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.      

Strong comparative statics of equilibria

Some results in the monotone comparative statics literature tell us that if a parameter increases, some old equilibria are smaller than some new equilibria. We give a sufficient condition such that at a new parameter value every old equilibrium is smaller than every new equilibrium. We also adapt a standard algorithm to compute a minimal such newer parameter value and apply this algorithm to a game of network externalities. Our results are independent of a theory of equilibrium selection and are valid for games of strategic complementarities.     

A two-country model of trade and growth with intersectoral knowledge spillovers

We formulate a two-country, two-good, two-factor endogenous growth model with learning by doing and intersectoral knowledge spillovers. Our model exhibits no transitional dynamics because of constant returns to capital, the existence of only one state variable for each country, and the factor price equalization theorem. By applying our model to the problem of aid and growth, we show that a permanent increase in untied aid raises the common growth rate if and only if the propensity to consume the capital-intensive good in the recipient country is larger than in the donor country.     

The trade balance and the terms of trade in a two-country two-sector OLG economy

We consider a two-country, two-sector OLG model. It is shown that the trade balance and the relative price of exports are always positively related when exports are labor intensive regardless of the elasticity of intertemporal substitution in consumption. A large response of savings to future prices becomes a sufficient condition for an inverse relation between these variables only if exports are capital intensive. In this case, a rise in the terms of trade can be followed by a trade balance decline if consumption goods are capital intensive and the income effect implied on savings is negative and large.     

Uniqueness and comparative statics of Nash equilibrium in a tariff retaliation model

This paper considers uniqueness and comparative statics of Nash equilibrium of a tariff retaliation model. The approach to the problem is geometrical and reminiscent of the analysis for the free trade competitive equilibrium. If the countries have constant elasticity of substitution utility functions, some simple conditions can be used to prove uniqueness of the Nash equilibrium of the tariff retaliation game. The welfare effects of endowment changes are analyzed in terms of the standard terms of trade and volume of trade effects. If the elasticity of substitution of one of the countries is sufficiently high, immiserizing growth will not occur.      

Leisure time, savings and trade patterns A two-country growth model

This paper proposes a simple two-country endogenous growth model with endogenous consumption, leisure time and wealth accumulation. The model examines possible causes for the world economic growth and the existence and persistence of trade patterns between countries with different preferceces and human capital under internationally free capital mobility. We show how differences in preferences in consumption, leisure time and wealth between the two countries may affect long-run world economic growth.     

Characterizing solutions of supermodular games; intuitive comparative statics,and unique equilibria

Summary We present a technique for locating both an upper and a lower bound on equilibrium points of supermodular games by looking only at the first derivatives of the payoff functions at points of disequilibrium. This technique is useful for characterizing equilibria of games when the closed form solution is difficult to calculate, for performing comparative statics analysis, and for determining the uniqueness of equilibria.I would like to thank David Easley, James Friedman, Ken Kasa, Rich McLean and Michael Waldman for their helpful comments.     

Indeterminacy in a dynamic two-country model

The purpose of this paper is to show that indeterminacy can arise in a simple competitive two-country dynamic model of international trade, free of externalities, imperfect competition, and government intervention. This seemingly surprising result is based on an assumption that there is no international credit market. As will be shown later, the assumption implies that dynamic equilibrium paths of our two-country, therefore heterogeneous consumer, model are not generally Pareto-optimal.The paper is dedicated to Professor Mukul Majumdar on the occasion of his 60th birthday with great respect. We thank Takashi Kamihigashi, Tapan Mitra and Makoto Yano for their useful comments on the earlier version of this paper.     

Existence of a continuum of equilibria in a monetary random-matching model

In this paper, we study a monetary random-matching model where both goods and money are perfectly divisible, production is costly, and there is no exogenous upper bound on agents' money holdings, information on which is private to the agent. We show that there is a continuum of stationary equilibria where agents have either no money or a set amount, and buyers spend all their money. As in the previous studies, the equilibrium value function is step-like, which emerges as a self-fulfilling prophecy. The endogenous upper bound on agents' money holdings is the result of private information on agents' money holdings. Buyers post an offer that is accepted only by sellers without money, who set a higher value on money.     

Monetary disinflation in a simple two-country model

A two-country model with sluggish goods and labour markets, efficient financial markets, flexible exchange rates and perfect capital mobility is considered. The rational expectations dynamics are considerably simplified when the effects of real interest rates on investment are small. It can then be shown that simultaneous monetary disinflation has no real effects, whilst independent disinflation leads to output losses at home and gains abroad.     

Endogenous inequality and fluctuations in a two-country model

We study a two-country version of Matsuyama's [K. Matsuyama, Financial market globalization, symmetry-breaking, and endogenous inequality of nations, Econometrica 72 (2004) 853-884] world economy model. As in Matsuyama's model, symmetry-breaking can be observed, and symmetry-breaking generates endogenously determined levels of inequality. In addition, we show that when the countries differ in population size, their interaction through credit markets may lead to persistent endogenous fluctuations.     

Existence of perfect equilibria: a direct proof

We provide a direct proof of the existence of perfect equilibria in finite normal form games and extensive games with perfect recall. It is done by constructing a correspondence whose fixed points are precisely the perfect equilibria of a given finite game. Existence of a fixed point is secured by a generalization of Kakutani theorem, which is proved in this paper. This work offers a new approach to perfect equilibria, which would hopefully facilitate further study on this topic. We also hope our direct proof would be the first step toward building an algorithm to find the set of all perfect equilibria of a strategic game.     

Existence of equilibria in the overlapping generations model: the nontransitive case

Summary This paper investigates the existence of competitive equilibria in dynamic exchange models with countably many periods and countably many agents. At each period the commodity space can be finite or infinite dimensional. The preferences of agents are not assumed to be transitive or complete. A first equilibrium existence theorem is established under the classical assumption that there exists a finite set of non-negligible agents. In the particular case of an overlapping generations model, a second existence theorem allows simultaneously for finite-lived assets and infinite-lived assets and limits the previous assumption to infinite-lived assets. This theorem covers obviously the standard case of an overlapping generations model where the agents have no endowment outside their lifetime.     

Core structure and comparative statics in a hybrid matching market

Flexible firms compete by means of wages in the Assignment market while rigid firms have no flexibility over terms of appointment in the Marriage market. Workers trade with both kinds of firms in the hybrid market.Examples show that standard results that characterize the core of the Marriage market (respectively, Assignment market) are not robust to the entrance of flexible (respectively, rigid) firms to this market. A new algebraic structure provides a different characterization for the core of the hybrid model and reflects a sort of robustness to the exit of rigid (respectively, flexible) firms from this market. Meaningful comparative static results are derived.     

Topics in nonparametric comparative statics and stability

This paper presents the analysis of the Jacobian matrix of a small, macroeconomic model to determine the robustness of the model's comparative statics. The values of the model's coefficients are assessed with respect to seven alternative estimation strategies such as ordinary least squares or two-stage least squares. For each alternative version, the invertibility and stability of the Jacobian matrix is studied. The model is robust to the degree that these characteristics are shared by any matrix with the same sign pattern or other similar nonparametric conditions on its entries. One way to address the relative success of the different estimation strategies is through the robustness of the comparative statics of the resulting model.     

Coordination of optimal taxation in a two-country equilibrium model

The optimal determination of distortionary taxes on labour income in order to finance the provision of publicly provided private goods is considered within the context of a static two-country equilibrium model. It is shown that, with Cobb-Douglas utility functions, the lack of international coordination of optimal taxation leads to excessive supplies of publicly provided private goods.     

Exchange rate instability in a two-country portfolio balance model

This paper considers the question of Walrasian stability in the context of a two-country model in which gross substitutability is assumed and negative net foreign asset positions are ruled out. It demonstrates that these assumptions neither guarantee stability nor guarantee that an increase in the factors deemed destabilizing (stabilizing) in the literature will not in fact turn out to be stabilizing (destabilizing). However, it derives a condition which guarantees stability, pointing out that this condition is more plausible than certain “smallness” assumptions which have performed a similar function in portfolio balance models.     

Weak and strong monotone comparative statics

Summary This paper develops necessary and sufficient conditions for the set of solutions to an optimization problem to be nondecreasing in a weak sense still strong enough to guarantee the existence of an increasing selection, and thus strong enough to guarantee monotonicity when the solution is unique, as well as necessary and sufficient conditions for the set of optimizers to be nondecreasing in a strong sense which is strong enough to rule out the possibility of a decreasing selection. These necessary and sufficient conditions are variations of quasisupermodularity and the single crossing property introduced in Milgrom-Shannon [13]. Moreover, to determine when an objective function satisfies these conditions, this paper develops several characterizations of quasisupermodularity and the single crossing property and their variants, both in terms of differential conditions and in terms of restrictions on the structure of the level sets of these functions. Several examples are given to choice theory under loss aversion and to an auction problem.I am grateful to Don Brown and Paul Milgrom for numerous helpful conversations concerning earlier versions of this paper. This paper is a revised and expanded version of the paper An Ordinal Theory of Games with Strategic Complementarities (Shannon [15]). I am pleased to acknowledge the financial support of the National Science Foundation, and an Alfred P. Sloan Foundation Doctoral Dissertation Fellowship.     

Open-access renewable resources and pollution: Trade and policy implications in a two-country model

We examine the interaction between the relative inter-industry pollution externality and resource stock externality of harvesting in deciding trade patterns and welfare gains from trade in a two-country model (less-developed countries) with renewable resources in the absence of resource management. This paper focuses on the impacts of trade policies on resource conservation and welfare outcomes in two countries with different environmental management regimes. Differences in pollution management standards between both countries determine the direction of trade flow and gains from trade in a diversified production case. The country with a lower pollution intensity parameter, an exporter of resource goods, certainly experiences welfare loss in the post-trade steady-state and may also suffer a decline in utility throughout the transition path. However, a country with higher pollution intensity and importers of resource goods tend to gain from trade. Under national open-access resources, given that pollution is regulated up to a certain point in both countries, this study finds that implementing better restrictions on only one externality factor is not optimal from a post-trade welfare perspective. Lastly, from the point of view of policy suggestion, this paper offers an optimal trade policy that the economic and environmental effects of enforcing import tax on resource goods are likely to be Pareto-improving consequences compared to the implications of using an export tax.     

Existence of voting-market equilibria

We show the existence of an equilibrium in a model where private goods are allocated by markets and the public good (bad) is allocated by majority rule voting.