The Important Thing Is Not (Always) Winning but Taking Part: Funding Public Goods with Contests

This paper considers a public good game with heterogeneous endowments and incomplete information affected by extreme free riding. I overcome this problem through the implementation of a deterministic contest in which several prizes may be awarded. I identify a monotone equilibrium, in which the contribution is strictly increasing in the endowment. I prove that it is optimal for the social planner to set the last prize equal to zero, but otherwise total expected contribution is invariant to the prize structure. Finally, I show that private provision via a contest Pareto‐dominates public provision and is higher than the total contribution raised through a lottery.     

Partial privatization in mixed duopoly with price and quality competition

We analyze price and quality competition in a mixed duopoly in which a profit-maximizing private firm competes against a state-owned public firm. We first show that the welfare-maximizing public firm provides a lower quality product than the private firm when they are equally efficient. In order to maximize social welfare, government manipulates the objective of the public firm that is given by a convex combination of profits and social welfare. It is demonstrated that an optimal incentive of the public firm is welfare maximization under the absence of quality competition, but it is neither welfare maximization nor profit maximization under the presence of quality competition. The result supports a completely mixed objective between welfare and profit maximizations or partial privatization of the public firm.      

Differential mortality and social security

Abstract This paper studies the normative problem of redistribution between individuals who differ in their lifespans. We discuss aspects related to the objective function and argue that aversion to multiperiod inequality should be taken into account. Then, we study the properties of the social optimum both with full information and with asymmetric information. We highlight the role of aversion to multiperiod inequality and show that it has substantial consequences on the design of Social Security schemes. In particular, we show that for a low (resp. high) aversion to multiperiod inequality, a negative (resp. positive) implicit tax rate on continued activity is desirable.     

Social network and private provision of public goods

Using a simple model with interdependent utilities, we study how social networks influence individual voluntary contributions to the provision of a public good. Departing from the standard model of public good provision, we assume that an agent’s utility has two terms: (a) ‘ego’-utility derived from the agent’s consumption of public and private goods, and (b) a social utility which is the sum of utility spillovers from other agents with whom the agent has social relationships. We establish conditions for the existence of a unique interior Nash equilibrium and describe the equilibrium in terms of network characteristics. We show that social network always has a positive effect on the provision of the public good. We also find that, in networks with “small world”-like modular structures, ‘bridging’ ties connecting distant parts of social network play an important role inducing an agent’s contribution to public good. Assumptions and results of the model are discussed in relation to the role of social capital in community-level development projects and to the effect of innovation networks on firms’ R&D investments.     

Chores

We analyze situations where the provision of each of c public goods must be voluntarily assumed by exactly one of n private agents in the absence of transfer schemes or binding contracts. We model this problem as a complete information, potentially infinite horizon game where n agents simultaneously wage c wars of attrition. Providing a public good commits an agent not to take on the provision of another public good for a fixed period. We explore the strategic trade-offs that this commitment ability and the multiplicity of tasks provide. Subgame perfect equilibria (SPEs) are characterized completely for games with two agents and two public goods. For games with two identical agents and c > 1 identical public goods, we establish that an equilibrium that yields a surplus-maximizing outcome always exists and we provide sufficient conditions under which it is the unique equilibrium outcome. We show that under mild conditions, the surplus-maximizing SPE is the unique symmetric SPE. Journal of Economic Literature Classification Number: H41, C72, D13.     

Regular Distributive Efficiency and the Distributive Liberal Social Contract

We consider abstract social systems of private property, made of n individuals endowed with nonpaternalistic interdependent preferences, who interact through exchanges on competitive markets and Pareto‐improving lump‐sum transfers. The transfers follow from a distributive liberal social contract defined as a redistribution of initial endowments such that the resulting market equilibrium allocation is both: (i) a distributive optimum (i.e., is Pareto‐efficient relative to individual interdependent preferences) and (ii) unanimously weakly preferred to the initial market equilibrium. We elicit minimal conditions for meaningful social contract redistribution in this setup, namely, the weighted sums of individual interdependent utility functions, built from arbitrary positive weights, have suitable properties of nonsatiation and inequality aversion; individuals have diverging views on redistribution, in some suitable sense, at (inclusive) distributive optima; and the initial market equilibrium is not a distributive optimum. We show that the relative interior of the set of social contract allocations is then a simply connected smooth manifold of dimension n ? 1. We also show that the distributive liberal social contract rules out transfer paradoxes in Arrow–Debreu social systems. We show, finally, that the liberal social contract yields a norm of collective action for the optimal provision of any pure public good.     

Private investment with social benefits under uncertainty: The dark side of public financing

We develop a game‐theoretic model of private–public contribution to a long‐term project with sequential actions and moral hazard. A private agent is one who is in charge of both the financial contribution and the management effort, these two actions entailing private costs and uncertain ex‐post private and social benefits. A public agent is one who decides the amount of public funding to this quasi‐public good, knowing that the size and the probability of attaining a surplus ex post depend on the private agent's effort. We consider four public‐funding scenarios: benefit‐sharing versus cost‐sharing crossed with ex‐ante versus ex‐interim government intervention. We test our theoretical predictions by means of an experiment that confirms the main result of the model: Cost‐sharing public intervention is more effective than benefit‐sharing in boosting private financial contribution to the project. Furthermore, when public intervention comes after private contribution ( ex‐interim government intervention), both public‐funding scenarios have a negative impact on the private management effort. In our model, the latter result is explained by the private agent's high degree of risk aversion. These results have policy implications for strategic investments with long‐term social consequences. In deciding the optimal timing and method of the contribution, governments should also consider the indirect effects on agents’ long‐term management efforts.     

Reducing Inefficiency in Public Good Provision Through Linking

We characterize the optimal mechanism for the provision of n public goods in an economy with m agents, binary valuations. The mechanism “links” the n problems together because decisions and transfers are based on the whole vector of valuations of the agents. In particular, the decision on whether or not to provide a public good depends not only on the valuations of the agents for that good but, in some cases, also on the valuations for the other goods reported by the low‐valuation agents. For the two‐agent case, we show that the mechanism is asymptotically efficient and we provide an example that compares its relative efficiency with optimal separate provision and with another asymptotically efficient mechanism in the literature.     

A Pie Allocation Among Sharing Groups

This paper deals with a pie allocation problem to users, who are divided intosharing groups, that are not necessarily disjoint. The pie is allocated among the groups, rather than the users. The portion of a sharing group is a public good for its members, that is, all of them can enjoy it. A non-cooperative game for allocating the pie and a special equilibrium outcome,strongly disappointment-free allocation, are defined. We prove the existence of a unique such allocation and show that it coincides with the Nash solution of the related bargaining problem.Journal of Economic LiteratureClassification Numbers: C70, C71, C72 and C78.     

Information Provision in Procurement Auctions

We study the optimal provision of information in a procurement auction with horizontally differentiated goods. The buyer has private information about her preferred location on the product space and has access to a costless communication device. A seller who pays the entry cost may submit a bid comprising a location and a minimum price. We characterize the optimal information structure and show that the buyer prefers to attract only two bids. Further, additional sellers are inefficient since they reduce total and consumer surplus, gross of entry costs. We show that the buyer will not find it optimal to send public information to all sellers. On the other hand, she may profit from setting a minimum price and that a severe hold‐up problem arises if she lacks commitment to set up the rules of the auction ex ante.     

The optimal harvesting problem with a land market: a characterization of the asymptotic convergence

We study the asymptotic behavior of the optimal harvesting policies for a multiple species forest with a land market, i.e., any fraction of the land can be traded at any time stage. We prove the existence of sustainable states and we discuss the conditions under which any optimal trajectory converges in the long run towards one of these states or towards the set of optimal periodic cycles. We also discuss briefly a more general problem that includes costs of converting land between the different species.      

The Political Economy of Clientelism*

In this paper, we argue that the political‐commitment problem provides an explanation for why much income redistribution takes an inefficient form, particularly employment in the public sector. A job is a credible way of redistributing when it provides rents (such as in situations with moral hazard), and employment is optimal ex post. Moreover, a job is selective and reversible, and thus ties the continuation utility of a voter to the political success of a particular politician. We show that the need to make offers of employment incentive‐compatible leads to inefficiencies in the supply of public goods. We also show that such inefficient redistribution becomes relatively attractive in situations with high inequality and low productivity. Inefficiency is increased when the stakes from politics are high, when inequality is high, and when money matters less than ideology in politics.     

Ramsey,Pigou, Heterogeneous Agents,and Nonatmospheric Consumption Externalities

This paper analyzes the effects of nonatmospheric consumption externalities on optimal commodity taxation and on the social cost and optimal levels of public good provision. A negative consumption externality, by lowering the social cost of public good provision, may require the second‐best level of public good provision to exceed the first‐best level. If those households who are most important for building up the consumption reference level respond the least to commodity taxation, the second‐best commodity tax rate may fall short of the first‐best rate. Moreover, in this case, heterogeneity may imply an equity‐efficiency tradeoff. This tradeoff is present only if the consumption externality is of the nonatmospheric type.     

Designing the optimal public pension system

This paper uses a two‐period overlapping generations model in order to provide a theoretical design for the optimal public pension system based on a partial equilibrium analysis. Household preferences depend on two periods' consumption and leisure and are positively homogeneous of degree m with respect to consumption in the working and retired periods. We present characteristic features of the optimal public pension system in this paper. First, differences in the population growth rate do not affect the large/small relation between the optimal net lifetime burden rates of generations. Second, we present the optimal public pension system explicitly if m < 1 and m ≠ 0. Third, the difference between the market time‐preference rate and the social time‐preference rate provides a crucial insight into the optimal burden rate of each generation.     

Ex Post Welfare under Alternative Health Care Systems

The implications of a societal aversion to inequality for the optimal structure of the health care system are studied. The agents are assumed to be ex ante identical, but to differ ex post in the state of their health. Inequality aversion is introduced by postulating a strictly concave ex post social welfare function. It is shown that the optimal public health care system allocates health care differently than would private health insurance; specifically, people who are relatively unhealthy with and without treatment receive more health care, and people who are relatively healthy with and without treatment receive less health care. The aggregate quantity of health care under the optimal public health care system can be either greater or smaller than under private health care insurance. If the public health care system is optimally designed, allowing agents to purchase supplementary private health care insurance cannot raise social welfare and is likely to decrease it.     

State-owned enterprises as indirect instruments of entry regulation

In the context of mixed markets, Matsumura and Kanda (J Econ 84(1): 27–48, 2005) show that social welfare in free entry equilibrium is maximized when there exists a public firm in the market. En passant, these authors state that this outcome is connected to the entry-deterring influence of a public firm. In this way, they counter-act the excess entry problem of Mankiw and Whinston (Rand J Econ 17(1): 48–58, 1986). We explain this result arguing that the state-owned firm can be an indirect instrument to regulate entry. In fact, under free entry equilibrium welfare may be greater with the presence of a public firm than with a social planner.      

Partial Privatization in a Differentiated Mixed Oligopoly

A model of differentiated mixed oligopoly is developed to systematically discuss the welfare consequences of partial privatization of a public firm. We analytically derive the optimal degree of partial privatization not only in the short run with restricted entry but also in the long run with free entry. It is shown that the short-run optimal policy is non-monotonic in the degree of love of variety, while the optimal degree of privatization is monotonically increasing in the consumer's preference for variety in the long run.      

An Experimental Investigation of Excludable Public Goods

This paper extends the research on incentive compatible institutions for the provision of public goods by imposing a minimum contribution that must be met in order for an individual to enjoy the benefits of the public good. Excluding individuals who do not contribute at least the minimum transforms the linear n-player pure public goods game to an n-player coordination game with multiple, Pareto-ranked Nash equilibria. The experimental results show that exclusion increases contributions to the public good in most cases. However, an increase in contributions may not be sufficient to increase social welfare because there is a welfare cost to excluding individuals when the good is non-rival. Furthermore, exclusion can decrease both contributions and welfare in environments in which individuals fail to coordinate their contributions. The results are sensitive to the minimum contribution requirement and to the relative returns from the public and private alternatives.     

Unspoken ethical issues in the climate affair: Insights from a theoretical analysis of negotiation mandates

Taking climate change as an example, this paper provides new insights on the optimal provision of a long-term public good within and across generations. We write the Bowen–Lindhal–Samuelson (BLS) conditions for the optimal provision of the public good in a world divided into N countries, with two periods, present and future, and we simultaneously determine the optimal response in the first and second periods for a given rate of pure time preference. However, the Negishi weights at second period cannot be determined unambiguously, even under a “no redistribution constraint” within each generation, because they depend on non-observable future incomes; and thus on the answers to two often-overlooked ethical questions: (i) Do rich countries agree on deals which recognize that developing countries may catch up with developed countries in the long run, or do they use their negotiating powers to preserve the current balance of power? And (ii) does each country consider only the welfare of its own future citizens (dynastic solidarity) or does it extend its concern to all future human beings (universal solidarity)? Answers to (i) and (ii)—critical in the debate about how to correct the market failures causing global warming—define four sets of Negishi weights and intertemporal welfare functions, which we interpret as four mandates that countries could give to the Chair of an international negotiation on climate change to find an optimal solution. We find that in all mandates, public good provision expenditures are decreasing functions of income at first period. But each mandate leads to a different allocation of expenditures at second period and to different optimal levels of public good provision at both first and second periods. Finally, we show that only one of these four mandates defines a space for viable compromises.     

Uncertainty, Commitment, and Optimal Taxation

This paper examines the optimal tax design problem in the presence of wage uncertainty. The wage has a continuous distribution, individuals are ex ante identical, preferences are separable in labor supply and goods, public policy aims at providing the population with social insurance, and the only restriction on the tax instruments is that emanating from lack of public observability of realized wages and labor supplies. We show that optimal tax structures depend crucially on whether it is labor supply or goods that consumers have to commit to before the resolution of uncertainty. Specifically, we prove that, in the absence of commitment, the social insurance problem collapses to the traditional optimal tax problem. Second, if labor supply is precommitted, it would be possible to effect a first-best outcome. Third, commitment to goods would make indirect taxation a useful instrument of tax policy even in the presence of a general income tax; it requires differential tax treatment of committed and noncommitted goods. Finally, if preferences are separable between the two types of goods, precommitted goods must be taxed at a uniform rate lower than that on the noncommitted goods.