Public Economics

P u b lic E c o n o mics Gareth D. Myles October 2001 ii Conten ts Introduction xiii IFoundations 1 1 Introduction 3 1.1 Publiceconomics 3 1.2 Motivation 5 1.3 Efficiencyversusequity 6 1.4 Information 7 1.5 Methodology 8 1.6 Preview 9 1.7 Publicsectorincomeandexpenditure 11 1.8 Notation 16 2 General Equilibrium and Welfare Economics 19 2.1 Introduction 19 2.2 TheArrow-Debreueconomy 20 2.2.1 Theinstitutionalframework 21 2.2.2 Commodities 21 2.2.3 Consumers 22 2.2.4 Producers 25 2.2.5 Equilibrium 27 2.2.6 Walras’law 28 2.2.7 Normalizations 29 2.2.8 Relaxationofstrictconvexity 30 2.2.9 Existenceofequilibrium 32 2.2.10 Analysisofpolicy 33 2.2.11 Coreoftheeconomy 35 2.2.12 Nettrades 37 2.3 Welfarepropertiesofcompetitiveequilibrium 38 2.3.1 Basic definitions 38 2.3.2 TheFirstTheorem 39 2.3.3 TheSecondTheorem 41 iii iv CONTENTS 2.4 Acriticalappraisal 45 2.4.1 Lump-sumtransfersandtaxes 45 2.4.2 Theinstitutionalassumptions 49 2.4.3 Paretooptimality 50 2.5 Interpersonalcomparisonsandsocialwelfare 53 2.5.1 Interpersonal comparability 53 2.5.2 Socialchoice 55 2.5.3 Bergson-Samuelsonsocialwelfarefunction 58 2.6 Summary 59 3 Topics in Measurement 61 3.1 Introduction 61 3.2 Themeasurementofincome 62 3.3 Equivalencescales 63 3.3.1 Minimumneeds 64 3.3.2 EngelandRothbarth 64 3.3.3 PraisandHouthakker 67 3.3.4 Barten 67 3.3.5 Generalcase 69 3.3.6 Inpractice 71 3.4 Themeasurementofinequality 72 3.4.1 Basic definitions 73 3.4.2 Statisticalmeasures 74 3.4.3 Statisticalmeasuresandwelfare 78 3.4.4 GeneralisedLorenzCurves 82 3.4.5 Welfare-theoreticindices 83 3.4.6 Axiomaticinequalitymeasures 86 3.4.7 Summary 88 3.5 Themeasurementofpoverty 88 3.5.1 Relativeorabsolute? 89 3.5.2 Thepovertyline 90 3.5.3 Standardmeasures 90 3.5.4 Axiomaticapproach 91 3.5.5 Variablepovertyline 95 3.6 Conclusions 95 II An a ly sis in the competitive model 97 4 Commodity Taxation 99 4.1 Introduction 99 4.2 Methodology 100 4.3 TheRamseyrule 101 4.3.1 Theeconomy 101 4.3.2 Derivation 102 4.3.3 Interpretation 104 CONTENTS v 4.3.4 Implications 106 4.3.5 Inverseelasticitiesrule 107 4.4 Extensiontomany-households 108 4.4.1 Theoptimaltaxrule 108 4.4.2 ReductiontotheRamseyrule 111 4.4.3 Acautionarynote 112 4.5 Numericalresults 113 4.5.1 Applications 113 4.5.2 Furtherresults 116 4.6 Generalisingtheproductiontechnology 117 4.7 Untaxedgoods 121 4.8 Uniformtaxes 124 4.9 Production efficiency 126 4.10Summary 129 5IncomeTaxation 131 5.1 Introduction 131 5.2 TheMirrleeseconomy 132 5.2.1 Theoptimisation 132 5.2.2 Basicstructure 133 5.2.3 Thestructureofutility 134 5.2.4 Self-selection 138 5.3 Characterisationofoptimaltaxfunction 140 5.3.1 Thegeneralproblem 140 5.3.2 Lineartaxation 141 5.3.3 Nonlineartaxation 144 5.3.4 Summary 153 5.4 Numericalresults 153 5.4.1 Simulations 154 5.4.2 Choice of specification 156 5.5 Extensionsandomissions 159 5.5.1 Incomeandcommoditytaxes 160 5.5.2 Omissions 162 5.6 Summary 163 6 Policy Reform 165 6.1 Introduction 165 6.2 Thereformproblem 165 6.2.1 Productiv e feasibility . 166 6.2.2 Improvingreforms 169 6.3 Characterising possibilities . . 171 6.3.1 SolutionviaTheoremsoftheAlternative 171 6.3.2 Geometricanalysis 172 6.3.3 Informationalrequirements 176 6.4 Productive efficiencyandmaximisingreforms 177 6.4.1 The possibility of inefficiency 178 vi CONTENTS 6.4.2 Interpretation 180 6.5 Lump-sumtaxes 181 6.6 Theinverseoptimum 182 6.6.1 Theory 183 6.6.2 Applications 184 6.7 Marginalsocialcostoftaxation 186 6.7.1 Derivation 187 6.7.2 Empiricalapplication 188 6.8 PoliticalConstraints 188 6.9 Conclusions 191 7Risk 193 7.1 Introduction 193 7.2 General equilibrium with risk . . . 194 7.2.1 RiskintheArrow-Debreueconomy 194 7.2.2 Efficiency 196 7.2.3 Includingtime 197 7.2.4 Completemarkets 198 7.2.5 Comments 199 7.3 Privateandsocialattitudestorisk 200 7.3.1 Privateattitudes 200 7.3.2 Socialattitudes 202 7.3.3 Summary 208 7.4 Householdchoiceandtaxation 208 7.4.1 Wealthtaxation 209 7.4.2 Incometax 212 7.4.3 Imperfect loss offsets 214 7.4.4 Generalisations 216 7.5 Laboursupplyandoccupationalchoice 217 7.5.1 Laboursupply 217 7.5.2 Occupationalchoice 218 7.6 Optimaltaxation 221 7.6.1 Privaterisk 221 7.6.2 Aggregaterisk 224 7.7 Conclusions 226 8 Corporate Taxation 227 8.1 Introduction 227 8.2 Taxation of t he firm 228 8.2.1 Input and output taxes . . 228 8.2.2 Profittax 229 8.2.3 Personaltaxes 230 8.2.4 Whytaxthecorporation? 230 8.3 Taxincidence 231 8.3.1 TaxincidenceintheHarbergereconomy 231 8.3.2 Extensions 237 CONTENTS vii 8.3.3 Taxation and finance 240 8.3.4 Systemsofcorporateandpersonaltaxation 241 8.3.5 Financeandinvestmentwithcertainty 242 8.3.6 Uncertainty 249 8.4 Conclusions 254 III Relaxing t he Assumptions 255 9 Public Goods 257 9.1 Introduction 257 9.2 Definitions 258 9.2.1 Purepublicgoods 258 9.2.2 Impurepublicgoodsandcongestion 259 9.3 Optimalprovision 259 9.3.1 Purepublicgood 260 9.3.2 Freedisposal 262 9.3.3 Withcongestion 262 9.3.4 Publicinput 263 9.4 Personalised prices and the Lindahl equilibrium 264 9.4.1 Simplemodel 265 9.4.2 Ageneraltreatment 267 9.4.3 Coreequivalence 270 9.4.4 Cost-share equilibria . 271 9.4.5 Comments 272 9.5 Private pro vision of public good 272 9.5.1 Equilibrium 273 9.5.2 Paretoimprovements 275 9.5.3 Quantityofprovision 276 9.5.4 Thenumberofhouseholds 277 9.5.5 Invarianceresults 279 9.5.6 Alternativeformulations 280 9.5.7 Summary 282 9.6 Financebytaxation 282 9.6.1 Identicalconsumers 282 9.6.2 Differentiatedhouseholds 286 9.6.3 Summary 287 9.6.4 Definitions 288 9.6.5 Dominantstrategies 289 9.6.6 Nashequilibrium 294 9.6.7 Bayesian equilibria . . 296 9.6.8 Conclusions 296 9.7 Experimentalevidenceandmarketdata 297 9.7.1 Experimentalevidence 297 9.7.2 Marketdata 300 9.8 Conclusions 301 viii CONTENTS 10 Externalities 303 10.1Introduction 303 10.2Externalities 304 10.2.1 Definitions 304 10.2.2 Representation 305 10.3 Market inefficiency 306 10.3.1 Equilibrium and inefficiency 306 10.3.2 Paretoirrelevantexternalities 308 10.4TheCoasetheorem 309 10.4.1 TheTheorem 309 10.4.2 Marketsforexternalities 311 10.4.3 Non-existenceofmarkets 313 10.4.4 Bargaining 316 10.4.5 Conclusions 320 10.5Welfare-improvingchanges 320 10.5.1 Localresults 321 10.5.2 Globalresults 323 10.6Correctivetaxation 324 10.6.1 Non-uniformtaxation 325 10.6.2 Uniformtaxation 327 10.6.3 Summary 331 10.7Tradeablelicenses 331 10.7.1 Certain costs and benefits 332 10.7.2 Pricesversusquantities 333 10.7.3 Nonlinearpricing 335 10.8Internalisation 335 10.9Conclusions 336 11 Imperfect Competition 337 11.1Introduction 337 11.2 Imperfect competition and general equilibrium 338 11.2.1 Objectiveandsubjectivedemand 338 11.2.2 Pricenormalisations 339 11.2.3 Theeconomy 340 11.3Imperfectcompetitionandwelfare 343 11.3.1 FailureofParetooptimality 343 11.3.2 Measuresofwelfareloss 344 11.4Commoditytaxation 346 11.4.1 Taxincidence 347 11.4.2 Optimaltaxes 351 11.5 Ad valorem and specifictaxes 357 11.5.1 Taxincidence 357 11.6Optimalcombinations 359 11.7 Production efficiencyandthetaxationoflabour 362 11.7.1 Production efficiency 363 11.7.2 Taxationoflabour 366 CONTENTS ix 11.8Otherformsofregulation 367 11.9Conclusions 368 12 Tax Eva sion 371 12.1Introduction 371 12.2Theextentoftaxevasion 371 12.3Evasionasadecisionwithrisk 373 12.4Optimalauditingandpunishment 376 12.5Taxevasionandlaboursupply 377 12.5.1 Labour supply 378 12.5.2 Allocationofhours 378 12.6Publicgoods 380 12.6.1 Thevaluationofpublicfunds 381 12.6.2 Congestible public goods 382 12.7Empiricalevidence 385 12.8Honestyandsocialnorms 387 12.9Optimalauditingwithanindependentrevenueservice 389 12.10Tax evasion by firms 392 12.10.1 Competitive firms 392 12.10.2Imperfectcompetition 394 12.11Optimaltaxationwithevasion 395 12.11.1Commoditytaxation 395 12.11.2Incometaxation 397 12.12Summary 397 IV I n troducing Real T ime 399 13 Ov erlapping Generations Economies 401 13.1Introduction 401 13.2Overlappinggenerationexchangeeconomies 402 13.2.1 TheSamuelsoneconomy 403 13.2.2 Overlapping generations as Arrow-Debreu economies . . . 405 13.2.3 Existenceofequilibrium 407 13.2.4 Money,dynamicsandindeterminacy 412 13.2.5 Summary 418 13.3 An aggregate production economy 419 13.3.1 Consumers 419 13.3.2 Production 420 13.3.3 Equilibrium 421 13.3.4 SteadyStateSolution 424 13.3.5 Goldenrules 425 13.3.6 Paretooptimality 428 13.4Conclusions 429 x CONTENTS 14 Social Security 431 14.1Introduction 431 14.2Fullyfundedandpay-as-you-go 432 14.3Anoptimalprogram 433 14.4Someextensions 436 14.4.1 Laboursupplyandretirement 436 14.4.2 Effectonsavingsandcapital 441 14.4.3 Ricardianequivalence 443 14.4.4 Demographics 445 14.5 Determination and justification 447 14.5.1 Votingequilibria 447 14.5.2 Altruism 449 14.5.3 Myopia 452 14.5.4 Uncertainty 454 14.6Lifetimeuncertainty 459 14.6.1 Symmetricinformation 460 14.6.2 Adverseselection 462 14.6.3 Moralhazard 466 14.7Conclusions 467 15 Debt and Taxes 469 15.1Introduction 469 15.2 The effectofdebt 470 15.2.1 Externalandinternaldebt 470 15.2.2 Effectsofdebt 471 15.3Optimisationofdebtandlump-sumtaxes 477 15.3.1 Lump-sumtaxationanddebt 478 15.3.2 Optimallump-sumtaxationanddebt 480 15.3.3 Summary 482 15.4Debtneutrality 483 15.4.1 Twospecialcases 484 15.4.2 Intergenerationalaltruism 485 15.4.3 Generalisations 490 15.5Incomeandinteresttaxation 492 15.6Conclusions 496 16 References 499 [...]... extension of the scope of public economics from its initial emphasis upon the collection and disbursement of government revenues to its present concern with all aspects of government economic intervention The intention of this book is to provide an introduction to the vast literature of public economics, emphasizing the foundations upon which future research can be laid Public economics has a long history... additional chapters on voting, rent seeking, political economy, clubs and local public goods, and international issues in taxation xi xii PREFACE Introduction Do I really need an introduction here? xiii xiv INTRODUCTION Part I Foundations 1 Chapter 1 Introduction 1.1 Public economics In the broadest interpretation, public economics is the study of economic policy, with particular emphasis upon taxation... the policy This evaluation process represents an application of normative economics The success of public economics has largely followed from the systematic application of these methods The theory that is described in the following chapters has developed mainly since 1970 and has built upon developments in microeconomics, macroeconomics, general equilibrium theory and game theory One of its characteristic... before a good policy can be designed an adequate theory must be developed One of the challenges of public economics is that much of the subject area is still in its infancy with considerable work still to be done Although a number of partitions could be used to break down the subject matter of public economics into convenient portions, the most instructive division is between that of determining the... clearly a direction in which the subject will continue to move Although this book is primarily intended to be a text on the theory of public economics, numerical results are given prominence due to their obvious importance The dominant setting for the analysis of public economics is within the mixed economy so that individual decisions are respected but the government intervenes to affect these choices... can only be justified by proving that the state can actually improve upon the market That it can always do so should not be taken for granted Extending the scope of the public economics to address such issues provides the breadth to public economics 1.3 Efficiency versus equity In conducting an economic policy the state will generally have two conflicting aims On the one hand, it will aim to implement the... Chapter 8 on public economics in the presence of risk completes part II The focus of Part III is upon the consequences of relaxing certain of the institutional assumptions on which the competitive economy is based Chapter 9 introduces public goods into the economy and contrasts the allocation that is achieved in the private provision equilibrium with the optimal allocation Methods of financing public goods... representing the breakdown of public sector objectives: defence expenditure is one of the minimal requirements; income support is evidence of concern for equity; and education represents provision of a public good to counter market failure Although brief, this review of statistics on the size and structure of public sector income and expenditure has illustrated the significant extent of public sector intervention... competitive equilibrium The mainstream of public economics combines parts of both of these caricatured viewpoints Many policy analyses take for granted the presumption that competitive behavior should be advocated and encouraged when it leads to economic efficiency However, its failings are also readily admitted and policies designed to correct for them Indeed, much of public economics implicitly takes as its... debt and taxation is the subject of Chapter 1.7 PUBLIC SECTOR INCOME AND EXPENDITURE 11 15 The effects of government debt and the issue of debt neutrality are considered Ricardian equivalence is linked to the existence of gifts and bequests The choice between the taxation of income and expenditure is also analyzed 1.7 Public sector income and expenditure The public sector plays an important role in the . Relaxing t he Assumptions 255 9 Public Goods 257 9.1 Introduction 257 9.2 Definitions 258 9.2.1 Purepublicgoods 258 9.2.2 Impurepublicgoodsandcongestion 259 9.3 Optimalprovision 259 9.3.1 Purepublicgood. always do so should not be taken for granted. Extending the scope of the public economics to address such issues provides the breadth to public economics. 1.3 Efficiency v ersus equity In conducting. necessitated re-typing all of t he maths, errors may have been introduced. You are welcome to use it provided you report any typing errors you discover to G. D. Myles@ ex.ac.uk so that I can put things right. I