microeconomics principles and analysis

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microeconomics principles and analysis

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. MICROECONOMICS Principles and Analysis Frank A. Cowell STICERD and Department of Economics London School of Economics December. cost function (Theorem 2.2) . . . . . . . 608 C.1.3 Firm’s demand and supply functions (Theorem 2.4) . . . 611 C.1.4 Firm’s demand and supply functions (continued) . . . . . 612 C.1.5 Properties. . . . . . . . . . . . . . . . . . 86 4.11 Compensated demand and the value of a price fall . . . . . . . . 90 4.12 Compensated demand and the value of a price fall (2) . . . . . . 91 4.13 Three

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  • Contents

  • List of Tables

  • List of Figures

  • Preface

  • 1 Introduction

    • 1.1 The rôle of microeconomic principles

    • 1.2 Microeconomic models

      • 1.2.1 Purpose

      • 1.2.2 The economic actors

      • 1.2.3 Motivation

      • 1.2.4 The economic environment

      • 1.2.5 Assumptions and axioms

      • 1.2.6 “Testing” a model

    • 1.3 Equilibrium analysis

      • 1.3.1 Equilibrium and economic context

      • 1.3.2 The comparative statics method

      • 1.3.3 Dynamics and stability

    • 1.4 Background to this book

      • 1.4.1 Economics

      • 1.4.2 Mathematics

    • 1.5 Using the book

      • 1.5.1 A route map

      • 1.5.2 Some tips

  • 2 The Firm

    • 2.1 Basic setting

      • 2.1.1 The firm: basic ingredients

      • 2.1.2 Properties of the production function

    • 2.2 The optimisation problem

      • 2.2.1 Optimisation stage 1: cost minimisation

      • 2.2.2 The cost function

      • 2.2.3 Optimisation stage 2: choosing output

      • 2.2.4 Assembling the solution

    • 2.3 The firm as a “black box”

      • 2.3.1 Demand and supply functions of the firm

      • 2.3.2 Comparative statics: the general case

    • 2.4 The short run

    • 2.5 The multiproduct firm

    • 2.6 Summary

    • 2.7 Reading notes

    • 2.8 Exercises

  • 3 The Firm and the Market

    • 3.1 Introduction

    • 3.2 The market supply curve

    • 3.3 Large numbers and the supply curve

    • 3.4 Interaction amongst firms

    • 3.5 The size of the industry

    • 3.6 Price-setting

      • 3.6.1 Simple monopoly

      • 3.6.2 Discriminating monopolist

      • 3.6.3 Entry fee

    • 3.7 Product variety

    • 3.8 Summary

    • 3.9 Reading notes

    • 3.10 Exercises

  • 4 The Consumer

    • 4.1 Introduction

    • 4.2 The consumer's environment

    • 4.3 Revealed preference

    • 4.4 Preferences: axiomatic approach

    • 4.5 Consumer optimisation: fixed income

      • 4.5.1 Cost-minimisation

      • 4.5.2 Utility-maximisation

    • 4.6 Welfare

      • 4.6.1 An application: price indices

    • 4.7 Summary

    • 4.8 Reading notes

    • 4.9 Exercises

  • 5 The Consumer and the Market

    • 5.1 Introduction

    • 5.2 The market and incomes

    • 5.3 Supply by households

      • 5.3.1 Labour supply

      • 5.3.2 Savings

    • 5.4 Household production

    • 5.5 Aggregation over goods

    • 5.6 Aggregation of consumers

    • 5.7 Summary

    • 5.8 Reading notes

    • 5.9 Exercises

  • 6 A Simple Economy

    • 6.1 Introduction

    • 6.2 Another look at production

      • 6.2.1 Processes and net outputs

      • 6.2.2 The technology

      • 6.2.3 The production function again

      • 6.2.4 Externalities and aggregation

    • 6.3 The Robinson Crusoe economy

    • 6.4 Decentralisation and trade

    • 6.5 Summary

    • 6.6 Reading notes

    • 6.7 Exercises

  • 7 General Equilibrium

    • 7.1 Introduction

    • 7.2 A more interesting economy

      • 7.2.1 Allocations

      • 7.2.2 Incomes

      • 7.2.3 An illustration: the exchange economy

    • 7.3 The logic of price-taking

      • 7.3.1 The core of the exchange economy

      • 7.3.2 Competitive equilibrium and the core: small economy

      • 7.3.3 Competitive equilibrium and the core: large economy

    • 7.4 The excess-demand approach

      • 7.4.1 Properties of the excess demand function

      • 7.4.2 Existence

      • 7.4.3 Uniqueness

      • 7.4.4 Stability

    • 7.5 The rôle of prices

      • 7.5.1 The equilibrium allocation

      • 7.5.2 Decentralisation again

    • 7.6 Summary

    • 7.7 Reading notes

    • 7.8 Exercises

  • 8 Uncertainty and Risk

    • 8.1 Introduction

    • 8.2 Consumption and uncertainty

      • 8.2.1 The nature of choice

      • 8.2.2 State-space diagram

    • 8.3 A model of preferences

      • 8.3.1 Key axioms

      • 8.3.2 Von-Neumann-Morgenstern utility

      • 8.3.3 The “felicity”function

    • 8.4 Risk aversion

      • 8.4.1 Risk premium

      • 8.4.2 Indices of risk aversion

      • 8.4.3 Special cases

    • 8.5 Lotteries and preferences

      • 8.5.1 The probability space

      • 8.5.2 Axiomatic approach

    • 8.6 Trade

      • 8.6.1 Contingent goods: competitive equilibrium

      • 8.6.2 Financial assets

    • 8.7 Individual optimisation

      • 8.7.1 The attainable set

      • 8.7.2 Components of the optimum

      • 8.7.3 The portfolio problem

      • 8.7.4 Insurance

    • 8.8 Summary

    • 8.9 Reading notes

    • 8.10 Exercises

  • 9 Welfare

    • 9.1 Introduction

    • 9.2 The constitution

    • 9.3 Principles for social judgments: efficiency

      • 9.3.1 Private goods and the market

      • 9.3.2 Departures from efficiency

      • 9.3.3 Externalities

      • 9.3.4 Public goods

      • 9.3.5 Uncertainty

      • 9.3.6 Extending the efficiency idea

    • 9.4 Principles for social judgments: equity

      • 9.4.1 Fairness

      • 9.4.2 Concern for inequality

    • 9.5 The social-welfare function

      • 9.5.1 Welfare, national income and expenditure

      • 9.5.2 Inequality and welfare loss

    • 9.6 Summary

    • 9.7 Reading notes

    • 9.8 Exercises

  • 10 Strategic Behaviour

    • 10.1 Introduction

    • 10.2 Games -- basic concepts

      • 10.2.1 Players, rules and payoffs

      • 10.2.2 Information and Beliefs

      • 10.2.3 Strategy

      • 10.2.4 Representing a game

    • 10.3 Equilibrium

      • 10.3.1 Multiple equilibria

      • 10.3.2 Efficiency

      • 10.3.3 Existence

    • 10.4 Application: duopoly

      • 10.4.1 Competition in quantities

      • 10.4.2 Competition in prices

    • 10.5 Time

      • 10.5.1 Games and subgames

      • 10.5.2 Equilibrium: more on concept and method

      • 10.5.3 Repeated interactions

    • 10.6 Application: market structure

      • 10.6.1 Market leadership

      • 10.6.2 Market entry

      • 10.6.3 Another look at duopoly

    • 10.7 Uncertainty

      • 10.7.1 A basic model

      • 10.7.2 An application: entry again

      • 10.7.3 Mixed strategies again

      • 10.7.4 A “dynamic” approach

    • 10.8 Summary

    • 10.9 Reading notes

    • 10.10 Exercises

  • 11 Information

    • 11.1 Introduction

    • 11.2 Hidden characteristics: adverse selection

      • 11.2.1 Information and monopoly power

      • 11.2.2 One customer type

      • 11.2.3 Multiple types: Full information

      • 11.2.4 Imperfect information

      • 11.2.5 Adverse selection: Competition

      • 11.2.6 Application: Insurance

    • 11.3 Hidden characteristics: Signalling

      • 11.3.1 Costly signals

      • 11.3.2 Costless signals

    • 11.4 Hidden actions

      • 11.4.1 The issue

      • 11.4.2 Outline of the problem

      • 11.4.3 A simplified model

      • 11.4.4 Principal-and-Agent: a richer model

    • 11.5 Summary

    • 11.6 Reading notes

    • 11.7 Exercises

  • 12 Design

    • 12.1 Introduction

    • 12.2 Social choice

    • 12.3 Markets and manipulation

      • 12.3.1 Markets: another look

      • 12.3.2 Simple trading

      • 12.3.3 Manipulation: power and misrepresentation

      • 12.3.4 A design issue?

    • 12.4 Mechanisms

      • 12.4.1 Implementation

      • 12.4.2 Direct mechanisms

      • 12.4.3 The revelation principle

    • 12.5 The design problem

    • 12.6 Design: applications

      • 12.6.1 Auctions

      • 12.6.2 A public project

      • 12.6.3 Contracting again

      • 12.6.4 Taxation

    • 12.7 Summary

    • 12.8 Reading notes

    • 12.9 Exercises

  • 13 Government and the Individual

    • 13.1 Introduction

    • 13.2 Market failure?

    • 13.3 Nonconvexities

      • 13.3.1 Large numbers and convexity

      • 13.3.2 Interactions and convexity

      • 13.3.3 The infrastructure problem

      • 13.3.4 Regulation

    • 13.4 Externalities

      • 13.4.1 Production externalities: the efficiency problem

      • 13.4.2 Corrective taxes

      • 13.4.3 Production externalities: Private solutions

      • 13.4.4 Consumption externalities

      • 13.4.5 Externalities: assessment

    • 13.5 Public consumption

      • 13.5.1 Nonrivalness and efficiency conditions

      • 13.5.2 Club goods

    • 13.6 Public goods

      • 13.6.1 The issue

      • 13.6.2 Voluntary provision

      • 13.6.3 Personalised prices?

      • 13.6.4 Public goods: market failure and the design problem

      • 13.6.5 Public goods: alternative mechanisms

    • 13.7 Optimal allocations?

      • 13.7.1 Optimum with lump-sum transfers

      • 13.7.2 Second-best approaches

    • 13.8 Conclusion: Economic Prescriptions

    • 13.9 Reading notes

    • 13.10 Exercises

  • Bibliography

  • A Mathematics Background

    • A.1 Introduction

    • A.2 Sets

      • A.2.1 Sets in Rn

    • A.3 Functions

      • A.3.1 Linear and affine functions

      • A.3.2 Continuity

      • A.3.3 Homogeneous functions

      • A.3.4 Homothetic functions

    • A.4 Differentiation

      • A.4.1 Function of one variable

      • A.4.2 Function of several variables

      • A.4.3 Function-of-a-Function Rule

      • A.4.4 The Jacobian derivative

      • A.4.5 The Taylor expansion

      • A.4.6 Elasticities

    • A.5 Mappings and systems of equations

      • A.5.1 Fixed-point results

      • A.5.2 Implicit functions

    • A.6 Convexity and Concavity

      • A.6.1 Convex sets

      • A.6.2 Hyperplanes.

      • A.6.3 Separation results

      • A.6.4 Convex and concave functions

      • A.6.5 quasiconcave functions

      • A.6.6 The Hessian property

    • A.7 Maximisation

      • A.7.1 The basic technique

      • A.7.2 Constrained maximisation

      • A.7.3 More on constrained maximisation

      • A.7.4 Envelope theorem

      • A.7.5 A point on notation

    • A.8 Probability

      • A.8.1 Statistics

      • A.8.2 Bayes' rule

      • A.8.3 Probability distributions: examples

    • A.9 Reading notes

  • B Answers to Footnote Questions

    • B.1 Introduction

    • B.2 The firm

    • B.3 The firm and the market

    • B.4 The consumer

    • B.5 The consumer and the market

    • B.6 A simple economy

    • B.7 General equilibrium

    • B.8 Uncertainty and risk

    • B.9 Welfare

    • B.10 Strategic behaviour

    • B.11 Information

    • B.12 Design

    • B.13 Government and individual

  • C Selected Proofs

    • C.1 The firm

      • C.1.1 Marginal cost and the Lagrange multiplier

      • C.1.2 Properties of the cost function (Theorem 2.2)

      • C.1.3 Firm's demand and supply functions (Theorem 2.4)

      • C.1.4 Firm's demand and supply functions (continued)

      • C.1.5 Properties of profit function (Theorem 2.7)

    • C.2 The consumer

      • C.2.1 The representation theorem (Theorem 4.1)

      • C.2.2 Existence of ordinary demand functions (Theorem 4.5)

      • C.2.3 Quasiconvexity of the indirect utility function

    • C.3 The consumer and the market

      • C.3.1 Composite commodity (Theorem 5.1):

      • C.3.2 The representative consumer (Theorem 5.2):

    • C.4 A simple economy

      • C.4.1 Decentralisation (Theorem 6.2)

    • C.5 General equilibrium

      • C.5.1 Competitive equilibrium and the core (Theorem 7.1)

      • C.5.2 Existence of competitive equilibrium (Theorem 7.4)

      • C.5.3 Uniqueness of competitive equilibrium (Theorem 7.5)

      • C.5.4 Valuation in general equilibrium (Theorem 7.6)

    • C.6 Uncertainty and risk

      • C.6.1 Risk-taking and wealth (Theorem 8.7)

    • C.7 Welfare

      • C.7.1 Arrow's theorem (Theorem 9.1)

      • C.7.2 Black's theorem (Theorem 9.2)

      • C.7.3 The support theorem (Theorem 9.5)

      • C.7.4 Potential superiority (Theorem 9.10)

    • C.8 Strategic behaviour

      • C.8.1 Nash equilibrium in pure strategies with infinite strategy sets (Theorem 10.2)

      • C.8.2 Existence of Nash equilibrium (Theorem 10.1)

      • C.8.3 The Folk theorem

    • C.9 Design

      • C.9.1 Revenue equivalence (Theorem 12.6)

      • C.9.2 The Clark-Groves mechanism (Theorem 12.7)

  • Index

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