Advanced Microeconomics

Preface
Contents
CHAPTER I. Cooperation as the central focus of microeconomics
1. Three modes of cooperation
1.1. Decentral mechanism.
1.2. Bargaining.
1.3. Dictatorship.
2. This book
2.1. Overview.
2.2. Concept.
Part A. Basic decision and preference theory
CHAPTER II. Decisions in strategic form
1. Introduction and three examples
2. Sets, functions, and real numbers
2.1. Sets, tuples, and Cartesian products.
2.2. Injective and surjective functions.
2.3. Real numbers.
3. Dominance and best responses
4. Mixed strategies and beliefs
4.1. Probability distribution.
4.2. Mixing strategies and states of the world.
4.3. Extending payoff definitions.
4.4. Four different best-response functions.
5. Rationalizability
6. Topics and literature
7. Solutions
8. Further exercises without solutions
CHAPTER III. Decisions in extensive form
1. Introduction and two examples
2. Decision trees and actions
2.1. Perfect information.
2.2. Imperfect information.
3. Strategies and subtrees: perfect information
3.1. Strategies.
3.2. Subtrees and subtree perfection.
3.3. Backward induction for perfect information.
3.4. The money pump.
4. Strategies and subtrees: imperfect information
4.1. Strategies and subtrees.
4.2. Behavioral strategies.
4.3. Imperfect recall and strategies.
4.4. Equivalence of mixed and behavioral strategies.
5. Moves by nature, imperfect information, and perfect recall
5.1. Decision situation.
5.2. Backward induction for imperfect information.
6. Topics
7. Solutions
8. Further exercises without solutions
CHAPTER IV. Ordinal preference theory
1. The vector space of goods and its topology
1.1. The vector space of goods.
1.2. Distance and balls.
1.3. Open and closed sets.
1.4. Sequences and convergence.
2. Preference relations
2.1. Relations and equivalence classes.
2.2. Preference relations and indifference curves.
3. Axioms: convexity, monotonicity, and continuity
3.1. Convex preferences.
3.2. Monotonicity of preferences.
3.3. Continuous preferences.
4. Utility functions
4.1. Definition.
4.2. Examples.
4.3. Strictly increasing transformations (uniqueness).
4.4. Existence.
4.4.1. Existence is not guaranteed.
4.4.2. Existence of a continuous utility function.
5. Quasi-concave utility functions and convex preferences
6. Marginal rate of substitution
6.1. Mathematics: some differentiation rules.
6.2. Economics: the marginal rate of substitution.
7. Topics
8. Solutions
9. Further exercises without solutions
CHAPTER V. Decisions under risk
1. Simple and compound lotteries
1.1. Simple lotteries as bundles and trees.
1.2. Compound lotteries.
2. The St. Petersburg lottery
2.1. The paradox.
2.2. Limited resources as a resolution?
2.3. Expected utility as a resolution?
2.4. Bounded utility.
3. Preference axioms for lotteries
3.1. Preference axioms.
3.2. A utility function for lotteries.
3.3. The construction of the vNM utility function.
4. Risk attitudes
4.1. Concave and convex functions.
4.2. Risk aversion and risk loving.
4.3. Certainty equivalent and risk premium.
4.4. Arrow-Pratt measure of risk aversion.
4.5. Risk aversion and risk loving in an X1-X2-diagram.
5. Stochastic dominance
5.1. Distribution and density functions.
5.2. First-order stochastic dominance.
5.3. Second-order stochastic dominance.
6. Topics
7. Solutions
8. Further exercises without solutions
Part B. Household theory and theory of the firm
CHAPTER VI. The household optimum
1. Budget
1.1. Money budget.
1.2. Endowment budget.
2. The household optimum
2.1. The household’s decision situation and problem.
2.2. MRS versus MOC.
2.3. Household optimum and monotonicity.
3. Comparative statics and vocabulary
3.1. Vocabulary.
3.2. Price-consumption curve and demand curve.
3.3. Income-consumption curve and Engel curve.
3.4. Defining substitutes and complements.
3.5. Price elasticities of demand.
3.6. Income elasticity of demand.
3.7. Aggregation of individual demand curves.
4. Solution theory
4.1. The general setup of an optimization problem.
4.2. Existence.
4.3. Uniqueness.
4.4. Local solutions and global solutions.
4.5. Interior solutions, boundary solutions, and corner solutions.
4.6. Boundary non-corner solutions and the Lagrange method.
4.6.1. The Lagrange theorem.
4.6.2. Applying the Lagrange method.
5. Indirect utility function
5.1. Definition.
5.2. Revisiting the Lagrange multiplier.
5.3. The indirect utility function is quasi-convex in prices and income.
6. Consumer’s rent and Marshallian demand
7. Topics
8. Solutions
9. Further exercises without solutions
CHAPTER VII. Comparative statics and duality theory
1. The duality approach
1.1. Maximization problem and minimization problem.
1.2. The expenditure function.
1.3. Applying the Lagrange method to expenditure minimization.
1.4. The duality theorem.
1.5. Main results.
2. Envelope theorems and Shephard’s lemma
2.1. The example of the expenditure function.
2.2. Envelope theorem without constraints.
2.3. Envelope theorem with equality constraints.
2.4. Application: Shephard’s lemma.
2.5. Application of the application: Roy’s identity.
3. Concavity, the Hesse matrix, and the Hicksian law of demand
3.1. Compensated (Hicksian) law of demand.
3.2. Concavity and the Hesse matrix.
3.3. The expenditure function is concave.
3.4. Application: the diagonal entries of the expenditure function’s Hesse matrix.
3.5. Application: the off-diagonal entries of the expenditure function’s Hesse matrix.
4. Slutsky equations
4.1. Three effects of a price increase.
4.2. Two different substitution effects.
4.3. The Slutsky equation for the money budget.
4.4. The Slutsky equation for the endowment budget.
4.4.1. Derivation.
4.4.2. Application: consumption today versus consumption tomorrow.
4.4.3. Application: leisure versus consumption.
4.4.4. Application: contingent consumption.
5. Compensating and equivalent variations
5.1. The case of good air quality.
5.2. Compensating or equivalent variation?
5.3. Price changes.
5.4. Applying duality.
5.5. Variations for a price change and Hicksian demand.
5.5.1. Applying the fundamental theorem of calculus.
5.5.2. Comparisons.
5.5.3. Consumers’ rent.
6. Topics
7. Solutions
8. Further exercises without solutions
CHAPTER VIII. Production theory
1. The production set
1.1. The vector space of goods and inputs.
1.2. Definition of a production set.
1.3. Further axioms.
2. Efficiency
2.1. Input efficiency and output efficiency.
2.2. Definitions: production function and isoquant.
2.3. Edgeworth box and transformation curve.
3. Convex production sets and convave production functions
3.1. Convexity of the production set and concavity of the production function.
3.2. Convex production sets versus convex better sets.
3.3. What about concave utility functions?
4. Exploring the production mountain (function)
4.1. Factor variations.
4.2. Partial factor variation: marginal productivity, average productivity and production elasticity.
4.3. Marginal something equals average something.
4.4. Proportional factor variation: returns to scale.
4.5. Isoquant factor variation: Marginal rate of technical substitution.
4.6. Isoclinic factor variation.
5. Topics
6. Solutions
7. Further exercises without solutions
CHAPTER IX. Cost minimization and profit maximization
1. Revisiting the production set
1.1. Definition of profit.
1.2. Which good is an input and which an output?
1.3. Revealed profit maximization.
2. Cost minimization
2.1. The problem.
2.2. A comparison with household theory.
2.3. Isoclinic factor variation and the graphical derivation of the cost function.
2.4. Cost-minimization and its dual.
2.5. Main results.
3. Long-run and short-run cost minimization
3.1. Fixed factors and short-run cost function.
3.2. Fixed and quasi-fixed cost.
4. Profit maximization
4.1. Profit maximization (output space).
4.2. Producer’s rent.
4.3. Solution theory, second part.
4.4. Profit maximization (input space).
5. Profit maximization?
5.1. Two problems of our theory of the firm.
5.2. Profit maximization!
5.3. Several owners and risk.
5.3.1. The consumer-owner economy.
5.3.2. Arrow securities. In the “Further exercises” section of chapter V, we introduce Arrow securities.
5.3.3. An instructive example.
5.4. The cost of managing one’s own firm.
5.4.1. Utility maximization by the owner-manager.
5.4.2. Does utility maximization imply profit maximization?
5.4.3. A market for manager effort.
6. The separation function of markets
7. Topics
8. Solutions
9. Further exercises without solutions
Part C. Games and industrial organization
CHAPTER X. Games in strategic form
1. Introduction, examples, and definition
1.1. Nobel prices in Game theory.
1.2. Some simple bimatrix games.
1.3. Definition of a game in strategic form.
2. Dominance
2.1. Definition.
2.2. The prisoners’ dilemma.
2.3. The second-price auction.
2.4. Take it or leave it.
2.5. The Basu game (the insurance game).
3. Best responses and Nash equilibria
3.1. Definition of the Nash equilibrium.
3.2. Matrix games and best responses.
4. ... for mixed strategies, also
4.1. Introductory remarks.
4.2. Definitions.
4.3. Equilibria.
4.4. The police game.
5. Existence and number of mixed-strategy equilibria
5.1. Number.
5.2. Existence.
6. Critical reflections on game theory
7. Topics
8. Solutions
9. Further exercises without solutions
CHAPTER XI. Price and quantity competition
1. Monopoly: Pricing policy
1.1. The linear model.
1.2. Marginal revenue and elasticity.
1.3. Profit maximization.
1.4. Price differentiation.
2. Price competition
2.1. The game.
2.2. Accomodation and Bertrand paradox.
2.3. Blockaded entry and deterred entry.
2.3.1. Market entry blockaded for both firms.
2.3.2. Market entry of firm 2 blockaded.
2.3.3. Market entry of firm 2 deterred.
2.3.4. Summary.
3. Monopoly: quantity policy
3.1. The linear model.
3.2. Marginal revenue.
3.3. Monopoly profit.
3.4. Profit maximization.
3.5. The influence of average cost on maximal profit.
3.6. Alternative expressions for profit maximization.
3.7. First-degree price differentiation.
3.8. Third-degree price differentiation (two markets, one factory).
3.9. One market, two factories.
3.10. Welfare-theoretic analysis of monopoly.
4. Quantity competition
4.1. Price versus quantity competition.
4.2. The game.
4.3. Accomodation.
4.3.1. Equilibrium.
4.3.2. Iterative rationalizability.
4.3.3. Cartel treaty between two duopolists.
4.3.4. Comparative statics and cost competition.
4.3.5. Replicating the Cournot model.
4.4. Blockaded entry and deterred entry.
4.4.1. Market entry blockaded for both firms.
4.4.2. Market entry of firm 2 blockaded.
4.4.3. Summary.
5. Topics and literature
6. Solutions
7. Further exercises without solutions
CHAPTER XII. Games in extensive form
1. Examples
1.1. Non-simultaneous moves in simple bimatrix games.
1.2. Three Indian fables.
1.2.1. The tiger and the traveller.
1.2.2. The lion, the mouse, and the cat.
1.2.3. The cat and the mouse.
1.3. Example: the Stackelberg model.
1.3.1. Recipe: How to solve the Stackelberg model.
1.3.2. Strategies and equilibria.
2. Defining strategies
3. Subgame perfection and backward induction
4. Multi-stage games
4.1. Definition.
4.2. Cournot and Stackelberg games.
4.3. Backward induction for multi-stage games.
5. Product differentiation
5.1. Hotelling’s one-street village.
5.2. Demand functions.
5.3. The game.
5.4. Solving the two-stage game.
5.4.1. The second stage.
5.4.2. The first stage.
5.5. Direct and strategic effects.
5.5.1. Accomodation.
5.5.2. Entry deterrence.
6. Application: Strategic trade policy
6.1. Free trade or strategic trade policy.
6.2. The model.
6.3. Understanding the logic of strategic trade policy.
6.4. Strategic trade policy for price competition.
6.5. Judging strategic trade policy.
7. Topics and literature
8. Solutions
9. Further exercises without solutions
CHAPTER XIII. Repeated games
1. Example: Repeating the pricing game
2. Definitions
3. Equilibria of stage games and of repeated games
4. The infinitely repeated prisoners’ dilemma
4.1. Worst punishment.
4.2. Folk theorems for equilibria.
5. Topics
6. Solutions
7. Further exercises without solutions
Part D. Bargaining theory and Pareto optimality
CHAPTER XIV. Pareto optimality in microeconomics
1. Introduction: Pareto improvements
2. Identical marginal rates of substitution
2.1. Exchange Edgeworth box.
2.1.1. Introducing the Edgeworth box for two consumers.
2.1.2. Equality of the marginal rates of substitution.
2.1.3. Deriving the utility frontier.
2.2. Production Edgeworth box.
2.3. Two markets — one factory.
2.4. Two firms (cartel).
3. Identical marginal rates of transformation
3.1. Two factories — one market.
3.2. Bargaining between countries (international trade).
4. Equality of marginal rates of substitution and transformation
4.1. Base case.
4.2. Perfect competition.
4.3. First-degree price discrimination.
4.4. Cournot monopoly.
4.5. Household optimum.
4.6. External effects and the Coase theorem.
4.6.1. External effects and bargaining.
4.6.2. Straying cattle.
4.7. Public goods.
5. Topics
6. Solutions
7. Further exercises without solutions
CHAPTER XV. Cooperative game theory
1. Introduction
2. The coalition function
3. Summing and zeros
4. Solution correspondences
4.1. Solutions functions and solution correspondences.
4.2. Solution correspondence: Pareto efficiency.
4.3. Solution correspondence: The core.
5. The Shapley value
5.1. The Shapley formula.
5.2. The Shapley axioms.
6. Simple games
6.1. Definition.
6.2. Veto players and dictators.
6.3. Simple games and voting mechanisms.
6.4. Unanimity games.
6.5. Apex games.
6.6. Weighted voting games.
6.6.1. Definition.
6.6.2. UN Security Council.
7. Five non-simple games
7.1. Buying a car.
7.2. The Maschler game.
7.3. The gloves game, once again.
7.4. The chess game.
7.5. Cost-division games.
8. Topics and literature
9. Solutions
CHAPTER XVI. The Rubinstein bargaining model
1. Introduction
2. Many equilibria
3. Backward induction for a three-stage Rubinstein game
4. Backward induction for the Rubinstein game
5. Subgame perfect strategies for the Rubinstein game
6. Patience in bargaining
7. Topics
8. Solutions
Part E. Bayesian games and mechanism design
CHAPTER XVII. Static Bayesian games
1. Introduction and an example
2. Definitions
2.1. Static Bayesian game.
2.2. Beliefs.
2.3. Actions, strategies, and equilibria.
2.4. Example: Cournot duopoly with one-sided uncertainty.
2.4.1. The model.
2.4.2. The static Bayesian equilibrium.
3. Revisiting mixed-strategy equilibria
3.1. Continuous types.
3.2. Introducing uncertainty.
3.3. The equilibria.
3.4. Purification.
4. Correlated equilibria
4.1. Telling how to play.
4.2. The recommendation game.
4.3. Going beyond the convex hull.
5. The first-price auction
5.1. The model.
5.2. Solution.
5.3. First-price or second-price auction?
6. The double auction
6.1. The model.
6.2. Equilibrium in linear strategies.
6.3. Inefficient trade.
7. Topics
8. Solutions
9. Further exercises without solutions
CHAPTER XVIII. The revelation principle and mechanism design
1. Introduction
2. Revisiting the first-price auction
3. Social choice problems and mechanisms
4. The revelation principle
5. The Clarke-Groves mechanism
5.1. Public-goods problems and functions.
5.2. The definition of the Clarke-Groves mechanism.
5.3. Lemma and proof.
5.4. Discussion.
6. Topics and literature
7. Further exercises without solutions
Part F. Perfect competition and competition policy
CHAPTER XIX. General equilibrium theory
1. Introduction to General Equilibrium Theory
1.1. Introductory remarks.
1.2. Nobel prizes.
2. Exchange economy: positive theory
2.1. Exchange Edgeworth box: prices and equilibria.
2.2. Definition of an exchange economy.
2.3. Excess Demand and Market Clearance.
2.4. Walras equilibrium.
2.4.1. Definition.
2.4.2. Market clearing in the Walras equilibrium.
2.4.3. Example: The Cobb-Douglas exchange economy with two agents.
2.5. Existence of the Walras equilibrium.
2.5.1. Proposition.
2.5.2. Brouwer’s fixed-point theorem.
2.5.3. Proof of the existence theorem XIX.1.
2.6. Existence of the Nash equilibrium.
3. Exchange and production economy: positive theory
4. Normative theory
4.1. The first welfare theorem from the point of view of partial analysis.
4.1.1. Marginal this and that.
4.1.2. Three steps, twice.
4.1.3. Exchange optimality.
4.1.4. Production optimality.
4.1.5. Optimal product mix.
4.1.6. Summary.
4.2. The first welfare theorem from the point of view of general equilibrium analysis.
4.3. The second welfare theorem.
5. Topics and literature
6. Solutions
7. Further exercises without solutions
CHAPTER XX. Beyond general equilibrium theory
1. Nobel price for Friedrich August von Hayek
2. Envy freeness
3. The jungle economy
3.1. Introduction.
3.2. Definition of a jungle economy.
3.3. The jungle equilibrium.
3.4. Welfare economics of the jungle equilibrium.
4. Applications
4.1. The economic theory of socialism.
4.2. The regime of competition of the Freiburg School of “Ordoliberalism”.
4.3. Computable General Equilibrium Theory.
5. Austrian critical perspectives and Schumpeter
5.1. Ludwig von Mises: the market process.
5.2. Friedrich August von Hayek: the price system as a machinery for registering change.
5.3. Friedrich August von Hayek: competition as discovery procedure.
5.4. Israel Kirzner: entrepreneurial discovery.
5.5. Joseph Schumpeter: creative destruction.
6. A critical review of GET
6.1. General equilibrium theory.
6.2. The two welfare theorems.
7. Topics
8. Solutions
9. Further exercises without solutions
CHAPTER XXI. Introduction to competition policy and regulation
1. Themes
2. Markets
2.1. The relevant market.
2.1.1. Cross price elasticity of demand.
2.1.2. Supply-side substitutes.
2.1.3. SSNIP-Test.
2.1.4. Price correlation test.
2.2. Measures of concentration.
3. Models
3.1. Introduction.
3.2. The structure-conduct-performance paradigm.
3.3. Cournot, concentration, and monopoly power.
3.4. Natural monopoly and Ramsey prices.
3.5. Restricting the rate of return in the private sector.
4. Overall concepts of competition (policy)
4.1. Classical liberalism.
4.2. Perfect competition and GET.
4.3. Freiburg school of “ordoliberalism”.
4.4. Chicago school of antitrust policy.
4.5. Harvard school of workable competition.
4.6. Contestable markets.
4.7. Kantzenbach’s model of optimal competition intensity.
4.8. The Austrian school.
4.9. Joseph Schumpeter.
4.10. Freedom and competition.
5. Topics
6. Solutions
7. Further exercises without solutions
Part G. Contracts and principal-agent theories
CHAPTER XXII. Adverse selection
1. Introduction and an example
2. A polypsonistic labor market
2.1. The market model.
2.2. Observable productivity.
2.3. Unobservable productivities.
2.4. Inefficient equilibria.
3. A polypsonistic labor market with education
3.1. Introduction.
3.2. The market model.
3.3. Observable productivity.
3.4. Unobservable productivity (pooling equilibrium).
4. A polypsonistic labor market with education and screening
4.1. Sequence and strategies.
4.2. Separating equilibria.
5. Revisiting the revelation principle
6. Topics and literature
7. Solutions
CHAPTER XXIII. Hidden action
1. Introduction
2. The principal-agent model
3. Sequence, strategies, and solution strategy
4. Observable effort
5. Unobservable effort
5.1. The model.
5.2. Applying the Lagrangean method to the participation constraint.
5.3. Applying the Kuhn-Tucker method to the incentive constraint.
6. Special case: two outputs
6.1. The model.
6.2. The indifference curves.
6.3. The principal’s iso-profit lines.
6.4. Solving the principal-agent problem.
7. More complex principal-agent structures
8. Topics and literature
9. Solutions
Index
Bibliography