Extension of a theorem of Smale on equilibria for pure exchange economies

The methods used by Smale in his paper Global Analysis and Economics IIa, seem to be heavily dependent on the hypothesis that utility functions have no critical points. In this paper we prove that the no critical point hypothesis can be dropped and the class of regular economies, for which the equilibria are locally continuous functions of the parameters of the economy, can be extended.     

Continuous mean demand functions derived from non-convex preferences

In this paper we show that for a large subset of utility functions in the space of all C¹ utility functions and for all prices the mean demand of those consumers whose taste is represented by a given utility function in that subset is uniquely determined. This implies that for a large set of economies mean demand is a continuous function. Our analysis uses derivatives of first and of higher order. The result is essentially a consequence of the multijet transversality theorem.     

The structure of technology in Brazilian sugarcane production, 1975–87: An application of a modified symmetric generalized McFadden cost function

Sugarcane-based ethanol has become a primary automotive fuel in Brazil over the past 15 years. Because sugarcane costs are over two-thirds of the costs of ethanol production, the economic efficiency of this renewable petroleum substitute hinges on the structure of technology in sugarcane production. In this paper a modified symmetric generalized McFadden (SGM) cost function for sugarcane is estimated and the presence of technical change and economies of scale are investigated. The original SGM proposed by Diewert and Wales (1987) is modified to allow for fixed factors of production. This allows the cost function to be applied to processes which have fixed factors. The results suggest that there is no empirical evidence of economies of scale and very little technical change, only in the north of Brazil. The implications for the future economic efficiency of this petroleum substitute are discussed.     

Stationary Markovian equilibrium in overlapping generation models with stochastic nonclassical production and Markov shocks

This paper provides new sufficient conditions for the existence and computation of Markovian equilibrium for a large class of OLG models with Markov shocks to production. The economies considered allow for a very large class of “reduced-form” production functions, including those that are nonclassical, encompassing stochastic OLG models with social security, income redistribution policies, taxation, valued fiat money, production nonconvexities, and monopolistic competition. Our approach combines aspects of both topological and order theoretic fixed point theory and provides globally stable successive approximations algorithms for computing extremal Markovian equilibrium objects.     

Urban agglomeration effects and employment and wage gradients

When employment occurs at both central and non-central points, but firms have a preference to be near the center, the rent gradient will decline, and a wage gradient is necessary to compensate workers for more centrally located employment. Wage gradients and rent gradients are jointly determined. The relationship between wage offer functions and the equilibrium wage gradient is derived, the latter dependent on utility functions and commuting costs. This is illustrated with a two sector model incorporating agglomeration economies in the export sector. Numerical solution reveals how agglomeration economies affect wages, employment, and city size.     

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.     

Regular production economies

In this paper we extend the concept of regularity developed by Mas-Colell and Kehoe for constant-returns production economies to economies with primary and intermediate goods. To do so, we must deal with consumer demand functions that satisfy boundary conditions more general than any considered previously. We initially specify the production technology as a linear activity analysis model that allows free disposal of all commodities. Later, we indicate how our results can be extended to economies with more general production technologies.     

Heavy Constraints on a “Weightless World”?

A bstract .   Late 1990s claims of a shift toward a new economy in the United States and other developed economies were said to accelerate earlier trends reducing the material content of production. The shift toward a postindustrial services economy is said to have been accentuated by application of new information and communications technologies, dramatically reducing the material content of production. This offers the possibility for continuous economic expansion unconstrained by resources supply. This paper provides a critical analysis of these trends in relation to resource use by developed economies. It shows that trends toward a lower material content of production are occurring, and this has led to poor demand conditions for primary producers. Nevertheless, these trends fall well short of eliminating Western economies' dependence on key resources. This paper shows the changing role of resources in economic activity among developed economies.     

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.     

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.     

Continuous economies with a finite set of equilibria

This paper extends the results of G. Debreu's ‘Economies with a Finite Set of Equilibria’, within the context of the finite dimensional space of economies used therein, to the case where demand functions are assumed only to be continuous and to satisfy a certain technical condition. This condition, involving the concept of approximate limit, does not even require that the function be anywhere differentiable. Our main result is that the complement of the set of economies with a finite set of equilibrium prices has Lebesgue measure zero, although it need not be closed and in fact, may very well be dense.     

The existence of rational expectations equilibria in a large economy with noisy price observations

Non-revealing rational expectations equilibria exist in microeconomic pure exchange economies in which a continuum of uninformed agents have suitably distributed noisy price observations. Slight dispersion in the prices observed by the subset of uninformed consumers is the key condition for continuity (and smoothness) of aggregate excess demand, although individual demands are discontinuous. It leads to equilibria in which markets approximately clear in a strong sense. The equilibria are obtained by applying a fixed point argument to state-dependent excess demand functions.     

Spatial duopoly with discriminatory pricing

The concept and existence of an equilibrium is established for profit maximizing competitors whose decisions involve choices of both delivered price schedules and firm locations. Each firm faces a production function; each is allowed to locate in the plane and to set discriminatory prices. Any transport cost function that is continuous in the firm location variable may be used. It is shown that the locations of the two firms are in equilibrium if each firm is minimizing social cost (i.e., the total cost to the firms of supplying the market with the good it demands is minimized) with respect to the opponent's fixed location.     

The joint continuity of the expected payoff functions

Glicksberg [Glicksberg, I.L., 1952. A further generalization of the Kakutani fixed point theorem, with applications to Nash equilibrium points. In: Proceedings of the American Mathematical Society 3, pp. 170–174] generalized the Kakutani fixed point theorem to the setting of locally convex spaces and used it to prove that every k-person strategic game with action sets convex compact subsets of locally convex spaces and continuous payoff functions has a Nash equilibrium. He subsequently used this result to establish the following fundamental theorem of game theory: Every k-person strategic game with action sets metrizable compact topological spaces and continuous payoff functions has a mixed strategies equilibrium. However, in his proof of the latter result, Glicksberg did not show that the expected payoff functions were jointly continuous, something that was required for the existence of a mixed strategies equilibrium.     

Product diversification,production systems,and economic performance in U.S. agricultural production

The U.S. agricultural sector is experiencing significant structural change. Farm size is rising and activities are broadening, including more off-farm employment, implying economic incentives for larger and more diversified farms, and complementarities among agricultural netputs. We quantify such patterns for farms in the corn belt, by measuring scale economies, and output and input contributions and jointness. We estimate the multi-output and -input production technology by stochastic frontier techniques applied to output and input distance functions. We find that both scope and scale economies have important economic performance implications, and that an input-oriented framework including off-farm income best characterizes agricultural production.     

Determination of general equilibrium with incomplete markets and default penalties

This paper is concerned with the existence and computation of general equilibrium with incomplete asset markets and default. Due to the incompleteness of asset markets, the excess demand functions are typically not continuous at prices and delivery rates for which the assets have redundant nominal deliveries. This discontinuity results in a serious problem for the existence and computation of general equilibrium. We show that this problem can be resolved by replacing the nominal delivery matrix with a constant-rank one and restricting the macro variables in a subset of the domains. With this approach, the economies with incomplete markets and default penalties can be analyzed with differentiable homotopy techniques, and thus in the same framework as standard general equilibrium models. As a by-product, the existence of equilibrium is ensured for generic economies. Several computational examples demonstrate the effectiveness of the algorithm and show some quantitative features of equilibria in the model with default penalties.     

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.     

Equilibria in large economies with a separable Banach commodity space and non-ordered preferences

The purpose of this paper is to provide an existence result of equilibria for economies with a measure space of agents, a non-trivial production sector and an infinite dimensional commodity space. The commodity space is modeled by an ordered separable Banach space whose positive cone has a non-empty interior. The discretization approach proposed in this paper, allows us to extend the existence results in Khan and Yannelis [Equilibrium in markets with a continuum of agents and commodities. In: Khan, M.A., Yannelis, N.C. (Eds.), Equilibrium Theory in Infinite Dimensional Spaces. Springer, Berlin, 1991] and Podczeck [Economic Theory 9 (1997) 585] to economies with a non-trivial production sector and with possibly non-ordered but convex preferences as well as partially ordered (possibly incomplete) but non-convex preferences.     

Walrasian social orderings in exchange economies

We study social ordering functions in exchange economies. We show that if a social ordering function satisfies certain Pareto, individual rationality, and local independence conditions, then (i) the set of top allocations of the chosen social ordering is contained in the set of Walrasian allocations and is typically non-empty, and (ii) all individually rational but non-Walrasian allocations are typically ranked indifferently. Thus, such a social ordering function is quite similar to the Walrasian correspondence, which can be regarded as the social ordering function whose associated indifference classes are the set of Walrasian allocations and the set of other allocations.     

Agglomeration economies with consistent productivity estimates

This paper investigates the relative impact of microeconomic agglomeration mechanisms on plant's total factor productivity (TFP) using German establishment and employment-level data. Contrasting different strategies for estimating TFP from plant-level production functions reveals that unobserved output prices bias true productivity and lead to underestimated agglomeration economies. With the corrected TFP measure, the largest impact is found for labor market pooling, which is captured by the correlation of the occupational composition between one county-industry and the rest of the county. This main result is robust, even when the spatial units are resized from counties to larger labor market regions. Input linkages appear to be relevant only at this larger regional scale. Overall, agglomeration economies differ substantially across industries. Only for a subset of industries, some positive evidence is detected for knowledge spillovers.