Monopoly regulation without the Spence–Mirrlees assumption

The paper extends the Baron and Myerson [Baron, D., Myerson, R.B., 1982. Regulating a monopolist with unknown costs. Econometrica 50, 911–930] model of monopoly regulation to bidimensional adverse selection: both the marginal cost and the fixed cost of the monopoly are unknown to the regulator. Like in Araujo and Moreira [Araujo, A., Moreira, H., 2000. Adverse section problems without the Spence–Mirrlees condition. Fundação Getulio Vargas, Rio de Janeiro, Ensaios Economicos 389], the paper provides an explicit solution of a screening model without the Spence–Mirrlees assumption.     

Mechanisms that efficiently verify the optimality of a proposed action

The best known achievement of the literature on resource-allocating mechanisms and their message spaces is the first rigorous proof of the competitive mechanism's informational efficiency. In an exchange economy withN persons andK+1 commodities (including a numeraire), that mechanism announcesK prices as well as aK-compenent trade vector for each ofN−1 persons, making a total ofNK message variables. Trial messages are successively announced and after each announcement each personprivately determines, usingprivate information, whether she finds the proposed trades acceptable at the announced prices. When a message is reached with which all are content, then the trades specified in that message take place, and they satisfy Pareto optimality and individual rationality. The literature shows that no (suitably regular) mechanism can achieve the same thing with fewer thanNK message variables. In the classic proof, all the candidate mechanisms have the privacy property, and the proof uses that property in a crucial way. ‘Non-private’ mechanisms are, however, well-defined. We present a proof that forN>K,NK remains a lower bound even when we permit ‘non-private’ mechanisms. Our new proof does not use privacy at all. But in a non-private mechanism, minimality of the number of message variables can hardly be defended as the hallmark of informational efficiency, since a non-private mechanism requires some persons to know something about the private information of othersin addition to the information contained in the messages. The new proof of the lower boundNK invites a new interpretation of the competitive mechanism's informational efficiency. We provide a new concept of efficiency which the competitive mechanism exhibits and which does rest on privacy even whenN>K. To do so, we first define a class ofprojection mechanisms, wherein some of the message variables are proposed values of the action to be taken, and the rest are auxiliary variables. The competitive mechanism has the projection property, with a trade vector as its action and prices as the auxiliary variables. A projection mechanism proposes an action; for each proposal, the agents then use the auxiliary variables, together with their private information, to verify that the proposed action meets the mechanism's goal (Pareto optimality and individual rationality for the competitive mechanism) if, indeed, it does meet that goal. For a given goal, we seek projection mechanisms for which theverification effort (suitably measured) is not greater than that of any other projection mechanism that achieves the goal. We show the competitive mechanism to be verification-minimal within the class of private projection mechanisms that achieve Pareto optimality and individual rationality; that proofdoes use the privacy of the candidate mechanisms. We also show, under certain conditions, that a verification-minimal projection mechanism achieving a given goal has smallest ‘total communication effort’ (which is locally equivalent to the classic ‘message-space size’) among all private mechanisms that achieve the goal, whether or not they have the projection property.     

A note on the structural stability of the equilibrium manifold

In a smooth pure exchange economy with fixed total resources we investigate whether the smooth selection property holds when endowments are redistributed across consumers through a continuous (non-local) redistribution policy. We show that if the policy is regular then there exists a unique continuous path of equilibrium prices which support it.     

Geodesics on the equilibrium manifold

We show the existence of a Riemannian metric on the equilibrium manifold such that a minimal geodesic connecting two (sufficiently close) regular equilibria intersects the set of critical equilibria in a finite number of points. This metric represents a solution to the following problem: given two (sufficiently close) regular equilibria, find the shortest path connecting them which encounters the set of critical equilibria in a finite number of points. Furthermore, this metric can be constructed in such a way to agree, outside an arbitrary small neighborhood of the set of critical equilibria, to any given metric with economic meaning.     

Dispersed initial ownership and the efficiency of the stock market under moral hazard

We generalize a standard general equilibrium framework extended for moral hazard to allow for a dispersed initial ownership distribution of firms. We show that the market allocation is constrained-efficient only when in each firm the entrepreneur who generates payoffs through unobservable effort has full initial ownership in his firm.     

Panel data models with multiple time-varying individual effects

This paper considers a panel data model with time-varying individual effects. The data are assumed to contain a large number of cross-sectional units repeatedly observed over a fixed number of time periods. The model has a feature of the fixed-effects model in that the effects are assumed to be correlated with the regressors. The unobservable individual effects are assumed to have a factor structure. For consistent estimation of the model, it is important to estimate the true number of individual effects. We propose a generalized methods of moments procedure by which both the number of individual effects and the regression coefficients can be consistently estimated. Some important identification issues are also discussed. Our simulation results indicate that the proposed methods produce reliable estimates.     

Erratum to “Do pure indivisibilities prevent core equivalence? Core equivalence theorem in an atomless economy with purely indivisible commodities only” [J. Math. Econ. 41 (4–5) (2005) 571–601]

We consider a pure exchange economy with a continuum of agents and finitely many indivisible commodities. Every commodity can be consumed only in integer amounts. Thus, agents’ preferences are locally satiated and no commodity bundle has necessarily local cheaper points. We introduce a core which is an intermediate concept between the strong core and the weak core. In our economy, this core is the most natural concept in the sense that it coincides with the set of all exactly feasible Walras allocations.     

Equilibria in vector lattices without ordered preferences or uniform properness

This paper extends a result by Mas-Colell and Richard (Journal of Economic Theory, 1991, 53, 1–11) on the existence of an equilibrium for exchange economies over a vector lattice to cover non-ordered preferences. Moreover, it is shown that the uniformity requirement in the properness assumption made by these authors can be weakened. Furthermore, it is shown that, as a consequence of properness, an equilibrium allocation which is supported by a discontinuous prices can also be supported by continuous prices.     

An index formula for production economies with externalities

We prove that the degree of the equilibrium correspondence of an economy with increasing returns and external effects is equal to (−1)^L−1${(-1)}^{L-1}$ where L is the dimension of the space of goods. This allows us to infer existence, finiteness and uniqueness results.     

Can we identify Walrasian allocations?

Abstract. We consider a discrete time, pure exchange infinite horizon economy with consumers and consumption goods per period. Within the framework of decentralized mechanisms, we show that for any given consumption trade at any period of time, say at time one, the consumers will need in general an infinite dimensional (informational) space to identify such a trade as an intertemporal Walrasian one. However, we show a set of environments where the Walrasian trades at each period of time can be achieved as the equilibrium trades of a sequence of decentralized competitive mechanisms, using only both current prices and quantities to coordinate decisions. Received: 1 December 1999 / Accepted: 31 October 2000     

Theorems on the core of an economy with infinitely many commodities and consumers

It is known that the classical theorems of Grodal [Grodal, B., 1972. A second remark on the core of an atomless economy. Econometrica 40, 581–583] and Schmeidler [Schmeidler, D., 1972. A remark on the core of an atomless economy. Econometrica 40, 579–580] on the veto power of small coalitions in finite dimensional, atomless economies can be extended (with some minor modifications) to include the case of countably many commodities. This paper presents a further extension of these results to include the case of uncountably many commodities. We also extend Vind’s [Vind, K., 1972. A third remark on the core of an atomless economy. Econometrica 40, 585–586] classical theorem on the veto power of big coalitions in finite dimensional, atomless economies to include the case of an arbitrary number of commodities. In another result, we show that in the coalitional economy defined by an atomless individualistic model, core–Walras equivalence holds even if the commodity space is non-separable. The above-mentioned results are also valid for a differential information economy with a finite state space. We also extend Kannai’s [Kannai, Y., 1970. Continuity properties of the core of a market. Econometrica 38, 791–815] theorem on the continuity of the core of a finite dimensional, large economy to include the case of an arbitrary number of commodities. All of our results are applications of a lemma, that we prove here, about the set of aggregate alternatives available to a coalition. Throughout the paper, the commodity space is assumed to be an ordered Banach space which has an interior point in its positive cone.     

Pareto improving interventions in a general equilibrium model with private provision of public goods

Most of the literature on government intervention in models of voluntary public goods supply focuses on interventions that increase the total level of a public good, which is considered to be typically underprovided. However, an intervention that is successful in increasing the public good level need not benefit everyone. In this paper we take a direct approach to welfare properties of voluntary provision equilibria in a full blown general equilibrium model with public goods and study interventions that have the goal of Pareto improving on the voluntary provision outcome. Towards this end, we study a model with many private goods and non-linear production technology for the public good, and hence allow for relative price effects to serve as a powerful channel of intervention. In this setup we show that Pareto improving interventions generally do exist. In particular, direct government provision financed by “small” , or “local” , lump-sum taxes can be used generically to Pareto improve upon the voluntary provision outcome.     

Complete monotonicity of the representative consumer’s discount factor

A univariate real-valued function is said to be completely monotone if it takes positive values and alternate the signs of its higher order derivatives, starting from everywhere negative first derivatives. We prove that the representative consumer’s discount factor of a continuous-time economy under uncertainty is a power function of some completely monotone function of time satisfying certain boundary conditions if and only if it may be derived from a group of consumers having constant and equal relative risk aversion, and constant and yet possibly unequal discount rates.     

Subjective expected utility theory without states of the world

This paper develops an axiomatic theory of decision-making under uncertainty that dispenses with the state-space. The results are subjective expected utility models with unique, action-dependent, subjective probabilities, and a utility function defined over wealth-effect pairs that is unique up to a positive linear transformation.     

Efficient,Pareto-improving processes

We give two optimization programs for determining whether Pareto improving local changes are possible. When they are, the programs compute them. Any procedure generating efficient and Pareto improving changes can be replicated by these programs. The two programs are dual to each other. We apply the programs to Pareto improving exchange processes and to Pareto-improving tax-tariff reforms.     

Commodity money equilibrium in a convex trading post economy with transaction costs

Existence and efficiency of general equilibrium with commodity money is investigated in an economy where N   commodities are traded at N(N−1)/2$N(N-1)/2$ commodity-pairwise trading posts. Trade is a resource-using activity recovering transaction costs through the spread between bid (wholesale) and ask (retail) prices. Budget constraints, enforced at each trading post separately, imply demand for a carrier of value between trading posts. Existence of general equilibrium is established under conventional convexity and continuity conditions while structuring the price space to account for distinct bid and ask price ratios. Commodity money flows are identified as the difference between gross and net inter-post trades.