Provision of public or private goods

Political scientists have long argued that unadulterated, fully participatory, median-voter democracy describes no actual political system – rather, the translation of resources into influence occurs in highly institutionalized environments that amplify some voices and mute others. Although we do not want to dispute the validity of this claim, in this paper we show that, in a median-voter framework, the relationship between inequality and redistribution is not always positive once we take into account that redistribution is often effected through the public provision of private goods 1 . For this purpose we construct a model in which the government uses the tax proceeds to finance the provision of a rival public good which is

Political scientists have long argued that unadulterated, fully participatory, median-voter democracy describes no actual political system – rather, the translation of resources into influence occurs in highly institutionalized environments that amplify some voices and mute others. Although we do not want to dispute the validity of this claim, in this paper we show that the median voter-framework can generate a more diverse set of outcomes once we take into account that redistribution is often effected through the public provision of private goods 1 . Moreover, we demonstrate that if the assumption of perfect competition is relaxed

The fundamental message of our paper is twofold. On one hand we claim that, in the presence of public provision of private goods, the distortionary part of a marginal tax rate does not necessarily coincide with its face value. On the other hand we also claim that economies with higher marginal tax rates might actually be less distortionary than economies with lower marginal tax rates. To illustrate the first claim, we will start by presenting the basics within a model which is stripped down to a bare minimum. There is a large population of identical individuals each of whom is a parent with a single child, and initially there is no public sector. Denote by w and h the wage rate and the working hours of the representative agent, respectively. We assume that the wage rate reflects the true productivity of the worker. Let p be the cost per hour of child care, and denote by C the consumption of the agent. The agent has preferences for consumption and labor expressed by the utility function u(C,h). According to the budget constraint of the agent C=wh-ph. Along the budget line, dC/dh=w-p. The net income obtained from an hour of work is the wage rate minus the cost of working, which is the price paid for child care. This is the net social income, and where the agent faces no taxes and buys child care in the market, the net private income is equal to the social one. There is no distortion. The agent will maximize utility by setting the marginal disbenefit from working equal to the net marginal income, and the demand for child care is determined by the hours of work.

In other words, the quality of Linux functions as the maximum performance capacity of Linux-based computers/applications. That is, the users benefit from high-quality Linux- based computers/applications only if the quality of Linux is high. In the presence of strong complementarity between public and private goods, as in Linux and its applications, beneficiaries of the public good are likely to participate volun- tarily in provision of the public good. For an individual to obtain substantial utility, it is necessary to consume large quantities of both public and private goods. Thus, when the public good is provided in sufficiently low quantities, an individual voluntarily produces the public good using private goods rather than by free riding. The complementarity between the public and the private goods may result in the participation of many individ- uals in providing public goods. In fact, there are many projects for OSS; many engineers voluntarily participate in the development of OSS, and many types of high-quality OSS are provided. 1 This situation concerning OSS seems different from that predicted by the

Several contributions in the optimal taxation literature have emphasized that, when in- dividuals’ preferences are not separable between leisure and other goods, it is desirable to supplement a nonlinear income tax with public provision of private goods. Moreover, it has also been shown that the choice between a topping-up and an opting-out scheme depends on whether the publicly provided good is a complement or substitute with leisure, with opting- out (topping-up) being the preferred scheme for goods which are substitutes (complements) for labor. In this paper, using the self-selection approach to tax analysis, we revisit these results in the presence of tax avoidance, and investigate how public provision interacts with the agents’incentives to engage in tax avoidance. Three results are obtained. First, we show that tax dodging opportunities imply that non-separability between labor and other goods is neither a necessary nor a su¢ cient condition to make public provision of private goods a welfare-enhancing policy instrument. Second, we show how tax dodging opportunities limit the scope for using topping-up provision schemes as a redistributive device. Finally, we show that, for most of the public provision schemes previously analyzed in the literature, being a welfare-enhancing policy instrument goes hand in hand with weakening the agents’incentives to shelter income from the tax authority. However, we also point out an important exception to this pattern.

child care services and elderly care services represent the best examples of private goods fitting their model of PP. Applying this idea to our model, the group of users could be thought as being composed of people with small children and of people with elderly relatives who need to be taken care of. Thus, increasing the fraction of users from 8 to 15% might be interpreted as a way to measure the welfare gains achievable by publicly providing both child care- and elderly-care services. Admittedly, the measure that we get represents only a crude estimate of the welfare effects. The reason is that it rests on two implicit assumptions that are unlikely to be satisfied in practice. The first is that the unitary price of child care services and the unitary price of elderly care services are the same. The second is that users either need child-care or elderly-care services but not both at the same time. Notice however that, once public provision of child care services is supplemented by public provision of elderly care services, the relative merits of PP, as compared to tagging, are likely to be magnified. The reason is that if one can in principle think at the implementation of a tagging scheme that offers different tax schedules to parents and non-parents, it seems unfeasible to implement a tagging scheme that discriminates between agents who have to take care of their older relatives and agents who do not.

1. Introduction A strong case for public provision of certain private goods has been established in an economy in which individuals have homogeneous preferences but differ in skill levels. 3 A non-linear, redistributive income tax is imposed under the asymmetric information that knowledge of who is high-skilled and who is low-skilled is private information not available to the government. The tax schedule must then be designed subject to the self-selection constraint ensuring that a high- skilled person does not select an income point intended for the low-skilled person. If the high- skilled person were to mimic, he would obtain more leisure than the low-skilled person with the same income as, being more productive, the high-skilled person could earn the same income in less time. However, if some of the transfer is given in kind, it may be of less value to the mimicker than to the genuine low-skilled type if the good that is transferred is less beneficial to someone who enjoys more leisure. Shifting to a transfer in kind may therefore make mimicking less appealing, and thus alleviate the self-selection constraint and enhance welfare. Day care for children may be a striking example of a good suitable for this purpose as a person who works less will need less day care. By pretending to be low-skilled, the high-skilled person will pay the same tax as the low-skilled person, but will obtain a smaller benefit in return.

Corollary 3. (Bergstrom, Blume, and Varian [6]) Suppose the public good is pure, that is, the network is complete, and assume both public and private goods are normal goods. Then relatively small transfers among contributors are neutral. Corollary 3 establishes the standard neutrality result of Warr [38] and Bergstrom, Blume, and Varian [6] by following an alternative approach based on analysis of the private provision of public goods on networks. More generally, the light shed by Theorem 3 on the neutrality of income redistribution in networks is insightful. In interpretation, although one might not expect the neutrality result from the usual pure public good setting to extend to other settings with local interaction patterns accounted for, it is still important to point out that the neutrality result has some serious limitations as it fails in all networks where the set of contributors is not neighborhood homogenous.

In this paper, we present a general proof of existence and uniqueness of a Nash equilibrium in the private provision of a public good on networks. We show that the shared ground of Bergstrom, Blume, and Varian (1986) and Bramoull´ e, Kranton, and D’Amours (2011) is beyond the trivial case of a complete network with linear best-reply functions. Indeed, our existence and uniqueness results simultaneously extend similar results in Bergstrom, Blume, and Varian (1986) on the private provision to networks and in Bramoull´ e, Kranton, and D’Amours (2011) on games of strategic substitutes to nonlinear best-reply functions. A crucial innovation of this paper is the uniqueness proof technique, which is based on an adaptation of Stiemke’s Lemma to the private provision of public goods. 5 In our approach, we overcome the lack of linear structure by resorting to a network-specific normality assumption of both public and private goods which stipulates bounds on the nonlinear best-reply functions. In addition, an inherent advantage of our proof technique is that it applies directly to the original public good game and, therefore, it provides insights on what is driving the uniqueness result in this class of games.

Remarks on selected literature on strategic market games: 1. A question that immediately arises in the strategic market game context is whether prices are positive. This question was addressed by Peck, Shell and Spear (1992) who demonstrate conditions on a private-goods economy under which there are strictly positive equilibrium bids for all goods (and provide an in-depth study of the model). 8 We cannot establish such a result and do not aim to do so, given that we wish to allow situations where some consumers do not contribute to public good provision and we allow production, with the possibility that some public goods are not produced. Like our paper, Peck, Shell and Spear consider an ‘inside’or …at money, representing the private debt of the consumers with default penalties but, unlike the situation in our continuum game model, there is no bound on consumer debt. We require such a bound; otherwise consumer demands would be unlimited and, as DG, we wish to demonstrate that, with many players, price-taking equilibrium outcomes arise as outcomes of strategic behavior. 9

Q.E.D. It is not surprising that proposition 2 is affiliated to results that were earlier obtained for non-excludable public goods, while proposition 1 is more similar to results of the private goods literature. A welfare-maximizer has less intention to exclude any agents, as long as congestion effects and distribution costs do not force her to do so. On the other hand, the possibility of exclusion certainly is important. There is indeed a fundamental difference between the allocation rules (5) and (6), which will become clear when we consider the case of many consumers.

Our paper is related to two main strands of literature: the literature on pri- vate contributions towards collective consumption (Malinvaud, 1972; Bergstrom, Blume and Varian, 1986; Andreoni, 1990; and subsequent contributions); and the literature on social learning (Banerjee, 1992; Ellison and Fudenberg, 1995; and sub- sequent contributions). Two recent papers that are somewhat related to ours are Dutta and Chatterjee (2010), and Bramoull´e and Kranton (2007). The first paper looks looks at costless information transmission across consumers for the case of private goods; as we have already noted, the public good case is fundamentally different from the private good case – where no costly transmission of informa- tion (fundraising) can occur. The second paper focuses on the provision of public

time and money to convince donors that they provide a useful service. If a new charity enters with a new ideology, that ideology will appeal to many donors. It will then be easier for the new charity to get money from those donors than it was for the old charities. The new charity therefore has to expend less effort to get donations, and the expenditures are basically wasted money. Yet in all cases, the entry leads to greater competition and thus higher total fundraising expenditures because old charities will Þght to keep their donors. Our result may be changed if increased competition leads to an increase in donations, but that is really a different issue. We are interested in the effects of competition for existing donors. The key proposition in this essay proved the result that increased competition always makes for less provision of public goods. In private goods markets, on the other hand, it is usually thought that more competition is a good thing.

(i) Any change in the wealth distribution that leaves unchanged the aggregate wealth of current contributors will either increase or leave unchanged the equilibrium[r]

To model private provision in a dynamic setting, I consider an infinitely repeated version of the static voluntary contributions game. To model public provision, I apply Bernheim and Slavov’s (2009) notion of a dynamic Condorcet winner (DCW), which extends the Condorcet winner concept to dynamic settings. A DCW prescribes a policy for every possible history in such a way that for any history, the prescribed policy choice is majority preferred to any other policy given the implications of the current choice for future outcomes. In contrast to the static setting, a one-parameter tax system is not required to ensure the existence of DCWs. Indeed, DCWs exist with a completely unrestricted tax system, in which each individual pays a different positive or negative tax rate. Lifting the one-parameter restriction on the tax system allows income redistribution to be chosen jointly with the level of the public good. 1 While the DCW concept is intuitively appealing because of its similarity to the static Condorcet concept, applying it in practice can be analytically difficult, even for very simple problems (see, e.g., Bernheim and Slavov 2004, Bernheim and Slavov 2009, Slavov 2006). Thus, an additional contribution of this paper is to demonstrate how DCWs can be found computationally, allowing one to apply it to more complex problems.

The questions designed to measure altruistic attitudes followed the same format. Re- spondents were asked to indicate on a …ve-point scale the extent to which they agree or disagree with a series of statements that probed di¤erent aspects of the Schwartz (1970, 1977) model for the activation of altruistic behavior. While questions of this type are com- monly used in experimental economics to explain private provision of public goods, they are less commonly used in the …eld where such data are more di¢ cult to obtain. 13 This, however, was not a limitation for this study given the household mail survey. The scale that we use is based on a subset of the items used by Clark, Kotchen, and Moore (2003). The speci…c items are listed in the Appendix Table, along with the statistics to test for internal consistency. Based on these results, it is reasonable to combine the responses to form another summated scale that measures a general altruistic attitude.

Cornes and Itaya (2010) show that in a one-shot, Nash provision game with many public goods, any income redistribution has no effect on the orig- inal equilibrium allocation, as long as that redistribution occurs within a set of linked individuals who are eventually connected each other through effective private contributions to many interfamily public goods. They call it “partial neutrality”. We shall show that their linkage concept plays a key role in generating the neutrality as well as non-uniqueness of an equilibrium allocation in the present two-stage provision game. In our model we define a “link” as either positive parent-to-child transfers or positive private dona- tions to interfamily public goods, and then show that when a redistribution of income is undertaken among the linked individuals who are eventually con- nected each other through the latter link, neutrality arises. Moreover, if the number of links is larger than the minimum number of links which connect individuals, the indeterminacy in terms of choice variables at the node where extra links emerge arises.

Finally, consider the implications of relaxing part (iii) of Assumption 1. If ® + ¯ < 1, individ- uals will never consume g, as they could always do better obtaining X and Y separately through c and d. In other words, the green technology is simply not viable. If, however, ® + ¯ = 1, individuals will be indi¤erent between obtaining characteristics jointly through g and separately through c and d. This follows because the green technology is simply a bundling of characteristics that produces no change in the production possibilities. In this case, it can be shown that the mapping between characteristics and goods is no longer unique with the green market. There are an in…nite number of Nash equilibria with respect to choices over market goods; however, every equilibrium supports the same levels of environmental quality and social welfare. These levels are also identical with and without the green market. Thus, green technologies that simply bundle characteristics and produce no change in the production possibilities will have no e¤ect on environmental quality or social welfare.

In 1986 the Environmental Protection Agency of the United States started a program with the intention of using information provision as a regulatory instrument. To this end, two years later the Toxic Release Inventory (TRI) was initiated. In 1992 the United Nations Conference on Environment and Development affirmed the right of communities to know about toxics, chem- icals, and other substances. Currently more than 30 countries have adopted so-called pollutant release and transfer registers. 1 These registers ensure the measurement of plant emissions above a certain threshold. Emission mea- surement is a necessary condition for efficient emission management. But is the mere measurement and disclosure of emissions enough to incentivize firms to reduce emissions? A pecuniary incentive for active emission management would be given if it were an obviously a profitable strategy from the firm’s perspective. However, whether unrealized profitable emission reductions ex- ist due to investment-inefficiencies in green technologies actually exist is a controversial subject.

In this paper, we provide simple geometrical proofs to various results from the public- goods literature using the Kolm triangle. The Kolm triangle is the analogue of the Edgeworth box for an economy with two agents, one private good and one pure pub- lic good. Malinvaud (1971) refers to unpublished ‘research papers’ by Serge-Christophe Kolm, while the triangle managed to appear a bit earlier than Malinvaud’s paper in Ch. 9 (pp. 211–221) of Kolm’s text on public economics (Kolm 1970). Schlesinger (1989) describes it in good detail and illustrates its use in analyzing Lindahl and Nash equilibria. Despite its potential, the Kolm triangle hardly appears in the literature. 1 Sullivan and Schlesinger (1986) analyze the relationship between various canons of ‘just’ taxation with the help of this graphical device. Groves and Ledyard (1987) use the triangle to illustrate incentive-compatibility problems in an economy with public goods. More re- cently, Chander (1993) uses the triangle to discuss dynamic procedures and incentives in public-good economies. William Thomson uses this tool in various papers dealing with allocation mechanisms (Thomson 1987), lecture notes (Thomson 1990), and concepts of equity (Thomson 1993). Leamer (1987) uses a similar device to prove factor price equalization in international trade. More surprising, perhaps, is the fact that the Kolm triangle has not found its way in public economics textbooks. An exception is Laffont (1988) who displays a few diagrams of the Kolm triangle, although he just barely refers to them in the text.