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Chapter 3 First Best and Second Best Analyses and the Political Economy of Public Sector Economics 2015 Public Finance Third Edition

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Politica Económica sobre impuestos
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  Chapter 3 First-Best and Second-Best Analysesand the Political Economy of PublicSector Economics Chapter Outline Lump-Sum Redistributions and Public Sector Theory 37First-Best Analysis 38 The Two Dichotomies in First-Best Models 38 Second-Best Analysis 40 Constrained Social Welfare Maximization 40The Most Common Policy and Market Constraints 41Distorting Taxes and Transfers 42Fixed Budget Constraints 42Drafting Resources or Giving away Goods 42Maintained Monopoly Power 42Asymmetric or Private Information 43Further Implications of Second-Best Modeling 43The Scope of Government Intervention 43Interpreting Second-Best Results 43Model and Policy Sensitivity 44 Similarities Between First-Best and Second-Best Analyses 44The Political Economy of the Social Welfare Function 45 The Form of the Social Welfare Function:From Utilitarian to Rawlsian 45Utiltarianism 45Rawlsianism 46A Flexible Social Welfare Function 47Arrow’s Impossibility Theorem 48Arrow’s Five Axioms 48Cycling Preferences 50The Gibbard e Satterthwaite Theorem 51Reactions to the Arrow and Gibbard e SatterthwaiteTheorems 52 Conclusion 53References 53 Chapter 3 concludes our introduction to normative publicsector economics with a discussion of two issues. One isthe distinction between  󿬁 rst-best and second-best analyses.The other is the political economy of public sector theory,centered on the social welfare function and Arrow ’ simpossibility theorem. The social welfare function is theone indispensable political element in normative main-stream public sector models. LUMP-SUM REDISTRIBUTIONSAND PUBLIC SECTOR THEORY Are lump-sum redistributions a feasible policy tool for thegovernment? This may appear to be a relatively uninter-esting question. One is tempted to answer:  “ Probably not,but even if they are feasible, it hardly matters because fewgovernments use lump-sum taxes and transfers. For instance, no major US tax or transfer program is lumpsum. ”  All this is true, yet it is hard to imagine a moreimportant question for normative public sector theory. Theanswer has a dramatic impact on all normative policyprescriptions in every area of public sector analysis,whether they are directed at distributional or allocationalproblems. In public sector theory, lump-sum redistributionsstand at the border between  󿬁 rst-best and second-best analyses.The issue is not so much the existence of lump-sum redistributions. Lump-sum tax and transfer programs areeasy enough to describe. Poll taxes have occasionally beenused as revenue sources and they are certainly lumpsum from an economic perspective. On the transfer side,many countries have instituted per-person demogrants(e.g., Canada, which provides a grant to all the elderly).The United States allows a personal exemption for eachdependent child under the federal personal income tax. It might be argued that decisions on family size are essentiallyeconomic and would in 󿬂 uence the amount of transfer received. If so, then tax exemptions and demogrants tochildren are not strictly lump sum, although the legislationcould be drafted such that only children already living at the time of passage would receive the transfers.The mere existence of lump-sum taxes and transfers isnot enough, however, to render them feasible policy tools Public Finance. http://dx.doi.org/10.1016/B978-0-12-415834-4.00003-0 Copyright   ©  2015 Elsevier Inc. All rights reserved. 37  in the pursuit of equity. The lump-sum taxes and transfersmust be  󿬂 exible enough so that they can be designed tosatisfy the interpersonal equity conditions for social welfaremaximization, and this is a very tall order indeed. To beeffective, the taxes and transfers would almost certainlyhave to be related to consumption or income or wealth inorder to distinguish the haves from the have-nots, but thenit is doubtful that they would be lump sum.Income taxes were thought to be essentially lump sum before 1970, because empirical research had been unable todiscoveranyrelationshipbetweenincometaxratesandeither work effort or saving. Research since then, employingdetailed micro data sets and sophisticated microeconometrictechniques, suggests that labor supply does respond tochangesinafter-taxwages,certainlythefemalelaborsupply.The evidence on saving behavior is more mixed, but savingalso appears to respond somewhat to changes in after-taxrates of return. 1 In any event, no one today believes that income-based taxes and transfers are lump sum. Therefore,the assumption that the government can pursue an optimallump-sum redistribution policy is heroic in the extreme.Nonetheless, public sector economists have been quitewilling to employ the assumption of optimal lump-sum redistributions to analyze allocational policy questions in a  󿬁 rst-best framework. FIRST-BEST ANALYSIS First-best analysis means that the government has a suf  󿬁 -cient set of policy tools for whatever problems may exist torestore the economy to the bliss point on its  󿬁 rst-best utility-possibilities frontier. By the  “ 󿬁 rst-best  ”  utility-possibilities frontier, we mean the locus of pareto-optimalallocations constrained only by three fundamentals of anyeconomy: individual preferences, production technologies,and market clearance. 2 The required set of policy tools is broad indeed. If theanalysis occurs within the context of a market economy, it is understood either that all markets are perfectly compet-itive or that the government can adjust behavior innoncompetitive markets to generate the perfectly competi-tive results. Faced with a breakdown in one of the technicalassumptions discussed in Chapter 1, the government must be able to respond with a policy that restores  󿬁 rst-best pareto optimality. As we shall discover in Part II, therequired policy responses may be exceedingly complex,enough so that they have little hope of practical application.Finally, the government must employ optimal lump-sum redistributions to equalize social marginal utilities of con-sumption (income) at the  󿬁 rst-best bliss point. The Two Dichotomies in First-Best Models Whatistheattractionof  󿬁 rst-bestanalysis,givenitsstringent and unrealistic assumptions? The answer is that   󿬁 rst-best analysis is really the only way to analyze the particular allocation problems caused by breakdowns in the technicalassumptions and market imperfections in and of themselves.Consider,  󿬁 rst, the role of lump-sum redistributions in thisregard.If lump-sum redistributions are feasible, then the prob-lem of social welfare maximization dichotomizes intoseparate ef  󿬁 ciency and distributional problems, exactly asthe model in Chapter 2 dichotomized into the pareto-optimal and interpersonal equity conditions. The intuitionfor why this is so can be seen in terms of concepts alreadydeveloped.Suppose one of the technical assumptions in Chapter 1fails to hold, for example, there exists a consumer eter-nality, meaning that at least one person ’ s utility depends onthe goods demanded and/or factors supplied by some other consumer(s). Suppose, further, that the government consistsof an allocation branch charged with designing policies tocorrect for allocational problems such as externalities and a distributional branch charged with creating an optimaldistribution of income. 3 If lump-sum redistributions arepossible, the allocation branch can ignore the existence of a social welfare function and analyze the externality in thecontext of the  󿬁 rst general equilibrium model presented inChapter 2, the model in which one consumer  ’ s utility ismaximized subject to the constraints of all other utilitiesheld constant (and production and market clearance). Thismodel is speci 󿬁 cally designed to  󿬁 nd the set of pareto-optimal allocations consistent with society ’ s  󿬁 rst-best util-ity-possibilities frontier given the presence of an externalityor any other imperfection. All relevant structural elementsof the policy necessary to correct for the externality follow 1. For an excellent review of the early empirical studies on labor supplyand savings elasticities, see Boskin (1976). The Tax Reform Act of 1986led to renewed interest in these elasticities. See Auerbach and Slemrod(1997).2. If some factors or production are supplied in absolutely  󿬁 xed amounts,they, too, act as constraints on the set of attainable utility possibilities.Recall that the general equilibrium model of Chapter 2 assumes variablefactor supplies so that, formally, consumers ’  disutility from supplyingfactors enters as an argument of the social welfare objective function rather than as a constraint.3. Richard Musgrave, the dean of living public sector economists, longago proposed the useful  󿬁 ction of government policy emanating from three distinct branches of government, an allocation branch, a distribu-tion branch, and a stabilization branch. The allocation branch wasdedicated to pursuing ef  󿬁 ciency, the distribution branch to pursuingequity, and the stabilization branch to pursuing long-run economicgrowth and the smoothing of the business cycle. One dif  󿬁 culty withMusgrave ’ s  󿬁 ction is the extent to which the three branches can designpolicies independently from one another. They can operate independentlyin a   󿬁 rst-best environment, but not in a second-best environment. SeeMusgrave (1959). 38 PART | I  Introduction: The Content and Methodology of Public Sector Theory  directly from the  󿬁 rst-order conditions of this model. Theallocational branch does not have to worry about socialwelfare. It knows that the distributional agency is simul-taneously designing policies to ensure that social marginalutilities are equalized along the  󿬁 rst-best utility-possibilitiesfrontier in accordance with the interpersonal equity condi-tions. Therefore, it knows that any unwanted distributionalconsequences of its allocational policies are being fullyoffset by the distribution branch.Suppose, instead, that a single superagency concernsitself with both the externality and the srcinal nonoptimalincome distribution and develops a full model of socialwelfare maximization to analyze these two problemssimultaneously. Since the  󿬁 rst-order conditions of themodel dichotomize, this agency would discover one set of pareto-optimal conditions that do not involve the socialwelfare rankings and one set of interpersonal equity con-ditions that equalize all social marginal utilities of income(or of one good or factor). These conditions would beidentical with those developed independently by the sepa-rate allocation and distribution branches. Since the pareto-optimal conditions contain no social welfare terms, theymust generate the  󿬁 rst-best utility-possibilities frontier. Noother result is consistent with social welfare maximizationunder   󿬁 rst-best assumptions. Similarly, the interpersonalequity conditions must be identical to those developed bythe independent distribution agency. Only one distributionis consistent with the bliss point on the  󿬁 rst-best utilitypossibilities frontier under the assumptions used throughout the text.The two independent branches would have to coordinatetheir efforts. Since an economy is an interdependent system,all allocational decisions have distributional consequences,and vice versa. Consequently, the allocation branch cannot  󿬁 nally set its policies until it knows what the distributionalbranchhasdoneorisabouttodo,andviceversa. Continuingwith the externality example, suppose the externality is a  “ bad ”  such as pollution. Moreover, suppose the correct policy takes the form of a tax on the polluters (a reasonablesupposition,asweshalldiscoverinChapter6).Byfollowingthe independent modeling process described above, theallocation branch can determine all the relevant designcharacteristics of the tax, such as what should be taxed andwhat parameters in the economy affect the level of the taxrates,buttheexactlevelofthetaxratecannotbedetermined.The criterion of pareto optimality admits to an in 󿬁 nity of allocations, all of those on the utility-possibilities frontier. Inthis example, each allocation has one particular tax rateassociated with it, so that the  󿬁 nal tax rate cannot beannounced until the distribution branch announces itsoptimal redistributional policy, thereby selecting the alloca-tion consistent with the bliss point.Turning the example around, the interpersonal equityconditionstellthedistributionalagencyalltherelevant  designcharacteristics  of the optimal lump-sum redistributions, but the exact   levels  of all individual taxes and transfers depend inpartuponthegainsandlossesoccasionedbythepollutiontax.Thus, while it is possible analytically to distinguish betweenthe design of allocational policies and the design of distribu-tional policies, as 󿬁 rst-bestanalysis does, the exact policies tobe followed must be simultaneously determined. In formalterms, the pareto-optimal and interpersonal equity conditionsarebothnecessaryconditionsforsocialwelfaremaximization.They must be solved simultaneously to determine a socialwelfare maximum.Despite the ultimate interdependence of allocational anddistributional policies, the  󿬁 rst-best literature on publicexpenditure theory typically analyzes only ef  󿬁 ciencyproblems inherent in the breakdown of the technical as-sumptions (or of market imperfections), ignoringcompletely the question of distributive equity. The analysisgenerally proceeds along the following lines. First, thepareto-optimal conditions are derived, given that one of thetechnical assumptions fails. Then policies are described that generate the pareto-optimal conditions, given the assump-tion that consumers and  󿬁 rms operate within a perfectlycompetitive market economy. Perfect competition is theonly market environment consistent with  󿬁 rst-best analysis.The assumption of perfect competition naturally leads totwo further questions: 1.  What allocation of resources would the competitivemarket generate in the absence of government intervention? 2.  Can the government restore  󿬁 rst-best pareto optimalitywhile maintaining existing competitive markets, or is a complete government takeover of some activity abso-lutelynecessary?Thatis,canthepolicybedecentralized?Distributional issues are ignored in the  󿬁 rst-best litera-ture not because they are unimportant but rather becausethey are relatively uninteresting. As noted in the conclusionto Chapter 2, having said that the government shouldredistribute lump sum to satisfy the interpersonal equityconditions necessary for social welfare maximization, thereis little else to say. A breakdown in one of the technicalassumptions may alter the precise form of the interpersonalconditions somewhat, but they still have the interpretationthat one good (or factor) should be redistributed lump sum to equalize the social marginal utilities of that good (or factor).In contrast, the pareto-optimal conditions often changesubstantially when the technical assumptions fail, both intheir form and their interpretation. Small wonder, then, that  󿬁 rst-best analysis tends to emphasize these conditions andoften relegates the interpersonal equity conditions to a foot-note,iftheyarementionedatall.Knowingthatthe 󿬁 rst-order conditions of a full model of social welfare maximizationdichotomize, there is no need to use the full model. A simple First-Best and Second-Best Analyses and the Political Economy of Public Sector Economics  Chapter | 3 39  model highlighting the  󿬁 rst-best pareto-optimal conditionsfor the allocational problem at hand is suf  󿬁 cient.The  󿬁 rst-best analysis in Part II of the text is careful,however, to use full models of social welfare maximizationwhen analyzing allocational problems. Keeping the socialwelfare function in the models serves to emphasize theimportance of lump-sum redistributions to all  󿬁 rst-best policy analysis.First-best models have a highlyuseful second dichotomyproperty besides the dichotomy between the pareto-optimaland interpersonal equity conditions. The pareto-optimalconditions themselves dichotomize. A breakdown in one of the technicalassumptions or a market imperfection alters thepareto-optimal conditions for those goods and factorsdirectlyaffectedbutleavesunchangedtheformofthepareto-optimal conditions of all the unaffected goods and factors.For example, suppose a competitive market satis 󿬁 es thepareto-optimal condition for the allocation of some good,withpriceequaltomarginalcost.Priceequaltomarginalcost continues to be the pareto-optimal pricing rule for that goodeven if other markets contain externalities or exhibit decreasing cost production, so long as the policy environ-ment is  󿬁 rst best. The government  ’ s response to the market failure can stay focused on the source of the market failure.To summarize, the double dichotomy of distributionaland allocational problems under   󿬁 rst-best assumptionsmakes  󿬁 rst-best analysis especially attractive for the  ceteris paribus  analysis of policy issues. An allocational problem associated with a particular economic activity can be iso-lated from distributional considerations and from all theother conditions within the economy that are required for pareto optimality. This property justi 󿬁 es the use of verysimple general equilibrium models that focus exclusivelyon one source of market failure and describe the rest of theeconomy by means of a single composite commodity that isassumed to be marketed competitively. Assuming a   󿬁 rst-best policy environment is a tremendous analyticalconvenience. SECOND-BEST ANALYSIS Suppose, realistically, that lump-sum taxes and transfers arenot available to the government, at least not with suf  󿬁 cient  󿬂 exibility to generate the interpersonal equity conditionsof the standard model. This changes the analysis rather drastically. To see why, consider two government policystrategies in the context of a market economy, one designedto produce distributive equity, the other designed to restore 󿬁 rst-best pareto optimality. Constrained Social Welfare Maximization Suppose that the government chooses to redistribute in-come until social marginal utilities are equalized by usingtaxes and transfers that are not lump sum. 4 The redistri-bution necessarily introduces distortions into the economybecause some consumers and/or producers now facedifferent prices for the same goods and/or factors. Sinceconsumers and producers equate relative prices to their marginal rates of substitution and transformation, respec-tively, and since pareto optimality requires that the mar-ginal rate of substitution (MRS) equals the marginal rate of transformation, some of the pareto-optimal conditions nolonger hold. The redistribution forces the economy beneathits  󿬁 rst-best utility-possibilities frontier.Suppose instead that the government focuses only onallocational problems and chooses allocational policiesdesigned to bring society to the  󿬁 rst-best utility-possibilitiesfrontier. 5 Without simultaneously employing lump-sum redistributions, however, the economy would not be at the bliss point, in general. The government may actuallychoose some policy mix designed to move the economysomewhat closer to full pareto optimality, and somewhat closer to distributive equity, but the point remains that removing the possibility of feasible lump-sum re-distributions restricts the set of solutions available to thegovernment, for example, to the shaded portion in Fig. 3.1.The viable allocations and distributions may or may not include points on the  󿬁 rst-best utility-possibilities frontier,but, importantly, they de 󿬁 nitely exclude the bliss point,point B. The policy problem now becomes one of   󿬁 ndingthe best policy option within this restricted set of oppor-tunities. As such it is part of   second-best analysis , de 󿬁 nedas the analysis of optimal public sector policy given that the 1 U 2 UB 2 W FIGURE 3.1 4. Assume it is possible to equalize social marginal utilities without lump-sum redistributions. It may not be, given the available policy tools.5. Again, assume this is possible. 40 PART | I  Introduction: The Content and Methodology of Public Sector Theory
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