Existence of equilibria in economies with externalities and non-convexities in an infinite-dimensional commodity space

We prove an equilibrium existence theorem for economies with externalities, general types of non-convexities in the production sector, and infinitely many commodities. The consumption sets, the preferences of the consumers, and the production possibilities are represented by set-valued mappings to take into account the external effects. The firms set their prices according to general pricing rules which are supposed to have bounded losses and may depend upon the actions of the other economic agents. The commodity space is L_∞(M,M,μ), the space of all μ-essentially bounded M-measurable functions on M.As for our existence result, we consider the framework of Bewley (1972). However, there are four major problems in using this technique. To overcome two of these difficulties, we impose strong lower hemi-continuity assumptions upon the economies. The remaining problems are removed when the finite economies are large enough.Our model encompasses previous works on the existence of general equilibria when there are externalities and non-convexities but the commodity space is finite dimensional and those on general equilibria in non-convex economies with infinitely many commodities when no external effect is taken into account.     

Implementation of marginal cost pricing equilibrium allocations with transfers in economies with increasing returns to scale

This paper considers implementation of marginal cost pricing equilibrium allocations with transfers for production economies with increasing returns to scale. We present a mechanism whose Nash equilibrium allocations coincide with the set of marginal cost pricing equilibrium allocations with transfers that characterizes Pareto efficient allocations for economies with non-convex production technologies. We allow production sets and preferences to be unknown to the planner. The mechanism has some nice properties such as feasibility, continuity, and finite-dimension of message space. Furthermore, it works not only for three or more agents, but also for two-agent economies.     

Imperfect competition à la Negishi,also with fixed costs

The paper studies equilibria for economies with imperfect competition and non-convex technologies. Following Negishi, firms maximise profits under downward-sloping perceived demand functions. Negishi’s assumptions, in particular the assumption of a single monopolistic competitor in each market, are relaxed. Existence of equilibria is obtained, under otherwise standard assumptions, for productions sets defined in each firm by the union of a convex technology and a technology subject to fixed costs. In the light of a counterexample, it is assumed that fixed factors are distinct from variable factors. Technically, the proof rests on pricing rules.     

An algebraic index theorem for non-smooth economies

In this paper, we prove an existence theorem for equilibria in production economies with increasing returns, which generalizes the classic results on this topic. In particular, we eliminate both the free-disposal assumptions and any smoothness requirements on the boundary of the production sets. For this purpose, we propose a new definition of the topological degree for non-convex-valued correspondences defined on non-smooth topological manifolds.     

Club theory and household formation

The relationship between our general equilibrium model with multi-member households and club models with multiple private goods is investigated. The main distinction in the definitions consists in the equilibrium concepts. As a rule, competitive equilibria among households where no group of consumers can benefit from forming a new household and valuation equilibria prove equivalent in the absence of consumption externalities, but not in their presence.     

Endowment-regarding preferences

We consider a general equilibrium model of pure exchange economies with endowment externalities. Consumers’ behaviors depend not only on their own consumption but also on the endowments of the other consumers. Applying the same method of analysis in Balasko (2015) about wealth concerns, we first show that almost all properties of equilibrium, including smooth equilibrium manifold and genericity of regular economies, can be directly extended to the economy where the demand function depends on the endowments of others and wealth of only one consumer. Next, we clarify the sufficient conditions under which those properties remain true in the economy with the most general form of endowment externalities. Finally, we generalize the above sufficient conditions to derive generic regularity results in the economy with both consumption and endowment externalities.     

Congestion,agglomeration, and the structure of cities

Congestion costs in urban areas are significant and clearly represent a negative externality. Nonetheless, economists also recognize the production advantages of urban density in the form of positive agglomeration externalities. The long-run equilibrium outcomes in economies with multiple correlated but offsetting externalities have yet to be fully explored in the literature. Therefore, I develop a spatial equilibrium model of urban structure that includes both congestion costs and agglomeration externalities. I then estimate the structural parameters of the model using a computational algorithm to match the spatial distribution of employment, population, land use, land rents, and commute times in the data. Policy simulations based on the estimates suggest that congestion pricing may have ambiguous consequences for economic welfare.     

Wealth concerns and equilibrium

Most properties of the classical general equilibrium model without externalities fail to extend to the wildest forms of consumption externalities. The recent interest for wealth concerns, a kind of externality associated with herding behavior and other-regarding preferences, motivates a study of the general equilibrium exchange model with those externalities. The diffeomorphism of the equilibrium manifold with a Euclidean space, the smoothness and properness of the natural projection and its non-zero degrees are shown to hold true for endowment spaces with variable total resources. Other properties of the classical exchange model without externalities are fragile in the sense that they do not resist the introduction of wealth concerns even in models where consumers preferences are represented by the simplest forms of utility functions like the log-linear (or Cobb–Douglas) functions. The most notable fragile properties are the uniqueness and regularity of equilibrium at equilibrium allocations and the stability of no-trade equilibria.     

Some new characterization of rational expectation equilibria in economies with asymmetric information

We compare the family of rational expectation equilibria with the ex-post Aubin core allocations in the framework of an economy with uncertainty and asymmetric information. We do it in a very general setting: an arbitrary space of agents and an infinite dimensional commodity space. We also present a characterization of the ex–post Aubin core by allocations belonging to the core of the associated complete information economies, and we use a suitable definition of Edgeworth equilibria to characterize the family of rational expectation equilibria. Moreover, we study some generalizations of the ex-post Aubin core obtained by making some restriction on the families of blocking coalitions.     

General consumption constraints and regular economies

In the spirit of Smale’s work, we consider pure exchange economies with general consumption sets. In this paper, the consumption set of each household is described in terms of a function called possibility function. The main innovation comes from the dependency of each possibility function with respect to the individual endowments. We prove that, generically in the space of endowments and possibility functions, economies are regular. A regular economy has a finite number of equilibria, which locally depend on endowments and possibility functions in a continuous manner.     

Sequential regularity in smooth production economies

In general equilibrium models where agents trade sequentially in multiple periods, the equilibria that endogenously occur in later periods can be robustly indeterminate if production sets are not everywhere differentiable (as. for example, with linear activities). The present paper proves that if technology is smooth, then equilibria are sequentially regular. That is. the equilibria of the endogenously generated economies occurring in later periods that confirm the unanimous expectations formed by agents in earlier periods are regular (and thus, for example, isolated from other equilibria). The paper also proves and utilizes the standard result that the overall intertemporal equilibria are regular.     

Coasian equilibrium

We consider a general equilibrium economy with public goods and externalities. Following Boyd and Conley (1997), we treat externality markets directly instead of indirectly through Arrovian commodities. Because such direct externality markets are not subject to the nonconvexities that Starrett [Starrett, D., 1972. Fundamental nonconvexities in the theory of externalities. Journal of Economic Theory 4, 180–199] shows are fundamental to Arrow’s externality markets, this new approach admits the use of largely standard methods to prove welfare and existence theorems in an economy with externalities. We extend the Boyd and Conley model to allow firms to benefit from public goods and be damaged by externalities, and to allow consumers to produce externalities. We state a first welfare theorem and prove the existence of a competitive equilibrium. Taken together, this can be viewed as a type of general equilibrium Coase theorem. Considered as a special case, these theorems also represent a significant generalization of existing results for pure public goods economies.     

Implementation of Pareto efficient allocations

This paper considers Nash implementation and double implementation of Pareto efficient allocations for production economies. We allow production sets and preferences are unknown to the planner. We present a well-behaved mechanism that fully implements Pareto efficient allocations in Nash equilibrium. The mechanism then is modified to fully doubly implement Pareto efficient allocations in Nash and strong Nash equilibria. The mechanisms constructed in the paper have many nice properties such as feasibility and continuity. In addition, they use finite-dimensional message spaces. Furthermore, the mechanism works not only for three or more agents, but also for two-agent economies.     

A dynamic equilibrium model of search, production, and exchange

We study a general equilibrium model where agents search for production and trading opportunities, that generalizes the existing literature by considering a large number of differentiated commodities and agents with idiosyncratic tastes. Thus, agents must choose nontrivial exchange as well as production strategies. We consider decreasing, constant, and increasing returns to scale in the matching technology, and characterize the circumstances under which there exist multiple steady state equilibria, or multiple dynamic equilibria for given initial conditions. We also characterize the existence of dynamic equilibria that are limit cycles. Equilibria are not generally optimal, and when multiple equilibria coexist they may be ranked. We analyze comparative statics and find that certain intuitive results do not necessarily hold without restrictions on the stochastic structure.     

Hoarding international reserves versus a Pigovian tax-cum-subsidy scheme: Reflections on the deleveraging crisis of 2008-2009, and a cost benefit analysis

We outline the case for supporting self-insurance by imposing a tax on external borrowing in a model of an emerging market. Entrepreneurs finance tangible investments via bank intermediation of foreign borrowing, exposing the economy to negative fire-sale externalities at times of deleveraging; a risk that increases with the ratio of aggregate external borrowing to international reserves. Price taking economic agents ignore their marginal impact on the expected cost of a deleveraging crisis. The optimal borrowing tax reduces the distorted activity, external borrowing, and induces borrowers to co-finance the precautionary hoarding of international reserves.     

Aggregation in economies with search frictions

We derive an aggregation result in economies with indivisible labor supply choices and frictional labor markets, obtaining a tractable model of gross worker flows in aggregate labor markets with search frictions. Our result explores the fact that economies with non-convex choice sets and idiosyncratic shocks allow for sunspot equilibria à la Kehoe et al. (2002). We use comparative steady state analysis to demonstrate the applicability of our aggregation result. Our framework reconciles the neoclassical growth model with search frictions with a mildly procyclical participation rate and matches the gross worker flows underpinning those dynamics.     

Voluntary contributions to multiple public goods in a production economy with widespread externalities

In a production economy, multiple public goods are produced by firms in competitive markets, and provided by the government together with contributions from consumers. There are widespread externalities: all consumers’ consumption and contributions and all firms’ production enter into utility functions. Public goods can be imperfect substitutes or complements, and they can be local public goods or club goods. Zero bounds that require consumers to make nonnegative contributions complicate the differentiable approach. Applying the transversality theorem for smooth economies in a regular parameterization, we obtain the existence of equilibrium in such an economy, and generically equilibria are regular and locally unique.     

The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options

We assess the predictive accuracies of a large number of multivariate volatility models in terms of pricing options on the Dow Jones Industrial Average. We measure the value of model sophistication in terms of dollar losses by considering a set of 444 multivariate models that differ in their specification of the conditional variance, conditional correlation, innovation distribution, and estimation approach. All of the models belong to the dynamic conditional correlation class, which is particularly suitable because it allows consistent estimations of the risk neutral dynamics with a manageable amount of computational effort for relatively large scale problems. It turns out that increasing the sophistication in the marginal variance processes (i.e., nonlinearity, asymmetry and component structure) leads to important gains in pricing accuracy. Enriching the model with more complex existing correlation specifications does not improve the performance significantly. Estimating the standard dynamic conditional correlation model by composite likelihood, in order to take into account potential biases in the parameter estimates, generates only slightly better results. To enhance this poor performance of correlation models, we propose a new model that allows for correlation spillovers without too many parameters. This model performs about 60% better than the existing correlation models we consider. Relaxing a Gaussian innovation for a Laplace innovation assumption improves the pricing in a more minor way. In addition to investigating the value of model sophistication in terms of dollar losses directly, we also use the model confidence set approach to statistically infer the set of models that delivers the best pricing performances.     

On financial equilibrium with intermediation costs

This paper studies the set of competitive equilibria in financial economies with intermediation costs. We consider an arbitrary dividend structure, which includes options and equity with limited liabilities. We show a general existence result and upper-hemi continuity of the equilibrium correspondence. Finally, we prove that when intermediation costs approach zero, unbounded volume of asset trades is a necessary and sufficient condition, provided that, there is no financial equilibrium without intermediation costs.     

Optimal policies in cities with congestion and agglomeration externalities: Congestion tolls,labor subsidies,and place-based strategies

This paper develops a spatial general equilibrium model that accommodates both congestion and agglomeration externalities, while firms’ and households’ land-use decisions are endogenous across continuous space. Focusing on the interaction between externalities and land use patterns, we examine the efficiencies of first-best policies and second-best pricing and place-based strategies using numerical simulations. A first-best policy must combine both Pigouvian congestion tolling (PCT) and Pigouvian labor subsidies (PLS) instruments, or design an optimal toll (or subsidy) internalizing agglomeration externalities (or congestion externalities). We also examine second-best pricing policies if only one instrument is adopted. Congestion pricing policies alone (e.g., a partial PCT or a flat-rate toll) can improve social welfare only in heavy-congestion cities, and their welfare gains may be insignificant (e.g., below 10% of the welfare improvement achieved by first-best policies). In contrast, second-best labor subsidy policies alone are a more effective alternative to first-best policies. As to place-based policies, the firm cluster zoning (FCZ) regulation is more efficient than the urban growth boundary (UGB) policy. UGBs only have small effects on the agglomeration economy but could worsen land market distortions via residential rent-escalation effects. These findings suggest that it is important to internalize business land use decisions and relax monocentricity assumptions, in order to appreciate the interplay of both urban externalities, since spatial adaptations to policy interventions can distort system efficiencies.