On the second optimality theorem of welfare economics

To what extent does the second optimality theorem of welfare economics (every Pareto optimal allocation can be repesented as a Walras equilibrium allocation) remain valid when preferences are allowed to be locally satiated? It is always valid for an exchange economy, and is valid for a production economy if there is a consumer who is not locally satiated, but not in general for a production economy where all consumers are locally satiated. A generalized equilibrium is defined, which includes the Walras equilibrium as a special case. Every Pareto optimum can be represented as a generalized equilibrium allocation. Furthermore, every Pareto optimal utility distribution can be realized by a Walras equilibrium allocation.     

Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies

In this paper we consider a class of economies with a finite number of divisible commodities, linear production technologies, and indivisible goods and a finite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on one of the divisible commodities and on all the indivisible commodities, if each agent initially owns a sufficient amount of one of the divisible commodities, and if a “no production without input”-like assumption on the production sector holds, then there exists a competitive equilibrium for any economy in this class. The usual convexity assumption is not needed here. Furthermore, by imposing strong monotonicity on one of the divisible commodities we show that any competitive equilibrium is in the core of the economy and therefore the first theorem of welfare also holds. We further obtain a second welfare theorem stating that under some conditions a Pareto efficient allocation can be sustained by a competitive equilibrium allocation for some well-chosen redistribution of the total initial endowments. Journal of Economic Literature Classification Numbers: D4, D46, D5, D51, D6, D61.     

EFFICIENT MIXED CLUBS: NONLINEAR-PRICING EQUILIBRIA WITH ENTREPRENEURIAL MANAGERS

Scotchmer and Wooders show that efficient clubs are homogeneous when consumers are divisible in Berglas's anonymous crowding model. However, if consumers are not divisible or if clubs have multiple facilities with economies of scope, mixed clubs are efficient. In such a model, we consider clubs with multiple membership policies for different types of consumers, and show the existence and efficiency of equilibrium with nonlinear policies. We employ entrepreneurial equilibrium, all equilibrium concept with profit-seeking entrepreneurs. Our theorem can be regarded as showing the existence of a core allocation that satisfies envy-free property in the absence of non-anonymous crowding effects.     

The core of an economy with satiation

Summary. It has long been known that in economies with satiation, the set of competitive equilibria does not coincide with the limiting core of an economy. In dividend equilibria, introduced independently by a number of authors, the budget excess is allowed to be divided among consumers as dividends and equilibrium existence is restored. In this paper a new notion of blocking which leads to core - dividend equilibrium equivalence is introduced. Specifically, it is shown that an allocation is a dividend equilibrium if and only if a corresponding equal treatment allocation of a large economy is in the core.Received: 21 June 2003, Revised: 3 December 2003, JEL Classification Numbers: D50.Alexander Konovalov: The author would like to thank M. Florig, P. J. J. Herings, V. Marakulin, D. Talman, V. Vasilev, and anonymous referees for helpful comments and suggestions.     

Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems

This paper analyses the sustainability of inter-generational transfers in Samuelson's consumption-loan model when agents are imperfectly informed about past events. We find that with mild informational constraints, transfers cannot be supported by pure-strategy equilibria. Mixed strategies allow transfers to be sustained even if agents have little information, so that a version of the Folk theorem holds. However, these equilibria are not robust. If each agent's utility function is subjected to a small random perturbation as in Harsanyi (1973), these mixed strategy equilibria unravel, and only the zero-transfer allocation survives as the unique rationalizable outcome. This result is an example of mixed strategy equilibrium of an extensive form game which cannot be purified.     

Non-myopic learning in differential information economies: the core

Summary. We study the process of learning in a differential information economy, with a continuum of states of nature that follow a Markov process. The economy extends over an infinite number of periods and we assume that the agents behave non-myopically, i.e., they discount the future. We adopt a new equilibrium concept, the non-myopic core. A realized agreement in each period generates information that changes the underlying structure in the economy. The results we obtain serve as an extension to the results in Koutsougeras and Yannelis (1999) in a setting where agents behave non-myopically. In particular, we examine the following two questions: 1) If we have a sequence of allocations that are in an approximate non-myopic core (we allow for bounded rationality), is it possible to find a subsequence that converges to a non-myopic core allocation in a limit full information economy? 2) Given a non-myopic core allocation in a limit full information economy can we find a sequence of approximate non-myopic core allocations that converges to that allocation? Received: May 25, 1999; revised version: August 9, 1999     

Ambiguity aversion and trade

What is the effect of ambiguity aversion on trade? Although in a Bewley??s model, ambiguity aversion always leads to less trade; in other models, this is not always true. However, we show that if the endowments are unambiguous, then more ambiguity aversion implies less trade for a very general class of preferences. The reduction in trade caused by ambiguity aversion can be as severe as to lead to no trade. In an economy with MEU decision makers, we show that if the aggregate endowment is unanimously unambiguous, then every Pareto optima allocation is also unambiguous. We also characterize the situation in which every unanimously unambiguous allocation is Pareto optimal. Finally, we show how our results can be used to explain the home-bias effect. As a useful result for our methods, we also obtain an additivity theorem for CEU and MEU decision makers that does not require comonotonicity.     

Cooperative games in permutational structure

Summary. By a cooperative game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a set of payoffs for each coalition being a nonempty subset of the grand coalition of all players. It is well-known that balancedness is a sufficient condition for the nonemptiness of the core of such a cooperative non-transferable utility game. In this paper we consider non-transferable utility games in which for any coalition the set of payoffs depends on a permutation or ordering upon any partition of the coalition into subcoalitions. We call such a game a cooperative game in permutational structure or shortly permutational game. Doing so we extend the scope of the standard cooperative game theory in dealing with economic or political problems. Next we define the concept of core for such games. By introducing balancedness for ordered partitions of coalitions, we prove the nonemptiness of the core of a balanced non-transferable utility permutational game. Moreover we show that the core of a permutational game coincides with the core of an induced game in coalitional structure, but that balancedness of the permutational game need not imply balancedness of the corresponding coalitional game. This leads to a weakening of the conditions for the existence of a nonempty core of a game in coalitional structure, induced by a game in permutational structure. Furthermore, we refine the concept of core for the class of permutational games. We call this refinement the balanced-core of the game and show that the balanced-core of a balanced permutational game is a nonempty subset of the core. The proof of the nonemptiness of the core of a permutational game is based on a new intersection theorem on the unit simplex, which generalizes the well-known intersection theorem of Shapley. Received: October 31, 1995; revised version: February 5, 1997     

Optimal jurisdictional fragmentation and mobility

Tiebout's hypothesis is examined in a model with the continuum of income classes and no economies of scale of population in public output provision. Any efficient allocation of resources can be achieved in this model by a system of jurisdictions, each containing a separate income class, and each using a local property tax to finance local public output. However, in general at most one such allocation will be an equilibrium if residents can ‘vote with their feet’. Conditions are derived under which higher-income residents will locate in jurisdictions providing a higher level of public output. These are shown necessary, given a separable utility function, for any optimal allocation to be sustainable as an equilibrium when residents are mobile.     

Waste management regulation: policy solutions and policy shortcomings

A model of packaging waste management is presented to explore the policy options available to governments to implement waste regulation in light of the Extended Producer Responsibility (EPR ). Our model endogenizes the packaging design as an additional determinant for the overall amount of waste jointly with consumers’ sorting effort and producers’ output decisions. The model shows that the policies that yield the first‐best allocation may not find public support. Furthermore, if the set of available policy instruments is limited, production and consumption of the good is likely to settle on a sub‐optimal level even though the optimal allocation may be achievable. Finally, the model demonstrates that a landfill tax may actually increase landfill waste in the presence of tradable credits for recycling activities. The results shed light on some shortcomings of existing regulatory schemes such as the Producer Responsibility Obligations (Packaging Waste) Regulations of the UK .     

Eco-Labeling and Horizontal Product Differentiation

This paper investigates the impact of eco-labels on the abatement of emissions in a market with horizontal product differentiation. A distinction is made between an end-of-pipe abatement method and a clean technology approach. In the former case underinvestment is likely to occur even if the marginal willingness to pay for abatement of consumers is equal to the social marginal benefit of abatement. The level of abatement depends on the number of firms and on the number of consumers. For a large market with few firms overinvestment in abatement is also possible. Clean technology abatement achieves a first best level regardless of market size if all consumers have a marginal willingness to pay for abatement equal to its social benefit.     

Achieving the first best in small economies

It is shown in the context of a simple example with a small two-class population, that the first best utilitarian allocation can sometimes be achieved as a dominant strategy equilibrium, even though leisure is a normal good. This occurs because person's optimal lump-sum tax depends both on his own announced ability and the distribution of announced abilities. It is also demonstrated that, in a wider class of cases, the first best can be achieved as a Bayes-Nash equilibrium.     

Symmetrically pairwise-bargained allocations in an assignment market

Consider an assignment game with transferable utility where the optimally assigned partners engage in bargaining of the sort modelled by Nash, using as their threats the maximum they could receive in an alternative match. A symmetrically pairwise-bargained (SPB) allocation is a core allocation such that all partners are in bargained equilibrium. It is shown that an SPB allocation always exists, that the set of SPB allocations coincides with the intersection of the kernel and the core, and that there is a rebargaining process which converges to an SPB allocation if it begins at a “distinguished point” in the core.     

A Property of the Core

For any transferable utility game in coalitional form with nonempty core we show that, given any allocation outside the core, there is an allocation in the core that indirectly dominates it.Journal of Economic LiteratureClassification Number: C71.     

Stable Provision vs. Cournot–Nash Equilibria in Pure Public Good Economies

Shitovitz and Spiegel (1998, Journal of Economic Theory 83 , pp. 1–18) demonstrated that in pure public good economies, for some consumers the Lindahl consumption bundles can be inferior (utility-wise) to their Cournot–Nash allocation. In this paper, we prove that in any finite pure public good economy there exists a core allocation that is unanimously preferred, utility-wise, by all consumers over their Cournot–Nash consumption bundles.     

Market Games in Large Economies with a Finite Number of Types

We study market games derived from an exchange economy with a continuum of agents, each having one of finitely many possible types. The type of agent determines his initial endowment and utility function. It is shown that, unlike the well-known Shapley–Shubik theorem on market games (Shapley and Shubik in J Econ Theory 1:9–25, 1969), there might be a (fuzzy) game in which each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a game needs also to be homogeneous. We also study investment games – which are fuzzy games obtained from an economy with a finite number of agents cooperating in one or more joint projects. It is argued that the usual definition of the core is inappropriate for such a model. We therefore introduce and analyze the new notion of comprehensive core. This solution concept seems to be more suitable for such a scenario. We finally refer to the notion of feasibility of an allocation in games with a large number of players. Some of the results in this paper appear in a previous draft distributed by the name “Cooperative investment games or Population games”. An anonymous referee of Economic Theory is acknowledged for his/her comments     

The core as the set of eventually stable outcomes: A note

As a justification of the core as a set of stable social states, Sengupta and Sengupta [1996. A property of the core. Games Econ. Behav. 12, 266–273] show that for any transferable utility (TU) cooperative game with non-empty core, for every imputation outside the core there is an element in the core that indirectly dominates the imputation in a desirable way. In this note we show that this appealing property of the core no longer holds even for the class of hyperplane games, an immediate generalization of TU games into the environments without side payments.     

Piecewise additivity for non-expected utility

A model of choice under purely subjective uncertainty, Piecewise Additive Choquet Expected utility, is introduced. PACE utility allows for optimism and pessimism simultaneously, but represents a minimal departure from expected utility. It can be seen as a continuous version of NEO-expected utility (Chateauneuf et al. in J Econ Theory 137:538–567, 2007) and, as such, is especially suited for applications with rich state spaces. The main theorem provides a preference foundation for PACE utility in the Savage framework of purely subjective uncertainty with an arbitrary outcome set.     

On exploitation in a class of differentiable mixed markets

Consider a core allocation in a differentiable mixed market. It is shown that if this allocation can be derived by splitting the market [see Definition (1) below], then the monetary exploitation of the small traders disappears. We present examples of particular economies to which our theorem applies.     

Incomplete risk sharing arrangements and the value of information

Summary. The paper constructs a theoretical framework in which the value of information in general equilibrium is determined by the interaction of two opposing mechanisms: first, more information about future random events leads to better individual decisions and, therefore, higher welfare. This is the ‘Blackwell effect’ where information has positive value. Second, more information in advance of trading limits the risk sharing opportunities in the economy and, therefore, reduces welfare. This is the ‘Hirshleifer effect’ where information has negative value. We demonstrate that in an economy with production information has positive value if the information refers to non-tradable risks; hence, such information does not destroy the Blackwell theorem. Information which refers to tradable risks may invalidate the Blackwell theorem if the consumers are highly risk averse. The critical level of relative risk aversion beyond which the value of information becomes negative is less than 0.5. Received: May 14, 2001; revised version: March 5, 2002