Existence,uniqueness, and stability of equilibrium in an OLG economy

Summary. This paper presents sufficient conditions for the existence of a unique and globally stable steady state equilibrium for OLG economies with production. The conditions impose separate requirements on the utility and production functions. Moreover, the conditions do not require assumptions concerning the third order derivatives of the production and utility functions.Received: 12 August 2002, Revised: 7 January 2003, JEL Classification Numbers: D50, D91, E13, O41.I would like to thank Nick Baigent, Laurie Conway, Karl Farmer, Christian Gehrke, and Hideo Konishi for helpful comments. I am grateful to an anonymous referee for his or her comments.     

Existence and uniqueness of stochastic equilibrium in a simple macro model

This paper demonstrates that even the simplest rational expectations macro model may be plagued by nonexistent or multiple equilibria. The reason for these problems is the postulated existence of risk-averse behavior on the part of labor suppliers and purchasers of durable commodities. This risk-averse behavior introduces the price forecast variance into the behavioral parameters of the model, thus leading to a simultaneous nonlinear system.     

Existence and uniqueness of steady-state equilibrium in a two-sector overlapping generations model

In his seminal paper Galor [A two-sector overlapping generations-model: a global characterization of the dynamical system, Econometrica 60 (1992) 1351-1386] establishes conditions for the existence of equilibrium in the two-sector overlapping generations (OLG) model. Although appealing theoretically, these conditions are implicit and not easy to apply. This paper develops new theorems on the existence and uniqueness of steady-state equilibrium in the two-sector OLG model. We provide explicit conditions on the utility and production functions for the existence and uniqueness of equilibrium, with which one only needs to check the derivatives of the production and utility functions and their interactions, without requiring solving for the savings function and its derivatives. We present detailed steps to check the existence and uniqueness of equilibrium and provide illustrative examples.     

Existence and efficiency of equilibrium in infinite economies with finite aggregate wealth

Summary. We prove the existence and efficiency of equilibrium in economies with infinitely many consumers in which there are finitely many agents who own a positive portion of the aggregate endowment. We prove existence for commodity spaces which are employed in the general equilibrium asset pricing models and use incomplete and intransitive preferences. We discuss the importance of existence of finitely many agents who own a positive portion of the aggregate endowment in obtaining efficient equilibrium. For general equilibrium asset pricing applications we require forward properness only at individually rational Pareto optimal allocations. We provide an Arrow-Debreu model for these economies. We also give an application of our approach and results by employing Stochastic Differential Utility as the utility of each consumer in an infinite horizon model.     

Existence and efficiency of a stationary subgame-perfect equilibrium in coalitional bargaining models with nonsuperadditive payoffs

We provide the existence theorem of stationary subgame-perfect equilibrium (SSPE) in a noncooperative coalitional bargaining game model with random proposers. Our model contains a bargaining situation where the coalitional game is nonsuperadditive. We also provide a necessary and sufficient condition for the existence of a pure-strategy SSPE satisfying the efficiency property when the discount factor is close to one. Furthermore, we provide examples where the delay in agreement occurs, even in a random-proposers model, when the game is nonsuperadditive. I am grateful to Akira Okada and an anonymous referee for their useful comments and helpful suggestions.     

Mechanism design with multidimensional, continuous types and interdependent valuations

We consider the mechanism design problem when agents’ types are multidimensional and continuous, and their valuations are interdependent. If there are at least three agents whose types satisfy a weak correlation condition, then for any decision rule and any ?>0 there exist balanced transfers that render truthful revelation a Bayesian ?-equilibrium. A slightly stronger correlation condition ensures that there exist balanced transfers that induce a Bayesian Nash equilibrium in which agents’ strategies are nearly truthful.     

Computable general equilibrium with financial markets

Summary. There are a wide variety of theoretical general equilibrium models with incomplete security markets. In this paper we give a general recipe for using homotopy algorithm to compute equilibria in these models. In many models, taxes, transaction-costs or other market frictions introduce the additional difficulty that equilibrium prices or choices (but not equilibrium allocations) may be undetermined. In order to demonstrate how these difficulties can be dealt with, we develop a globally convergent algorithm to compute equilibria in a model with cash-in-advance constraints, several goods and incomplete financial markets. Furthermore we describe how to implement the algorithm using a publicly available suite of subroutines for homotopy-pathfollowing. Received: October 1, 1999; revised version: December 16, 2000     

Core and equilibrium in incomplete markets

Conclusions The classical foundation of general equilibrium analysis by the cooperative concept of the core has been extended to an economy with incomplete trading possibilities. This has been accomplished by restricting the exchange possibilities of coalitions of traders in accordance with the available market structure. However, compared with the classical result, the present foundation of rational expectations equilibria may appear much weaker. The reason is that in reality consumers may sign contracts which are more complex than the existing market structure. Therefore, it may happen that prices cannot decentralize all cooperative transactions by markets, in spite of perfect competition. With an incomplete set of markets, therefore, a cooperative exchange of commodities by individual contracts may coexist with trading in non-cooperative, competitive markets.I wish to thank Martin Hellwig for helpful comments and suggestions. Of course, I remain responsible for all shortcomings of the paper.     

On the uniqueness of competitive equilibrium

Summary . The paper is concerned with the following question: in addition to local uniqueness, what other conditions must be imposed to ensure global uniqueness of competitive equilibrium? The answer is provided within a standard framework involving excess demand functions. Conditions are identified which have the nice property that they are true close to a regular equilibrium. Uniqueness is established by considering an adjustment process and showing that under the mentioned conditions, every equilibrium is locally asymptotically stable and moreover the process itself is globally stable; uniqueness follows from an Arrow and Hahn (1971) result. Alternatively, the paper may be seen as identifying conditions under which there is a vectorfield satisfying the requirements of an uniqueness result due to Dierker (1974). Received: July 1, 1996; revised version October 7, 1996     

Arbitrage and equilibrium in strategic security markets

Summary. In view of the fundamental price taking hypothesis, arbitrage is never compatible with equilibrium in Walrasian markets because the existence of an arbitrage opportunity in a competitive situation always leads to unbounded arbitrage activity. In strategic markets however, the mere effort of individuals to profit alters market clearing prices and thus distorts arbitrage opportunities as well. This observation suggests a different relationship between arbitrage and equilibrium, than in the competitive model. Indeed, we show that in such markets a spread between the cost of a portfolio and its returns is compatible with equilibrium. We provide an example of an equilibrium where a resourceless individual holds a portfolio with zero cost and positive return in every state. We further demonstrate via an asymptotic result, that no arbitrage is intimately related to price taking behaviour.Received: 8 September 2001, Revised: 6 March 2003, JEL Classification Numbers: G12, D4, D5, D52. Correspondence to: Leonidas C. Koutsougeras     

Stochastic dominance, efficiency and separation in financial markets

A portfolio problem exhibits separation when all of its solutions can be expressed as affine combinations of a small number of mutual funds. The concept of separation is one of the cornerstones of modern portfolio theory, underlying everything from the mean-variance portfolio selection rule of [7. and 8.] and [11.] to the equilibrium pricing model of [10.], [6.] and [2.]. A great deal of effort has been put into investigating conditions which validate separation assumptions: [3.] as well as [4.] study this problem in terms of utility functions while [9.] takes a distributional approach. The purpose of this note is to show that for the distributional approach, the so-called weak and strong forms of separation are actually equivalent.     

Recursive equilibrium in endogenous growth models with incomplete markets

This paper analyzes the existence of recursive equilibria in a class of convex growth models with incomplete markets. Households have identical CRRA-preferences, production displays constant returns to scale with respect to physical and human capital, and all markets are competitive. There are aggregate productivity shocks that affect aggregate returns to physical and human capital investment (stock returns and wages), and there are idiosyncratic shocks to human capital (idiosyncratic depreciation shocks) that only affect individual human capital returns. Aggregate and idiosyncratic shocks follow a joint Markov process. Conditional on the aggregate state, idiosyncratic shocks are independently distributed over time and identically distributed across households. Finally, households have the opportunity to trade assets in zero net supply with payoffs that depend on the aggregate shock, but markets are incomplete in the sense that there are no assets with payoffs depending on idiosyncratic shocks. It is shown that there exists a recursive equilibrium for which equilibrium prices (returns) only depend on the exogenous aggregate shock variable (the wealth distribution is not a relevant state variable). Moreover, the allocation associated with this recursive equilibrium is identical to the equilibrium allocation of an economy in which households live in autarky and face both aggregate and idiosyncratic risk.I would like to thank for helpful comments Peter Howitt, Bob Lucas, Michael Magill, Tomo Nakajima, Herakles Polemarchakis, Martine Quinzii, Kevin Reffett, an anonymous referee, and seminar participants at various universities and conferences.     

Labour markets, social justice and economic efficiency

In conventional economic theory, a trade-off supposedly existsbetween social justice and economic efficiency. In reality,market and other economic institutions are dominated by powerrelations, so that the sponsorship of social justice is a productivefactor. Neo-liberal economic policies, by lifting the constraintson the exercise of unequal power, increased injustice and triggereda downward economic and social spiral. Reversing this requiresa revolution in economic theory and policy focused on full employment,the working of labour markets, the organisation of work, andhousehold organisation, social provision and self-sufficiency.     

Existence,uniqueness and some comparative statics for ratio and Lindahl equilibria

We present a rigorous, yet elementary, demonstration of the existence of a unique Lindahl equilibrium under the assumptions that characterize the standard n-player public good model. Indeed, our approach, which exploits the aggregative structure of the public good model, lends itself to a transparent geometric representation. Moreover, it can handle the more general concept of the cost share or ratio equilibrium. Finally, we indicate how it may be exploited to facilitate comparative static analysis of Lindahl and cost share equilibria.      

Globalization of labor markets and macroeconomic equilibrium

It is shown that under all-round ‘atomistic’ behavior, international mobility of labor has a beneficial effect on national employment levels but an adverse effect on consumer-price-indices (CPIs) inflation rates. Accordingly, whether or not policymakers in individual countries will be prepared to welcome on macroeconomic grounds the increasing globalization of the labor markets will depend on how they evaluate lower unemployment relative to lower CPI inflation. On the other hand, mobility of labor has an overall positive effect on the wage-setters' position, implying that, contrary to the findings of much of the international-trade literature, an increasing globalization of labor markets would be welcome by unions. It is also shown that with globalization both of the labor markets and of the wage-setting processes, atomistic behavior by monetary policymakers may well lead to both high unemployment and high inflation. Indeed, we find that in such a situation, the best option for monetary policymakers is also to cooperate. Given the recent tendency for a greater globalization of the labor markets in the OECD both in terms of labor mobility and in the sphere of wage setting, this result provides support for more monetary co-operation among the industrialized countries. Finally, with international mobility of labor, inter-union co-operation coupled with inter-government co-operation may prove to be preferable even relative to all-round nonco-operative play.     

Nonconvexity,efficiency and equilibrium in exhaustible resource depletion

We consider the problem of efficiency and existence of a competitive equilibrium in exhaustible resource markets where extraction costs are nonconvex. Nonconvexity is shown to imply that (1) (efficient) extraction ceases to the left of the minimum efficient scale, i.e., where average costs exceed marginal costs; and (2) a competitive equilibrium does not exist. Introduction of a backstop technology (which induces a flat portion of the industry demand curve) restores both existence and efficiency, provided that the backstop price is sufficiently low. If firms face even a small amount of uncertainty regarding their rivals' stocks, a backstop technology is sufficient to restore existence of competitive equilibrium, even if the backstop price is very high. In this case, however, the competitive equilibrium is not efficient.     

Modeling equilibrium trends and interventions in commodity markets

The monthly spot prices in the international tin and copper and U.S. domestic lead markets are modeled based on the “supply of storage” concept. In all cases the lag-1 natural logS/C (stocks/consumption) was highly important in the final fitted equation. For copper and lead, trend directions in the U.S. Index of Leading Economic Indicators modified theS/C dependency. Disaggregation of the tin stocks showed the special model sensitivity to the level of the ITC buffer stock. The underlying econometric models are used to estimate the price intervention effects of international political-economic crises, and commodity producer cartel actions.     

General equilibrium, markets, macroeconomics and money in a laboratory experimental environment

Summary. This paper reports on the use of laboratory experimental techniques to create relatively complete economic systems. The creation of these market systems reflects a first attempt to explore the nature of inherently interdependent environments and to assess the ability of simultaneous equations equilibrium models like the classical static general competitive equilibrium model, to predict aspects of system behaviors. In addition, the impact of the quantity of a fiat money was studied. The economies were successfully created. Classical models capture much of what was observed. Received: May 21, 1996; revised version: May 21, 1997     

General equilibrium, markets, macroeconomics and money in a laboratory experimental environment

Summary. This paper studies a version of war of attrition where two agents with private information make irreversible investment decisions in continuous time. It analyzes a monotone equilibrium where the amount of delay in the timing of decisions is a monotone function of the strength of ones private signal: an agent with a clear signal makes a prompt decision, whereas an agent with a weak signal delays a decision to gather more information from the move of the other agent. Equilibrium delay is characterized under different assumptions about the number of investment options available.Received: 4 October 1996, Revised: 16 May 1997, JEL Classification Numbers: C72, D82, L13.Masaki Aoyagi: I am very grateful to an anonymous referee of this journal for helpful comments. I also thank seminar participants at the University of Tokyo and Kyoto University.