 Expected Utility ................................................................................................................96 4.2.3 Uniqueness of the Expected Utility Function ...................................................................98 4.2.4 Other Notations for Expected Utility ................................................................................98 4.3 Riskaversion .................................................................................................................................99 4.3.1 Absolute Risk Aversion .....................................................................................................99 4.3.2 Global Risk Aversion ......................................................................................................101 4.3.3 Relative Risk Aversion ....................................................................................................103 4.4 State Dependent Utility ...............................................................................................................104 4.5 Subjective Probability Theory ....................................................................................................104 XIV Modern Microeconomics PART - С Strategic Behavior and Markets 5. Theory of Game ..................................................................................................................................109 5.1 Introduction .................................................................................................................................109 5.2 Description of a game .................................................................................................................109 5.2.1 Strategic Form .................................................................................................................109 5.3 Solution Concepts .......................................................................................................................112 5.3.1 Mixed Strategies and Pure Strategies ..............................................................................112 5.3.2 Nash equilibrium .............................................................................................................113 5.3.3 Dominant strategies ........................................................................................................114 5.4 Repeated games ..........................................................................................................................115 5.5 Refinements of Nash equilibrium ...............................................................................................116 5.5.1 Elimination of dominated strategies ...............................................................................117 5.5.2 Sequential Games and Subgame Perfect Equilibrium ....................................................117 5.5.3 Repeated games and subgame perfection .......................................................................121 5.6 Games with incomplete information ...........................................................................................121 5.6.1 Bayes-Nash Equilibrium .................................................................................................121 5.6.2 Discussion of Bayesian-Nash equilibrium ......................................................................123 6. Theory of Market ...............................................................................................................................125 6.1 Introduction .................................................................................................................................125 6.2 The Role of Prices ......................................................................................................................125 6.3 Perfect Competition ....................................................................................................................126 6.3.1 Assumptions on Competitive Market .............................................................................126 6.3.2 The Competitive Firm .....................................................................................................126 6.3.3 The Competitive Firmis Short-Run Supply Function .....................................................126 6.3.4 Partial Market Equilibrium .............................................................................................128 6.3.5 Competitive in the Long Run ..........................................................................................129 6.4 Pure Monopoly ...........................................................................................................................130 6.4.1 Profit Maximization Problem of Monopolist ..................................................................130 6.4.2 Inefficiency of Monopoly ...............................................................................................131 6.4.3 Monopoly in the Long Run .............................................................................................132 6.5 Monopolistic Competition ..........................................................................................................132 6.6 Oligopoly ....................................................................................................................................134 6.6.1 Cournot Oligopoly ..........................................................................................................134 6.6.2 Stackelberg Model ..........................................................................................................135 6.6.3 Bertrand Model ...............................................................................................................136 6.6.4 Collusion .........................................................................................................................137 6.7 Monopsony .................................................................................................................................137 Preface XV Part - D Theory of General Equilibrium and Social Welfare 7. Theory of Equilibrium: Existence, Uniqueness, and Stability (A Positive Appraoch) .................141 7.1 Introduction .................................................................................................................................141 7.2 The Structure of General Equilibrium Model .............................................................................142 7.2.1 Economic Environments .................................................................................................142 7.2.2 Institutional Arrangement: Private Market Mechanism ..................................................143 7.2.3 Individual Behavior Assumptions: ..................................................................................143 7.2.4 Competitive Equilibrium ................................................................................................144 7.3 Some Examples of GE Models: Graphical Treatment ................................................................145 7.3.1 Pure Exchange Economies ..............................................................................................145 7.3.2 The One-Consumer and One Producer Economy ...........................................................149 7.4 The Existence of Competitive Equilibri urn .................................................................................151 7.4.1 The Existence of CE for Aggregate Excess Demand Functions .....................................151 7.4.2 The Existence of CE for Aggregate Excess Demand Correspondences .........................161 7.4.3 The Existence of CE for General Production Economies ...............................................162 7.5 The Uniqueness of Competitive Equilibria .................................................................................162 7.6 Stability of Competitive Equilibrium ..........................................................................................163 7.7 Abstract Economy .......................................................................................................................169 7.7.1 Equilibrium in Abstract Economy ...................................................................................169 7.7.2 The Existence of Equilibrium for General Preferences ..................................................170 8. Theory of Equilibrium: Its Welfare Properties (A Normative Appraoch) ....................................173 8.1 Introduction .................................................................................................................................173 8.2 Pareto Efficiency of Allocation ...................................................................................................173 8.3 The First Fundamental Theorem of Welfare Economics ............................................................177 8.4 Calculations of Pareto Optimum by First-Order Conditions ......................................................179 8 4.1 Exchange Economies ......................................................................................................179 8.4.2 Production Economies ....................................................................................................180 8.5 The Second Fundamental Theorem of Welfare Economics ........................................................181 8.6 Non-Convex Production Technologies and Marginal Cost Pricing ............................................184 8.7 Pareto Optimality and Social Welfare Maximization .................................................................187 8.7.1 Social Welfare Maximization for Exchange Economies .................................................187 8.7.2 Welfare Maximization in Production Economy ..............................................................188 8.8 Political Overtones ......................................................................................................................189 9. Economic Core, Fair Allocations, and Social Choice Theory .........................................................191 9.1 Introduction .................................................................................................................................191 9.2 The Core of Exchange Economies ..............................................................................................191 9.3 Fairness of Allocation .................................................................................................................195 9.4 Social Choice Theory ..................................................................................................................198 XVI Modern Microeconomice 9.4.1 Introduction ..................................................................................................................... 198 9.4.2 Basic Settings .................................................................................................................. 199 9.4.3 Arrowis Impossibility Theorem...................................................................................... 200 9.4.4 Some Positive Result: Restricted Domain ......................................................................202 9.4.5 Gibbard-Satterthwaite Impossibility Theorem ................................................................204 10. Theory of General Equilibrium Under Uncertainty .......................................................................207 10.1 Introduction .................................................................................................................................207 10.2 A Market Economy with Contingent Commodities ....................................................................207 10.3 Arrow-Debreu Equilibrium .........................................................................................................210 10.4 Sequential Trade .........................................................................................................................215 10.5 Incomplete Markets ....................................................................................................................220 Part - E Externalities and Public Goods 11. Externalities .......................................................................................................................................225 11.1 Introduction .................................................................................................................................225 11.2 Consumption Externalities ..........................................................................................................225 11.3 Production Externality ................................................................................................................232 11.4 Solutions to Externalities ............................................................................................................233 11.4.1 Pigovian Tax .................................................................................................................233 11.4.2 Coase Voluntary Negotiation ........................................................................................234 11.4.3 Missing Market .............................................................................................................236 11.4.4 The Compensation Mechanism .....................................................................................236 12. Public Goods .......................................................................................................................................239 12.1 Introduction .................................................................................................................................239 12.2 Notations and Basic Settings ......................................................................................................239 12.3 Discrete Public Goods ................................................................................................................240 12.3.1 Efficient Provision of Public Goods .............................................................................240 12.3.2 Free-Rider Problem ......................................................................................................241 12.3.3 Voting for a Discrete Public Good ................................................................................242 12.4 Continuous Public Goods ...........................................................................................................242 12.4.1 Efficient Provision of Public Goods .............................................................................242 12.4.2 Lindahl Equilibrium ......................................................................................................244 12.4.3 Free-Rider Problem ......................................................................................................247 Part- F Incentives, Information, and Mechanism Design 13. Principal-Agent Model: Hidden Information ..................................................................................251 13.1 Introduction .................................................................................................................................251 13.2 The Basic Model .........................................................................................................................252 Preface XVII 13.2.1 Economic Environment (Technology, Preferences, and Information) ..........................252 13.2.2 Contracting Variables: Outcomes................................................................................. 252 13.2.3 Timmg ...........................................................................................................................252 13.3 The Complete Information Optimal Contract (Benchmark Case) ..............................................253 13.3.1 First-Best Production Levels ........................................................................................253 13.3.2 Implementation of the First-Best ..................................................................................253 13.3.3 A Graphical Representation of the Complete Information Optimal Contract ...............254 13.4 Incentive Feasible Contracts .......................................................................................................255 13.4.1 Incentive Compatibility and Participation ....................................................................255 13.4.2 Special Cases ................................................................................................................255 13.4.3 Monotonicity Constraints .............................................................................................256 13.5 Information Rents .......................................................................................................................256 13.6 The Optimization Program of the Principal ................................................................................257 13.7 The Rent Extraction-Efficiency Trade-Off .................................................................................258 13.7.1 The Optimal Contract Under Asymmetric Information ................................................258 13.7.2 A Graphical Representation of the Second-Best Outcome ...........................................259 13.7.3 Shutdown Policy ...........................................................................................................260 13.8 The Theory of the Firm Under Asymmetric Information ............................................................260 13.9 Asymmetric Information and Marginal Cost Pricing ..................................................................261 ІЗ.ІОТЬе Revelation Principle ............................................................................................................261 13.11 A More General Utility Function for the Agent ..........................................................................262 13.11.1 The Optimal Contract .................................................................................................263 13.11.2 More than One Good ..................................................................................................264 13.12EX Ante versus Ex Post Participation Constraints ......................................................................265 13.12.1 Risk Neutrality ............................................................................................................265 13.12.2 Risk Aversion ..............................................................................................................266 13.13 Commitment ................................................................................................................................269 13.13.1 Renegotiating a Contract ............................................................................................269 13.13.2 Reneging on a Contract ...............................................................................................269 13.14 Informative Signals to Improve Contracting ...............................................................................269 13.14.1 Ex Post Verifiable Signal ............................................................................................270 13.15 Contract Theory at Work .............................................................................................................270 13.15.1 Regulation ...................................................................................................................271 13.15.2 Nonlinear Pricing by a Monopoly ..............................................................................271 13.15.3 Quality and Price Discrimination ................................................................................272 13.15.4 Financial Contracts .....................................................................................................273 13.15.5 Labor Contracts ..........................................................................................................273 13.16The Optimal Contract with a Continuum of Types .....................................................................274 13.17 Further Extensions ......................................................................................................................277 XVIII Modern Microeconomice 14. Moral Hazard: The Basic Trade-Offs .............................................................................................. 279 14.1 Introduction .................................................................................................................................279 14.2 The Model ...................................................................................................................................279 14.2.1 Effort and Production ...................................................................................................279 14.2.2 Incentive Feasible Contracts .........................................................................................280 14.2.3 The Complete Information Optimal Contract ...............................................................281 14.3 Risk Neutrality and First-Best Implementation ..........................................................................282 14.4 The Trade-Off Between Limited Liability Rent Extraction and Efficiency ................................283 14.5 The Trade-Off Between Insurance and Efficiency ......................................................................284 14.5.1 Optimal Transfers .........................................................................................................285 14.5.2 The Optimal Second-Best Effort ..................................................................................286 14.6 More than Two Levels of Performance .......................................................................................286 14.6.1 Limited Liability ...........................................................................................................287 14.6.2 Risk Aversion ................................................................................................................288 14.7 Contract Theory at Work .............................................................................................................289 14.7.1 Efficiency Wage ............................................................................................................289 14.7.2 Sharecropping ...............................................................................................................289 14.7.3 Wholesale Contracts .....................................................................................................291 14.7.4 Financial Contracts .......................................................................................................291 14.8 A Continuum of Performances ....................................................................................................292 14.9 Further Extension ........................................................................................................................293 15. General Mechanism Design ...............................................................................................................295 15.1 Introduction .................................................................................................................................295 15.2 Basic Settings ..............................................................................................................................296 15.2.1 Economic Environments ...............................................................................................296 15.2.2 Social Goal ...................................................................................................................296 15.2.3 Economic Mechanism ...................................................................................................297 15.2.4 Solution Concept of Self-Interested Behavior ..............................................................297 15.2.5 Implementation and Incentive Compatibility ................................................................298 15.3 Examples .....................................................................................................................................299 15.4 Dominant Strategy and Truthful Revelation Mechanism ............................................................300 15.5 Gibbard-Satterthwaite Impossibility Theorem ............................................................................301 15.6 Hurwicz Impossibility Theorem .................................................................................................302 15.7 Groves-Clarke-Vickrey Mechanism ............................................................................................303 15.7.1 Groves-Clark Mechanism for Discrete Public Good ....................................................303 15.7.2 The Groves-Clark-Vickery Mechanism with Continuous Public Goods ......................306 15.8 Nash Implementation ............................................................................. 309 15.8.1 Nash Equilibrium and General Mechanism Design ......................................................309 15.8.2 Characterization of Nash Implementation ....................................................................310 ___________________________________________________________________ Preface ХІХ 15.9 Better Mechanism Design ...........................................................................................................314 15.9.1 Groves-Ledyard Mechanism .........................................................................................314 15.9.2 Walkerís Mechanism .....................................................................................................315 15.9.3 Tianís Mechanism .........................................................................................................317 15.10 Incomplete Information and Bayesian Nash Implementation .....................................................319
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