Double implementation of the Lindahl equilibrium by a continuous mechanism

We consider a class of economies with public goods that have the following properties: (i) The preferences of the agents are convex, interior, and strictly increasing. (ii) The technology for production of public goods is a closed convex cone that satisfies free disposal and an additional mild assumption. No assumptions are made on continuity, completeness or transitivity of preferences. We provide a continuous and feasible mechanism that implements the Lindahl equilibrium by Nash equilibria, and has the following property: For every economy in our class every Nash equilibrium of the game induced by the mechanism is a strong Nash equilibrium.     

Erratum to “Walras and dividends equilibrium with possibly satiated consumers”

The main contribution of the paper is to provide a weaker nonsatiation assumption than the one commonly used in the literature to ensure the existence of competitive equilibrium. Our assumption allows for satiation points in the set of individually feasible consumptions, provided that the consumer has satiation points available to him outside this set. As a result, we show the concept of equilibrium with dividends (see Aumann, R.J., Drèze, J.H., 1986. Values of markets with satiation or fixed prices. Econometrica 54, 1271–1318; Mas-Collel, A., 1992. Equilibrium theory with possibly satiated preferences. In: Majumdar, M. (Ed.), Equilibrium and Dynamics: Proceedings of the Essays in Honour of David Gale. MacMillan, London, pp. 201–213) is pertinent only when the set of satiation points is included in the set of individually feasible consumptions. Our economic motivation stems from the fact that in decentralized markets, increasing the incomes of consumers through dividends, if it is possible, is costly since it involves the intervention of a social planner. Then, we show, in particular, how in securities markets our weak nonsatiation assumption is satisfied by Werner’s (1987) assumption.     

The Influence of Auguste Walras on Léon Walras

A bstract . Auguste Walras' interest in and contribution to economic theory were prompted mainly by his quest for a valid theory of property. After a critical analysis of the current theories of value , he singled out scarcity as the only significant cause of value. He concluded that land was scarce in a very special sense and, hence, should belong not to single individuals but to society as a whole. This is not, however, incompatible with private ownership of non-land capital. His famous son. Léon Walras , not only adopted this theory but also proved the feasibility of a laissez-faire type of economy in which land is nationalized. His debt to his father is also evident in his analysis of general economic equilibrium in which he makes use of valuable economic ideas and tools devised or inspired by Auguste Walras.     

Cournot vs. Walras: A reappraisal through simulations

Best-reply behavior in Cournot oligopolies generally leads to Cournot-Nash equilibrium, but imitative behavior selects the Walrasian equilibrium as the unique stochastically stable state. Previous work (Alós-Ferrer, 2004) showed that in the presence of memory, imitative behavior leads to a non-trivial dynamics selecting all quantities between the Cournot and Walrasian outcomes. However, the scope of previous results was limited to specific assumptions on demand and cost functions, and did not provide information on the shape of the distribution of outcomes. We use computational simulations to address these limitations. We show that the selection result for non-trivial memory holds beyond the set of well-behaved Cournot games previously analyzed. Further, we find that, in Cournot games, the limit distribution of long-run outcomes is highly skewed towards the Walrasian quantity. Although longer memory increases the importance of the Cournot equilibrium, the competitive outcome remains the dominant prediction.     

Some consequences of the unknottedness of the Walras correspondence

Two basic properties concerning the dynamic behavior of competitive equilibria of exchange economies with complete markets are derived essentially from the fact that the Walras correspondence has no knots.     

An equilibrium model of insider trading in continuous time

We study a Bayesian–Nash equilibrium model of insider trading in continuous time. The supply of the risky asset is assumed to be stochastic. This supply can be interpreted as noise from nonrational traders (noise traders). A rational informed investor (the insider) has private information on the growth rate of the dividend flow rewarded by the risky asset. She is risk averse and maximizes her inter-temporal utility rate over an infinite time-horizon. The market is cleared by a risk neutral market maker who sets the price of the risky asset competitively as the conditional present value of future dividends, given the information supplied by the dividend history and the cumulative order flow. Due to the presence of noise traders, the market demand does not fully reveal the insider’s private information, which slowly becomes incorporated in prices. An interesting result of the paper is that a nonstandard linear filtering procedure gives an a priori form for the equilibrium strategy to be postulated. We show the existence of a stationary linear equilibrium where the insider acts strategically by taking advantage of the camouflage provided by the noise which affects the market maker’s estimates on private information. In this equilibrium, we find that the insider’s returns on the stock are uncorrelated over long periods of time. Finally, we show that the instantaneous variance of the price under asymmetric information lies between the instantaneous variance of the price under complete and incomplete information. The converse inequalities hold true for the unconditional variance of the price.     

The Walras core of an economy and its limit theorem

The Walras core of an economy is the set of allocations that are attainable for the consumers when their trades are constrained to be based on some agreed price system, such that no alternative price system exists for any sub-coalition that allows all members to trade to something better. As compared with the Edgeworth core, both coalitional improvements and being a candidate allocation for the Walras core become harder. The Walras core may even contain allocations that violate the usual Pareto efficiency. Nevertheless, the competitive allocations are the same under the two theories, and the equal-treatment Walras core allocations converge under general conditions to the competitive allocations in the process of replication.     

Walras degrees and probability of a blocking coalition at pareto allocations

We attempt to determine the probability of a blocking coalition from a notion of being non- Walrasian which does not rely on the explicit use of norms. The key concept introduced is that of Walras degrees. Theorem 1 gives the bounds of the probability of blocking in terms of these degrees. Theorem 2 gives the asymptotic conditional probability of a blocking coalition given that coalitions are losing. The relationship between the degrees of the conventional norms on allocations is also investigated.     

The 'Socialism' of Léon Walras and His Economic Thinking

A bstract . Léon Walras was one of the few outstanding 19th century economists who, though as a theoretician belonged to the mainstream of orthodox economics , expressed views which at one time were considered to be too radical. He advocated in particular the nationalization of land as the solution to the social problem. This would generate sufficient revenue to government to enable it to do away with taxing income derived from wages and salaries. As a result workers would be in a position to invest their untaxed income and thus acquire their rightful share in the national wealth. Contrary to what many have argued, such 'socialistic' policy was not incompatible with Walras' theoretical model of perfect competition. In the absence of private ownership of land and natural resources , there would be no place for big enterprises and monopolies. His great compromise was: allow social reforms in the realm of distribution, but promote lassser-faire in the production of goods and services. Walras was convinced that if, on top of a radical land reform, the State sought to secure the working of a free competitive system , then the economic system could function very closely to the theoretical model. Though there are flaws in his proposals, his ideas no longer appear as preposterous as they did in his own time.     

Natural and double implementation of public ownership solutions in differentiable production economies

This paper examines the implementation of two public ownership solutions in convex production economies with differentiable production functions. The two public ownership solutions we focus on are the proportional and equal benefit solutions. Two “natural” mechanisms which doubly implement the proportional and equal benefit solutions respectively in Nash and strong Nash equilibria are proposed without assuming free disposal. Received: 7 May 1996 / Accepted: 1 December 1998     

Menger, Jevons, and Walras Un-homogenized, De-homogenized, and Homogenized: A Comment on Peart

Abstract . Response to Sandra J, Peart, “Jevons and Menger Re-homogenized?: Jaffé After 20 Years,” 1998. The American Journal of Economics and Sociology 57(July): 307-325.     

A sufficiency result for constrained economies

This paper presents a general sufficiency result for constrained economies. The result shows that, when an equilibrium allocation satisfies the first order necessary conditions for hybrid efficiency (a new type of constrained efficiency), there exists a marginal cost pricing equilibrium in an associated economy. If this equilibrium is Pareto efficient in the associated economy, then the original equilibrium allocation is hybrid efficient. Hence. the necessary conditions are also sufficient.     

A study of the MRP implementation process

This paper reports on a large-scale survey of companies involved in MRP implementation. Survey responses are used to develop a profile of problems typically encountered during the implementation process. Discriminant analysis is used to determine which of those problems, and additional factors, appear to affect the success or failure of MRP implementation. Finally, comparisons are made between the problems encountered during implementation and problems which were found to significantly discriminate between successful and unsuccessful MRP implementors.     

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.     

A general equilibrium analysis of strategic arbitrage

We analyze a general equilibrium framework with Cournot arbitrageurs and with price-taking investors who are subjected to restricted participation constraints. Restricted participation may leave some arbitrage opportunities unexploited by investors.We show existence of Cournot–Walras equilibria with an endogenous number of arbitrageurs. The number of arbitrageurs is endogenous since they have to sink entry costs in order to arbitrage across the relevant markets. We characterize equilibria and analyze the effects on equilibrium prices and quantities of increased competition among arbitrageurs due to lower entry costs.     

A statistical equilibrium model of competitive firms

We find that the empirical density of firm profit rates, measured as returns on assets, is markedly non-Gaussian and reasonably well described by an exponential power (or Subbotin) distribution. We start from a statistical equilibrium model that leads to a stationary Subbotin density in the presence of complex interactions among competitive heterogeneous firms. To investigate the dynamics of firm profitability, we construct a diffusion process that has the Subbotin distribution as its stationary probability density. This leads to a phenomenologically inspired interpretation of variations in the shape parameter of the Subbotin distribution, which essentially measures the competitive pressure in and across industries. Our findings have profound implications both for the previous literature on the ‘persistence of profits’ as well as for understanding competition as a dynamic process. Our main formal finding is that firms' idiosyncratic efforts and the tendency for competition to equalize profit rates are two sides of the same coin, and that a ratio of these two effects ultimately determines the dispersion of the equilibrium distribution.