On economies of scope in communication

A classic puzzle in the economic theory of the firm concerns the fundamental cause of decreasing returns to scale. If a plant producing product quantityX at costC can be replicated as often as desired, then the quantityrX need never cost more thanrC. Traditionally the firm is imagined to take its identity from a fixednon-replicable input, namely a ‘top manager’; as more plants or divisions are added, the communication and computation burden imposed on the top manager (who has information not possessed by the divisions) grows more than proportionately. Decreasing returns are experienced as the top manager hires more variable inputs to cope with the rising burden. Suppose it turns out, however, that when the divisions are assembled, and are given exactly the same totally independent tasks that they fulfilled when they were autonomous, then asaving can be achieved if they adopt a joint procedure for performing those tasks rather than replicating their previous separate procedures. Then the top manager's rising burden must be shown to be particularly onerous—otherwise there may actually beincreasing returns. We show that for a certain model of the information-processing procedure used by the separate divisions and by the firm, there may indeed be such an odd unexpected saving. The saving occurs with respect to the size of the language in which members of each division, or of the firm, communicate with one another, provided that language is finite. If instead the language is a continuum then the saving cannot occur, provided that the procedures used obey suitable ‘smoothness’ conditions. We show that the saving for the finite case can be ruled out in two ways: by requiring the procedures used to obey a regularity condition that is a crude analogue of the smoothness conditions we impose on the continuum procedures, or by insisting that the procedure used be a ‘deterministic’ protocol. Such a protocol prescribes a conversation among the participants, in which a participant has only one choice, whenever that participant has to make an announcement to the others. The results suggest that a variety of information-processing models will have to be studied before the traditional explanation for decreasing returns to scale is understood in a rigorous way.     

Economies of scope and economies of agglomeration

Agglomeration economies are economies external to the firm, and plant, but internal to a particular location. In this paper the notion of agglomeration economies is formally investigated. The implications of the concept for urban structure and industrial organization are then traced. Under specified considerations, weak economies of agglomeration, as defined in this paper, are shown to be necessary for the existence of an urban area.     

Technical choice and reswitching in space economies

This paper seeks to apply some of the arguments of the ‘capital controversy’ in economics (originally sparked by Piero Sraffa's work) to a spatial context. In particular, technical choice, switching of techniques and reswitching are given spatial counterparts. The main conclusion of the paper is that parts of orthodox theory in regional economics are open to question when they are scrutinized by a perspective based on Sraffa's ideas.     

Scale and scope economies of Japanese private universities revisited with an input distance function approach

This paper examines the scale and scope economies of higher education institutions in Japan assuming the presence of productive inefficiency. The standard approach to testing the scope economies is to apply the cost function. However, the cost function approach often entails the difficulty of obtaining reliable data on input prices, especially the input prices of capital for higher education institutions. This paper proposes a duality approach based on the input distance function. The scope economies are tested under a necessary and sufficient condition by retrieving the costs of joint and separate production from the input distance function. We apply the testing procedure to data pertaining to 218 Japanese private universities in 1999 and 2004. The results indicate the scale economies and the scope diseconomies.     

Non-jointness and scope economies in the multiproduct symmetric generalized McFadden cost function

The multiproduct symmetric generalized McFadden cost function is increasingly prominent in empirical production analysis. Researchers should be aware that the scope for imposing and testing non-jointness in this model is limited. In the general version of the model non-jointness requires the non-testable maintained hypothesis of similar (in a sense we define) single-output production technologies, a maintained hypothesis for which there is not normally any basis. The apparent imposition and testing of non-jointness must be qualified accordingly. The attempt to impose non-jointness and global separability simultaneously necessarily imposes constant returns to scale and the implication that outputs are identical up to a scalar multiple. In this special case the model therefore effectively describes merely the production of a single output, and in this sense is only trivially multiproduct.     

Market economies with many commodities

In this survey problems from the consideration of infinite dimensional commodity spaces in the Arrow-Debreu-McKenzie model are discussed. It has become clear in the last couple of decades that in order to address real policy questions, economic models that are both stochastic and dynamic have to be employed. These models lead naturally to infinite dimensional commodity spaces.

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Riassunto In questo lavoro si discutono i problemi che si presentano quando, in connessione all'esistenza e all'efficienza di equilibri Walrasiani nel modello di Arrow-Debreu-McKenzie, si ammette che lo spazio dei beni sia di dimensione non finita. è diventato chiaro nei due ultimi decenni che per affrontare questioni reali è necessario usare modelli sia dinamici che stocastici e ciò conduce in modo naturale alla considerazione di spazi infinito-dimensionali. Si rimane principalmente confinati alle economie di puro scambio al solo scopo di semplificare la trattazione.

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This paper has been presented atWorkshop in Economic Theory, Venice-June 2–7, 1997 organized by Istituto Veneto di Scienze, Lettere ed Arti and atXXI Convegno AMASES, Rome-September 10–13, 1997. It is an expanded version of our paper [5] that appeared inJournal of Economic Theory, vol. 74, n. 1, 1997, pp. 62–105. We are grateful to Karl Shell and Academic Press for permission to include that portion of the material here. The research of C. D. Aliprantis was supported in part by the NATO Collaborative Research Grant #941059.     

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.     

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.     

Efficient paired choice designs with fewer choice pairs

For paired choice experiments, two new construction methods of designs are proposed for the estimation of the main effects. In many cases, these designs require about 30–50% fewer choice pairs than the existing designs and at the same time have reasonably high D-efficiencies for the estimation of the main effects. Furthermore, as against the existing efficient designs, our designs have higher D-efficiencies for the same number of choice pairs.     

Robust efficiency in mixed economies with asymmetric information

In this paper, we study robustly efficient allocations in a pure exchange economy. Answering a question of Hervés-Beloso and Moreno-García (2008), we present an extension of their main result to an asymmetric information mixed economy whose commodity space is an ordered separable Banach space having an interior point in its positive cone.     

An index formula for production economies with externalities

We prove that the degree of the equilibrium correspondence of an economy with increasing returns and external effects is equal to (−1)^L−1${(-1)}^{L-1}$ where L is the dimension of the space of goods. This allows us to infer existence, finiteness and uniqueness results.     

Finitely additive economies with free extremely desirable commodities

Continuing the investigation on finitely additive economies with infinite dimensional commodity space, we state a core-walras individualistic equivalence for an economy where preferences admit a summable map of extremely desirable commodities. The main result extends previous equivalences obtained both in the countably additive and in the finitely additive setting. Extra assumptions on the model are discussed via a pair of examples.     

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.     

Arbitrage and equilibrium in unbounded exchange economies with satiation

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner’s existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents’ preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades– that is, as long as agents’ preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation – a condition considerably weaker than local or global nonsatiation – that makes possible this transformation.     

Endogenous debt constraints in collateralized economies with default penalties

The objective of the paper is to propose endogenous debt constraints that rule out Ponzi schemes and ensure the existence of equilibria in a model with limited commitment and (possible) default. We appropriately modify the definition of finitely effective debt constraints, introduced by Levine and Zame (1996) (see also Levine and Zame (2002)), to encompass models with limited commitment, default penalties and collateral. Along this line, we introduce in the setting of Araujo et al. (2002), Kubler and Schmedders (2003) and Páscoa and Seghir (2009) the concept of actions with finite equivalent payoffs. We show that, independent of the level of default penalties, restricting plans to have finite equivalent payoffs rules out Ponzi schemes and guarantees the existence of an equilibrium that is compatible with the minimal ability to borrow and lend that we expect in our model.     

Arbitrage and equilibrium in economies with infinitely many commodities

An ‘arbitrage opportunity’ for a class of agents is a commodity bundle that will increase the utility of any of the agents and that has non-positive price. The non-existence of ‘arbitrage opportunities’ is necessary and sufficient for the existence of an economic equilibrium. A bundle is ‘priced by arbitrage’ if there is a unique price that it can command without causing an ‘arbitrage opportunity’ to exist. For economies that have infinitely many commodities, appropriate notions of ‘arbitrage opportunities’ and ‘bundles priced by arbitrage’ depend on the continuity of agents’ preferences. This paper develops these notions, thereby providing a foundation for recent work in financial theory concerning arbitrage in continuous-time models of securities markets.