MICROECONOMICS

1 MICROECONOMICSP rinciples and AnalysisFrank A. CowellSTICERD and Department of EconomicsLondon School of EconomicsDecember 2004iiContentsContentsiiiList of TablesxiiiList of FiguresxvPrefacexxiii1 The r le of microeconomic principles .. Microeconomic models .. Purpose .. The economic actors .. Motivation .. The economic environment .. Assumptions and axioms .. Testing a model .. Equilibrium analysis .. Equilibrium and economic context .. The comparative statics method .. Dynamics and stability .. Background to this book .. Economics .. Mathematics .. Using the book .. A route map .. Some tips .. 72 The Basic setting .. The rm: basic ingredients .. Properties of the production function .. The optimisation problem .. Optimisation stage 1: cost minimisation .. The cost function .. Optimisation stage 2: choosing output.

2 Assembling the solution .. The rm as a black box .. Demand and supply functions of the rm .. Comparative statics: the general case .. The short run .. The multiproduct rm .. Summary .. Reading notes .. Exercises .. 443 The Firm and the Introduction .. The market supply curve .. Large numbers and the supply curve .. Interaction amongst rms .. The size of the industry .. Price-setting .. Simple monopoly .. Discriminating monopolist .. Entry fee .. Product variety .. Summary .. Reading notes .. Exercises .. 644 The Introduction .. The consumer s environment .. Revealed preference .. Preferences: axiomatic approach .. Consumer optimisation: xed income .. Cost-minimisation .. Utility-maximisation .. Welfare .. An application: price indices .. Summary .. Reading notes .. Exercises .. 945 The Consumer and the Introduction.

3 The market and incomes .. Supply by households .. Labour supply .. Savings .. Household production .. Aggregation over goods .. Aggregation of consumers .. Summary .. Reading notes .. Exercises .. 1176 A Simple Introduction .. Another look at production .. Processes and net outputs .. The technology .. The production function again .. Externalities and aggregation .. The Robinson Crusoe economy .. Decentralisation and trade .. Summary .. Reading notes .. Exercises .. 1397 General Introduction .. A more interesting economy .. Allocations .. Incomes .. An illustration: the exchange economy .. The logic of price-taking .. The core of the exchange economy .. Competitive equilibrium and the core: small economy .. Competitive equilibrium and the core: large economy .. The excess-demand approach .. Properties of the excess demand function.

4 Existence .. Uniqueness .. Stability .. The r le of prices .. The equilibrium allocation .. Decentralisation again .. Summary .. Reading notes .. Exercises .. 172viCONTENTS8 Uncertainty and Introduction .. Consumption and uncertainty .. The nature of choice .. State-space diagram .. A model of preferences .. Key axioms .. Von-Neumann-Morgenstern utility .. The felicity function .. Risk aversion .. Risk premium .. Indices of risk aversion .. Special cases .. Lotteries and preferences .. The probability space .. Axiomatic approach .. Trade .. Contingent goods: competitive equilibrium .. Financial assets .. Individual optimisation .. The attainable set .. Components of the optimum .. The portfolio problem .. Insurance .. Summary .. Reading notes .. Exercises .. 2209 Introduction .. The constitution .. Principles for social judgments: e ciency.

5 Private goods and the market .. Departures from e ciency .. Externalities .. Public goods .. Uncertainty .. Extending the e ciency idea .. Principles for social judgments: equity .. Fairness .. Concern for inequality .. The social-welfare function .. Welfare, national income and expenditure .. Inequality and welfare loss .. Summary .. Reading notes .. Exercises .. 26510 Strategic Introduction .. Games basic concepts .. Players, rules and payo s .. Information and Beliefs .. Strategy .. Representing a game .. Equilibrium .. Multiple equilibria .. E ciency .. Existence .. Application: duopoly .. Competition in quantities .. Competition in prices .. Time .. Games and subgames .. Equilibrium: more on concept and method .. Repeated interactions .. Application: market structure .. Market leadership .. Market entry .. Another look at duopoly.

6 Uncertainty .. A basic model .. An application: entry again .. Mixed strategies again .. A dynamic approach .. Summary .. Reading notes .. 32011 Introduction .. Hidden characteristics: adverse selection .. Information and monopoly power .. One customer type .. Multiple types: Full information .. Imperfect information .. Adverse selection: Competition .. Application: Insurance .. Hidden characteristics: Signalling .. Costly signals .. Costless signals .. Hidden actions .. The issue .. Outline of the problem .. A simpli ed model .. Principal-and-Agent: a richer model .. Summary .. Reading notes .. Exercises .. 37412 Introduction .. Social choice .. Markets and manipulation .. Markets: another look .. Simple trading .. Manipulation: power and misrepresentation .. A design issue? .. Mechanisms .. Implementation .. Direct mechanisms .. The revelation principle.

7 The design problem .. Design: applications .. Auctions .. A public project .. Contracting again .. Taxation .. Summary .. Reading notes .. Exercises .. 42413 Government and the Introduction .. Market failure? .. Nonconvexities .. Large numbers and convexity .. Interactions and convexity .. The infrastructure problem .. Regulation .. Externalities .. Production externalities: the e ciency problem .. Corrective taxes .. Production externalities: Private solutions .. Consumption externalities .. Externalities: assessment .. Public consumption .. Nonrivalness and e ciency conditions .. Club goods .. Public goods .. The issue .. Voluntary provision .. Personalised prices? .. Public goods: market failure and the design problem .. Public goods: alternative mechanisms .. Optimal allocations? .. Optimum with lump-sum transfers .. Second-best approaches .. Conclusion: Economic Prescriptions.

8 Reading notes .. 468 Bibliography473A Mathematics Introduction .. Sets .. Sets inRn.. Functions .. Linear and a ne functions .. Continuity .. Homogeneous functions .. Homothetic functions .. Di erentiation .. Function of one variable .. Function of several variables .. Function-of-a-Function Rule .. The Jacobian derivative .. The Taylor expansion .. Elasticities .. Mappings and systems of equations .. Fixed-point results .. Implicit functions .. Convexity and Concavity .. Convex sets .. Hyperplanes.. Separation results .. Convex and concave functions .. quasiconcave functions .. The Hessian property .. Maximisation .. The basic technique .. Constrained maximisation .. More on constrained maximisation .. Envelope theorem .. A point on notation .. Probability .. Statistics .. Bayes rule .. Probability distributions: examples.

9 Reading notes .. 519B Answers to Footnote Introduction .. The rm .. The rm and the market .. The consumer .. The consumer and the market .. A simple economy .. General equilibrium .. Uncertainty and risk .. Welfare .. Strategic behaviour .. Information .. Design .. Government and individual .. 598C Selected The rm .. Marginal cost and the Lagrange multiplier .. Properties of the cost function (Theorem ) .. Firm s demand and supply functions (Theorem ) .. Firm s demand and supply functions (continued) .. Properties of pro t function (Theorem ) .. The consumer .. The representation theorem (Theorem ) .. Existence of ordinary demand functions (Theorem ) .. Quasiconvexity of the indirect utility function .. The consumer and the market .. Composite commodity (Theorem ): .. The representative consumer (Theorem ): .. A simple economy .. Decentralisation (Theorem ).

10 General equilibrium .. Competitive equilibrium and the core (Theorem ) .. Existence of competitive equilibrium (Theorem ) .. Uniqueness of competitive equilibrium (Theorem ) .. Valuation in general equilibrium (Theorem ) .. Uncertainty and risk .. Risk-taking and wealth (Theorem ) .. Welfare .. Arrow s theorem (Theorem ) .. Black s theorem (Theorem ) .. The support theorem (Theorem ) .. Potential superiority (Theorem ) .. Strategic behaviour .. Nash equilibrium in pure strategies with in nite strategysets (Theorem ) .. Existence of Nash equilibrium (Theorem ) .. The Folk theorem .. Design .. Revenue equivalence (Theorem ) .. The Clark-Groves mechanism (Theorem ) .. 630 Index632xiiCONTENTSList of The Firm: Basic Notation .. The Firm: Solution Functions .. The Consumer: Basic Notation .. Own-wage labour-supply responses for di erent types of UK work-ers.