General equilibrium without utility functions: how far to go?

How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known not to require transitivity and completeness of consumers’ preferences. We show in this paper that if consumers’ non-ordered preferences satisfy a mild version of convexity already considered in the literature, then the following properties are also satisfied: (1) the smooth manifold structure and the diffeomorphism of the equilibrium manifold with a Euclidean space; (2) the diffeomorphism of the set of no-trade equilibria with a Euclidean space; (3) the openness and genericity of the set of regular equilibria as a subset of the equilibrium manifold; (4) for small trade vectors, the uniqueness, regularity and stability of equilibrium for two version of tatonnement; (5) the pathconnectedness of the sets of stable equilibria.     

Options and sunspots in a simple monetary economy

Summary. We study sunspot immunity in a dynamic monetary economy in which consumers are allowed to trade put and call option contracts on the general price level. We define the concept of strong sunspot immunity to characterize economies that have no sunspot equilibria regardless of the number of extrinsic states and their probabilities of occurrence. We show that a small number of option contracts can make an economy strongly sunspot immune. In addition, we demonstrate how asset re-trading opportunities, and the associated capital gains and losses, reduce the number of options needed for this result to obtain. Received: August 13, 1996; revised version: January 20, 1997     

Welfare and excess volatility of exchange rates

We study the properties of a GEI model with nominal assets, outside money (injected into the economy as in Magill and Quinzii (J Math Econ 21:301–342, 1992)), and multiple currencies. We analyze the existence of monetary equilibria and the structure of the equilibrium set under two different assumptions on the determination of the exchange rates. If currencies are perfect substitutes, equilibrium allocations are indeterminate and, generically, sunspot equilibria exist. Generically, given a nonsunspot equilibrium, there are Pareto improving (and Pareto worsening) sunspot equilibria associated with an increase in the volatility of the future exchange rates. We interpret this property as showing that, in general, there is no clear-cut effect on welfare of the excess volatility of exchange rates, even when due to purely extrinsic phenomena.     

Out-of-equilibrium price dynamics

A trading-post organization of exchange is shown to determine an out-of-equilibrium price dynamics. The unique equilibrium of quasi-linear economies (defined by log-linear utility functions) is stable for the discrete time version of the dynamics. Equilibria that are stable for the continuous time version include those that satisfy the gross-substitutability property, the no-trade equilibria and, more generally, those for which trade intensity is relatively small. In addition, the set of stable equilibria is path-connected when endowments are allowed to vary without sign restrictions.      

International trade and consumption network externalities

This paper studies the effects of trade liberalization in the presence of consumption network externalities. The framework is applicable to the choice of network products and sheds light on the debate on globalization and culture. In an extended Ricardian model of international trade the paper shows that: (i) trade is not Pareto inferior to autarky if the free trade equilibrium is unique; (ii) trade is not Pareto superior to autarky if both countries are diverse (network competition) under free trade, but can be if each country is homogenous (network monopoly); (iii) and when multiple free trade equilibria exist everybody in a country can lose from free trade if that country is homogenous under autarky. Consumers of imported network goods tend to gain, while consumers of exported network goods tend to lose from trade liberalization.     

A THEORY OF MONEY AND MARKETPLACES*

This article considers an infinitely repeated economy with divisible fiat money. The economy has many marketplaces that agents choose to visit. In each marketplace, agents are randomly matched to trade goods. There exist a variety of stationary equilibria. In some equilibrium, each good is traded at a single price, whereas in another, every good is traded at two different prices. There is a continuum of such equilibria, which differ from each other in price and welfare levels. However, it is shown that only the efficient single‐price equilibrium is evolutionarily stable.     

The government's time discount rate: Choices and consequences in a dynamic framework

This paper considers a closed macroeconomy where the monetary authority pursues an inflation target and policy outcomes are the consequence of a Nash game between fiscal and monetary authorities. The specification of the macroeconomic framework is characterized by nonlinearities which lead to multiple equilibria with differing stability properties. Employing a calibrated model and simulations derived using the Mathematica package, the stability properties of the economy and the likely choice of equilibrium are examined. Within this framework, the dynamic consequences of different time discount rates for the fiscal authority are investigated, both in a world of certainty and also in a world of uncertainty. It is shown that, in a world of certainty, it will be optimal to choose the fiscal authority's time discount rate equal to the market rate of interest. However, depending on the degree of uncertainty in evaluating the time discount rates of consumers and of the fiscal authority, it may be appropriate to bias the fiscal authority's discount rate above or below the expected interest rate.     

Markov equilibria in dynamic matching and bargaining games

Rubinstein and Wolinsky [Rev. Econ. Stud. 57 (1990) 63] show that a simple homogeneous market with exogenous matching has a continuum of (non-competitive) perfect equilibria; however, the unique Markov-perfect equilibrium of this model is competitive. By contrast, in the more general case of heterogeneous markets, even the Markov property is not enough to guarantee the perfectly competitive outcome. We define a market game that allows for heterogeneous values on both sides of the market and exhibit a number of examples of (non-competitive) Markov-perfect equilibria, with and without discounting. Unlike the homogeneous case, these equilibria allow for inefficient trades and for trade at non-uniform prices. The non-competitive equilibrium may be unique.     

Demand regimes and income distribution reconsidered in an open economy portfolio balance framework

A large body of neo-Kaleckian literature has debated the distributional determinants of demand and growth. One general conclusion has been that open economy considerations weaken the potential for a wage-led growth regime. However, this literature has largely ignored asset portfolio considerations and the stock and flow interactions that result from the feedback from savings to wealth and from wealth to the current account. This study develops a theoretical framework that specifies a fuller system of (instantaneous) flow equilibria embedded in a medium-run framework with stable steady-state stocks of real and financial assets. The balance-of-payments constraint that results ensures that simply raising the wage does not yield a higher stock of real capital. A lower markup may increase the steady-state stock of capital but only through the relative price channel. These results are much stronger than those derived in the existing literature, and more important, emerge regardless of whether the demand regime is wage-led or profit-led in the absence of international trade.     

Bilateral Trade Agreements and the Feasibility of Multilateral Free Trade

We studied how the pursuit of bilateral free‐trade agreements (FTAs) affects the likelihood of achieving multilateral free trade. We derive and compare the stable Nash equilibria of two games of trade liberalization: in the FTA game, each country can either form an FTA with one of its trading partners or both of them or none of them, whereas in the (restricted) No FTA game, purely bilateral FTAs are not permitted. The major result is that there exist circumstances under which the freedom to pursue (discriminatory) bilateral FTAs is necessary for achieving multilateral free trade.     

How reasonable are assumptions used in theoretical models? Computational evidence on the likelihood of trade pattern changes

Abstract .  In theoretical literature it is common to make the assumption that in a multi-country, multi-good world, the direction of trade (import and export by commodity) is predetermined and fixed for each good for each country. We consider a simple three-country, three-good, pure-exchange model with CES preferences. We compute free trade competitive equilibria, three-country non-cooperative Nash equilibria, and customs union equilibria for randomised parameterizations, and find that trade pattern changes between free trade and customs union equilibria in around 35% of cases.     

Quota Wars In Conjectural Variations*

This paper uses a two-country, two-good, conjectural-variations model of trade to show that a quota war will not end in autarky as Rodriguez (1974) and Tower (1975) concluded. Since both countries expect retaliatory responses to reductions in their quotas, both countries are willing to stop the trade war before autarky is reached. the possible equilibria are free trade, two equilibria in which one country has its optimal quota while the other country chooses free trade, and an interior solution. It is possible that some, all, or none of these equilibria will exist.     

Evolutionary stability and lexicographic preferences

We explore the interaction between evolutionary stability and lexicographic preferences. To do so, we define a limit Nash equilibrium for a lexicographic game as the limit of Nash equilibria of nearby games with continuous preferences. Nash equilibria of lexicographic games are limit Nash equilibria, but not conversely. Modified evolutionarily stable strategies (Binmore and Samuelson, 1992. J. Econ. Theory 57, 278–305) are limit Nash equilibria. Modified evolutionary stability differs from “lexicographic evolutionarily stability” (defined by extending the common characterization of evolutionary stability to lexicographic preferences) in the order in which limits in the payoff space and the space of invasion barriers are taken.     

Indeterminacy of intertemporal equilibria under imperfect competition

Summary. It is known that overlapping generations models with imperfectly competitive firms may exhibit a continuum of stationary equilibria. The reason of this indeterminacy is that different price expectation functions of consumers lead to different objective demand functions against which firms maximize. All these expectation functions fulfill perfect foresight in the equilibrium, but they can be arbitrary off the equilibrium. In this paper it is shown that it is not this arbitrariness which is responsible for the indeterminacy, but that the continuum of stationary equilibria emerges even if expectation functions are rational. Received: March 25, 1999; revised version: February 16, 2000     

Asymmetry, stability and growth in a step-by-step R&D-race

We define a notion of stability of equilibrium in an infinitely repeated step-by-step R&D race. The unique symmetric equilibrium is shown to be unstable, and stable asymmetric equilibria arise, if product market competition is intense, firms are patient, imitation is difficult and innovations are large. Some predictions based on symmetric equilibria, e.g. that less patient firms always invest less in research, or that more intensive competition leads to higher economic growth, are reversed for “realistic” values of the underlying parameters.     

Determinacy of competitive equilibria in economies with many commodities

This paper provides a framework for establishing the determinacy of equilibria in general equilibrium models with infinitely many commodities and a finite number of consumers and producers. This paper defines a notion of regular economy for such models and gives sufficient conditions on the excess savings equations characterizing equilibria under which regular economies have a finite number of equilibria, each of which is locally stable with respect to perturbations in exogenous parameters, and under which regular economies are generic. This paper also defines two notions of concavity, called uniform concavity and weighted uniform concavity, which generalize standard finite-dimensional notions of differential concavity to an infinite-dimensional setting by prohibiting goods from becoming perfect substitutes asymptotically. For the case of economies in which there are countably many commodities, such as discrete time models or markets with countably many assets, results in this paper show that equilibria are generically determinate as long as utility functions and production sets are uniformly concave or weighted uniformly concave. Received: November 7, 1996; revised version: March 13, 1998     

Structural Change and Growth in a NEG Model

This paper presents a New Economic Geography model of structural change, agglomeration and growth. Assuming a non‐homothetic preference structure, our results show that a progressive reduction of trade costs allows the economy to pass from a pre‐industrialized to an industrialized stage and then, within the latter, from a dispersed to an urbanized regime. However, the introduction of capital accumulation and the dynamic setting of our model opens the door to a richer set of implications. First, an additional stage is introduced as, for some intermediate values of trade costs, a multiple equilibria regime emerges with simultaneously stable symmetric and core‐periphery equilibria. Second, the introduction of non‐homotheticity introduces a new channel through which growth is affected by trade costs and agglomeration. In particular, integration is always growth‐enhancing while agglomeration is growth‐detrimental.     

Probabilistic Voting and Accountability in Elections with Uncertain Policy Constraints

We consider accountability in repeated elections with two long‐lived parties that have distinct policy preferences and different levels of valence. In each period the government faces a privately observed feasibility constraint and selects a publicly observed policy vector. While pure strategy equilibria do not exhibit tight control on government policy making, complete control is possible in mixed strategies. In optimal equilibria voters use reelection functions which depend on policy in a manner that causes the governing party to internalize voter preferences. In these optimal equilibria the voters use different reelection functions for different parties.     

Dynamic Interactions in Trade Policy in a Differential Game Model of Tariff Protection

This paper develops a two‐country dynamic game model of tariff protection to reconsider optimal trade policies and their implications for welfare. The authors show that an import subsidy is optimal in the feedback Nash equilibria, which results in a curious possibility that the domestic market is monopolized by the foreign firrm. However, welfare comparisons among Nash equilibria, free trade, and autarky reveal that feedback Nash equilibria involve higher welfare than both autarky and free trade, i.e. dynamic noncooperative choices of policy serve as tacit policy coordination and ensure larger trade gains relative to free trade.     

Efficient Equilibria in the Voluntary Contributions Mechanism with Private Information

We characterize generally the Bayesian Nash equilibria of a voluntary contributions public goods game for two consumers with private information.The two consumers simultaneously make voluntary contributions to the public good, and the contributions are refunded if the total falls short of the cost of the public good. Several families of equilibria (step‐function, regular and semi‐regular) are studied. Necessary and sufficient conditions for regular and semi‐regular equilibrium allocations to be interim incentive efficient are derived. In the uniform distribution case we prove (i) the existence of an open set of incentive efficient regular equilibria when the cost of production is large enough and (ii) the existence of an open set of incentive efficient semi‐regular equilibria when the cost of production is low enough. Step‐function equilibra are proved to be interim incentive inefficient.