Welfare Theorem Research Articles

A Critique of Shareholder Value Maximization

The majority of academic economists share the view that a corporation should serve the exclusive interests of its shareholders (shareholder value maximization). This view is fi rmly grounded on the extension, by Arrow (1953) and Debreu (1959) of the two welfare theorems to production economies with uncertainty and complete markets. This paper considers a variant of the Arrow-Debreu model where uncertainty is endogenous: probabilities of productive outcomes depend on decisions made by fi rms. In that case, a competitive equilibrium with shareholder value maximizing fi rms (capitalist equilibrium) is never Pareto optimal. This is because endogenous uncertainty implies that firms exert externalities on their consumers and their employees. When rms are stakeholder oriented, in that their managers are instructed to maximize a weighted sum of their shareholder value and of their contributions to consumer and employee welfares, the new competitive equilibrium (stakeholder equilibrium) improves upon the capitalist equilibrium.

Optimality and Representation of Competitive Equilibria with Time-Dependent Preferences

This paper focuses on the welfare properties of equilibria in exchange economies with time-dependent preferences. We introduce a notion of recursive efficiency and show that any quilibrium allocation is efficient in the sense defined. Therefore, we present a version of the First Fundamental Welfare Theorem for this class of economies. Moreover, we present a social welfare function with maximisers that coincide with recursively efficient allocations, and prove that every equilibrium can be represented by a solution to a social welfare optimisation problem.

Fragility of competitive equilibrium with risk of default

We study competitive equilibrium in sequential economies under limited commitment. Default induces permanent exclusion from financial markets and endogenously determined solvency constraints prevent debt repudiation. Our analysis shows that such an enforcement mechanism is essentially fragile, leading to equilibrium multiplicity. We accomplish this by establishing Welfare Theorems under a weaker notion of constrained efficiency, inspired by Malinvaud, corresponding to the absence of welfare improving feasible redistributions over finite (though indefinite) horizons. A Negishiʼs Method permits to show that, for any arbitrary value of social welfare in between autarchy and constrained optimality, there exists an equilibrium attaining that value. Thus, competitive equilibria might differ dramatically in terms of volumes of trade, asset price volatility, individualsʼ ability to insure against idiosyncratic risk and consumption inequality.

Nonseparable, Concave Utilities Are Easy---in a Perfect Price Discrimination Market Model

Recent results establishing evidence of intractability for such restrictive utility functions as additively separable, piecewise-linear and concave, under both Fisher and Arrow--Debreu market models, have prompted the question of whether we have failed to capture some essential elements of real markets, which seem to do a good job of finding prices that maintain parity between supply and demand. The main point of this paper is to show that even nonseparable, concave utility functions can be handled efficiently in a suitably chosen, though natural, realistic, and useful, market model. Our model allows for perfect price discrimination, supports unique equilibrium prices, and satisfies both welfare theorems.

Household Formation and Markets

We consider competitive markets for multiple commodities with endogenous formation of one- or two-person households. Within each two-person household, externalities from the partner’s commodity consumption and unpriced actions are allowed. Each individual has two types of traits: observable characteristics and unobservable taste characteristics. Each individual gets utility from his/her own private con- sumption, from discrete actions such as job-choice, from the partner’s observable characteristics such as appearance and hobbies, from some of the partner’s consumption vectors, and from the partner’s action choices. We investigate competitive market outcomes with an endoge- nous household structure in which no individual and no man/woman-pair can deviate profitably. We find a set of sufficient conditions under which a stable matching equilibrium exists. We further establish the first welfare theorem for this economy.

The housing problem and revealed preference theory: duality and an application

This paper exhibits a duality between the theory of Revealed Preference of Afriat and the housing allocation problem of Shapley and Scarf. In particular, it is shown that Afriat's theorem can be interpreted as a second welfare theorem in the housing problem. Using this duality, the revealed preference problem is connected to an optimal assignment problem, and a geometrical characterization of the rationalizability of experiment data is given. This allows in turn to give new indices of rationalizability of the data, and to define weaker notions of rationalizability, in the spirit of Afriat's efficiency index.

Exchange Efficiency with Weak Property Rights

We show that the first welfare theorem obtains independently of the strength of property rights protection. In an exchange setting, a large class of legal rules (what we call generalized liability rules) are exchange-efficient. Included in this class are property rules (generalized liability rules with very large damages Ds), standard liability rules (generalized liability rules with Ds that track the owner's valuation), and even rules which afford possessory interests only very weak protection (generalized liability rules with very small Ds). This result corrects a previous misconception in the literature, and yields the provocative conclusion that strong property rights are not required for exchange efficiency.

Golden rule optimality in stochastic OLG economies

This study examines conditional golden rule optimality (CGRO) in stochastic overlapping generations models to complement the existing results on conditional Pareto optimality (CPO). Although an example in which CPO implies CGRO is presented, it is shown that such a situation is avoidable under strictly convex preferences. Under such preferences, both CPO and CGRO are characterized by the conditions on the dominant root for the agents’ common matrix of marginal rates of substitution. We demonstrate that CGRO requires the dominant root being exactly equal to one, whereas CPO allows it to be less than one. By adopting CGRO rather than CPO, we provide welfare theorems in the financial economy.

Computing Alternating Offers and Water Prices in Bilateral River Basin Management

This contribution deals with the fundamental critique in Dinar et al. (1992, Theory and Decision 32) on the use of Game theory in water management: People are reluctant to monetary transfers unrelated to water prices and game theoretic solutions impose a computational burden. For the bilateral alternating-offers model, a single optimization program significantly reduces the computational burden. Furthermore, water prices and property rights result from exploiting the Second Welfare Theorem. Both issues are discussed and applied to a bilateral version of the theoretical river basin model in Ambec and Sprumont (2002). Directions for future research are provided.

ON THE FOUNDATIONS OF MATHEMATICAL ECONOMICS

Kumaraswamy Vela Velupillai74 presents a constructivist perspective on the foundations of mathematical economics, praising the views of Feynman in developing path integrals and Dirac in developing the delta function. He sees their approach as consistent with the Bishop constructive mathematics and considers its view on the Bolzano-Weierstrass, Hahn-Banach, and intermediate value theorems, and then the implications of these arguments for such "crown jewels" of mathematical economics as the existence of general equilibrium and the second welfare theorem. He also relates these ideas to the weakening of certain assumptions to allow for more general results as shown by Rosser51 in his extension of Gödel's incompleteness theorem in his opening section. This paper considers these arguments in reverse order, moving from the matters of economics applications to the broader issue of constructivist mathematics, concluding by considering the views of Rosser on these matters, drawing both on his writings and on personal conversations with him.

A Perfect Price Discrimination Market Model with Production, and a Rational Convex Program for It

Recent results showing PPAD-completeness of the problem of computing an equilibrium for Fisher's market model under additively separable, piecewise-linear, concave (PLC) utilities have dealt a serious blow to the program of obtaining efficient algorithms for computing equilibria in “traditional” market models, and has prompted a search for alternative models that are realistic as well as amenable to efficient computation. In this paper, we show that introducing perfect price discrimination into the Fisher model with PLC utilities renders its equilibrium polynomial time computable. Moreover, its set of equilibria are captured by a convex program that generalizes the classical Eisenberg-Gale program, and always admits a rational solution. We also give a combinatorial, polynomial time algorithm for computing an equilibrium. Next, we introduce production into our model, and again give a rational convex program that captures its equilibria. We use this program to obtain surprisingly simple proofs of both welfare theorems for this model. Finally, we also give an application of our price discrimination market model to online display advertising marketplaces.

General Equilibrium in the Presence of Time Costs

If consumption takes time, and time is limited, there exists a time constraint in addition to the expenditure constraint of a consumer. This may lead to a form of satiation, where consumers cannot consume all commodities they purchase. We establish existence of competitive equilibrium in the presence of a time constraint and recover a version of the first and second welfare theorem. While all equilibria are weakly Pareto-optimal, they may fail to be strongly Pareto-optimal: taking from satiated consumers and giving to non-satiated consumers increases social welfare. We give an example with identical consumers, where equal share is the only strongly Pareto-optimal allocation and should be chosen by a planner maximizing social welfare. We also suggest a simple explanation for the Easterlin Paradox.

Economies with observable types

We study economies of asymmetric information with observable types. Trade takes place in lotteries. Individuals face a standard budget constraint, while the incentive compatibility constraints are imposed on the production set of the intermediaries. This formalization encompasses moral hazard, as in Jerez (2003, 2005), and private information economies. Equilibrium allocations are constrained efficient, but, contrary to what stated for example in Jerez (2005), the set of equilibrium allocations may be empty and the Second Welfare Theorem may fail. This happens for two reasons. First, constrained efficient allocations may violate the necessary and sufficient conditions of price supportability for the individuals. Second, even when constrained efficient allocation are price supportable, they may fail to be a profit maximizing choice of the firm at the individual supporting prices. To restore existence of an equilibrium the firm has to be restricted to supply allocations with support in the set of incentive compatible contracts.

Other-Regarding Preferences in General Equilibrium

We study competitive market outcomes in economies where agents have other-regarding preferences (ORPs). We identify a separability condition on monotone preferences that is necessary and sufficient for one's own demand to be independent of the allocations and characteristics of other agents in the economy. Given separability, it is impossible to identify ORPs from market behaviour: agents behave as if they had classical preferences that depend only on own consumption in competitive equilibrium. If preferences, in addition, depend only on the final allocation of consumption in society, the Second Welfare Theorem holds as long as any increase in resources can be distributed in a way that makes all agents better off. The First Welfare Theorem generally does not hold. Allowing agents to care about their own consumption and the distribution of consumption possibilities in the economy, the competitive equilibria are efficient given prices if and only if there is no Pareto-improving redistribution of income.

General Equilibrium with Multi-Member Households and Production

We consider firms and multi-member households operating in a competitive market environment. Households are endowed with resources (commodity bundles) and shares of firm ownership. Household members are characterized by individual preferences, possibly with intra-household consumption externalities. Household decisions adhere to the collective rationality model. Existence of general equilibrium and validity of the first welfare theorem are investigated.

The Housing Problem and Revealed Preference Theory: Duality and an Application

This paper exhibits a duality between the theory of Revealed Preference of Afriat and the housing allocation problem of Shapley and Scarf. In particular, it is shown that Afriat’s theorem can be interpreted as a second welfare theorem in the housing problem. Using this duality, the revealed preference problem is connected to an optimal assignment problem, and a geometrical characterization of the rationalizability of experiment data is given. This allows in turn to give new indices of rationalizability of the data, and to define weaker notions of rationalizability, in the spirit of Afriat’s efficiency index.

An efficiency theorem for incompletely known preferences

There are n agents who have von Neumann–Morgenstern utility functions on a finite set of alternatives A. Each agent i's utility function is known to lie in the nonempty, convex, relatively open set U i . Suppose L is a lottery on A that is undominated, meaning that there is no other lottery that is guaranteed to Pareto dominate L no matter what the true utility functions are. Then, there exist utility functions u i ∈ U i for which L is Pareto efficient. This result includes the ordinal efficiency welfare theorem as a special case.

Sharing Risk Efficiently under Suboptimal Punishments for Defection

I study efficient risk-sharing in an endowments economy when enforcement is achieved by the threat of reversion to punishments that may be less severe than autarkic consumption. I characterize (up to a technical condition) the set of allocations that may be interpreted as efficient with respect to some punishment convention. The conditions rationalizing such efficiency are very weak; they are (i) resource exhaustion, (ii) satisfaction of individual rationality constraints at each continuation, and (iii) finiteness of the value of the allocation under the implicit decentralizing price system. I show how efficient allocations may be decentralized, and I state versions of the Welfare Theorems for these economies.

What’s wrong with the fundamental existence and welfare theorems?

The definition of Walrasian competitive equilibrium, on which the Fundamental Existence and Welfare Theorems rest, assumes that all trading in decentralized exchange economies takes place at the final equilibrium prices, which further implies that at equilibrium prices the value of each agent’s equilibrium commodity bundle is equal to the value of her endowment, and equal treatment of agents with the same preferences, technology and endowment. The logic of the theorems supports the conclusion that in competitive economies prices, the allocation of commodities, and the distribution of income and material welfare are determined by the preferences, technology, and endowments of the agents. In real-world markets, however, agents can discover equilibrium prices only by making mutually advantageous transactions at disequilibrium prices. Any sequence of such transactions leads stably to an exchange equilibrium at which the offer prices of all agents are close to each other, and which exhausts all private opportunities to realize economic surpluses. The exchange equilibrium set, however, is in general a continuum, and the exact equilibrium reached depends on the path of transactions. In general, exchange equilibria do not treat agents with the same preferences and endowments equally, and the exchange equilibrium allocation of commodities does not conserve the values of individual agent endowments. Existence and stability of exchange equilibrium are transparent consequences of the logic of voluntary exchange, but because of transaction path dependence, equilibrium prices, allocations of commodities, and the distribution of wealth and economic welfare are not determined by agents’ preferences and endowments.

Core equivalence and welfare properties without divisible goods

We study an economy where all goods entering preferences or production processes are indivisible. Fiat money not entering consumers’ preferences is an additional perfectly divisible parameter. We establish a First and Second Welfare Theorem and a core equivalence result for the rationing equilibrium concept introduced in Florig and Rivera (2005a). The rationing equilibrium can be considered as a natural extension of the Walrasian notion when all goods are indivisible at the individual level but perfectly divisible at the level of the entire economy. As a Walras equilibrium with money is a special case of a rationing equilibrium, our results also hold for Walras equilibria with money.