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.     

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.     

Competitive equilibria in economies with multiple indivisible and multiple divisible commodities

In this paper we consider a general equilibrium model with a finite number of divisible and a finite number of indivisible commodities. In models with indivisibilities it is typically assumed that there is only one divisible good, which serves as money. The presence of money in the model is used to transfer the value of certain amounts of indivisible goods. For such economies with only one divisible commodity Danilov et al. showed the existence of a general equilibrium if the individual demands and supplies belong to a same class of discrete convexity. For economies with multiple divisible goods and money van der Laan et al. proved existence of a general equilibrium if the divisible goods are produced out of money using a linear production technology and no other producers are present in the model.     

Existence of equilibria with infinitely many commodities: Banach lattices reconsidered

The purpose of this paper is twofold. The first aim is to present an extension of the results on the existence of Walrasian equilibrium to the infinite dimensional setting. The result depends on two crucial assumptions. These are the compactness of the collection of feasible allocations and the non-emptiness of the interior of the production set. The proof is a direct generalization of Bewley's (1972) proof for the L_∞ case. The second purpose of this paper is to show that the recent result of Mas-Colell (1986) on the existence of equilibrium for exchange economies on Banach lattices can be obtained through an argument based on the result outlined above. That is, exchange economies on Banach lattices with ‘uniformly proper’ preferences behave as though they were production economies in which the production sets have non-empty interior.     

Theorems on the core of an economy with infinitely many commodities and consumers

It is known that the classical theorems of Grodal [Grodal, B., 1972. A second remark on the core of an atomless economy. Econometrica 40, 581–583] and Schmeidler [Schmeidler, D., 1972. A remark on the core of an atomless economy. Econometrica 40, 579–580] on the veto power of small coalitions in finite dimensional, atomless economies can be extended (with some minor modifications) to include the case of countably many commodities. This paper presents a further extension of these results to include the case of uncountably many commodities. We also extend Vind’s [Vind, K., 1972. A third remark on the core of an atomless economy. Econometrica 40, 585–586] classical theorem on the veto power of big coalitions in finite dimensional, atomless economies to include the case of an arbitrary number of commodities. In another result, we show that in the coalitional economy defined by an atomless individualistic model, core–Walras equivalence holds even if the commodity space is non-separable. The above-mentioned results are also valid for a differential information economy with a finite state space. We also extend Kannai’s [Kannai, Y., 1970. Continuity properties of the core of a market. Econometrica 38, 791–815] theorem on the continuity of the core of a finite dimensional, large economy to include the case of an arbitrary number of commodities. All of our results are applications of a lemma, that we prove here, about the set of aggregate alternatives available to a coalition. Throughout the paper, the commodity space is assumed to be an ordered Banach space which has an interior point in its positive cone.     

Existence of equilibria with infinitely many consumers and infinitely many commodities: A theorem based on models of commodity differentiation

This paper presents a general result on the existence of competitive equilibria in exchange economies in which consumers and commodities are both infinite in number. The result shows that — in this framework at least — the added assumptions necessary to handle models with infinitely many agents are remarkably similar to the additional restrictions needed when only finitely many commodities are available for trade.It is shown that the results apply, in a straightforward manner, to two of the common models of consumer choice when commodity differentiation is an important consideration.     

Equilibrium storage with multiple commodities

This paper introduces a multisector model of commodity markets with storage, where equilibrium is defined by profit maximization, arbitrage and market clearing conditions. We then solve for the decentralized equilibrium via a corresponding dynamic program. We also describe the dynamics of the model, establishing geometric ergodicity, a Law of Large Numbers and a Central Limit Theorem.     

Core equivalence with differentiated commodities

This paper presents improved core equivalence results for atomless economies with differentiated commodities in the framework of Ostroy and Zame (1994). Commodity bundles are elements of the space $M\left(K\right)$ of signed Borel measures on a compact space $K$ of commodity characteristics. Ostroy and Zame provide two sufficient conditions for core equivalence: It is sufficient that markets are “physically thick”, so that there are many suppliers of every commodity, or that markets are “economically thick”, so that consumers are sufficiently willing to substitute commodities with a similar composition for each other. The sufficient conditions in Ostroy and Zame (1994) all imply that there are “many more agents than commodities”, an idea of Aumann that was formalized and discussed in Tourky and Yannelis (2001) and Greinecker and Podczeck (2016). We generalize the framework in Ostroy and Zame (1994) and weaken their sufficient conditions to not imply the presence of “many more agents than commodities”. In particular, we drop the requirement that $K$ is metrizable from the basic model, the requirement of an uniform bound on endowments from the condition of “physically thick markets”, and the requirement that preferences are weak${}^1$-continuous from the condition of “economically thick markets”. Core equivalence still holds, showing that “many more agents than commodities” are not needed for core equivalence in models of commodity differentiation.     

Regular economies with ambiguity aversion

We consider a family of exchange economies with complete markets where consumers have multiprior preferences representing their ambiguity aversion. Under a linear independence assumption, we prove that regular economies are generic. Regular economies exhibit enjoyable properties: odd finite number of equilibrium prices, local constancy of this number, local differentiable selections of the equilibrium prices.Thus, even if ambiguity aversion is represented by non-differentiable multiprior preferences, economies retain generically the properties of the differentiable approach.     

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.     

Product choice with economies of scope

This paper develops a model in which two competing firms on a bounded line each sell two products. Production costs for each firm are lower the closer are its two products. It is shown that there may be anywhere from zero to three possible equilibrium configurations. Equilibrium may entail market segmentation, market interlacing or an intermediate case. The paper contributes to two bodies of literature: (i) Industrial organization. When the line is interpreted as a one-dimensional characteristic space, the model provides an appealing explanation of economies of scope in multi-product firms. (ii) Firm location theory. The model relaxes the unrealistic assumption made in spatial models that each firm has a single outlet and obtains significantly different results.     

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.     

Equilibria in markets with a Riesz space of commodities

We present a new proof of the existence of competitive equilibrium for an economy with an infinite dimensional space of commodities.     

Hedonic prices and composite commodities

In this paper we conjecture and, to an extent, prove that recently noted restrictions required for the logical coherence and empirical relevance of hedonic price models make these models no more general than traditional housing services models. In particular, intra-urban variation in hedonic prices may not be substantively related to market equilibration at all, and therefore is not evidence for the existence of housing sub-markets. Moreover, in the case of jointly produced housing characteristics, the hedonic price models are found to be less general than the traditional homogeneous housing services models.     

论商品质量特性

准确地评价、检验和监督商品的质量，有赖于对质量特征的正确理解和把握。由于消费的需求是多种多样的，所以反映商品质量的特性也是多种多样的，商品质量的适用性就是建立在质量特性基础之上的。     

Testing with many weak instruments

This paper establishes the asymptotic distributions of the likelihood ratio (LR), Anderson–Rubin (AR), and Lagrange multiplier (LM) test statistics under “many weak IV asymptotics.” These asymptotics are relevant when the number of IVs is large and the coefficients on the IVs are relatively small. The asymptotic results hold under the null and under suitable alternatives. Hence, power comparisons can be made.     

Resource allocation and public commodities

This paper characterizes Pareto efficient allocations by means of prices within a public-goods economy. The underlying notion of public commodities is a generalization covering private and pure public ones as extreme cases. The model uses as measure space of agents.     

Volatility transmission across currencies and commodities with US uncertainty measures

This paper uses the Multi-chain Markov Switching model (MCMS) conditioned on US uncertainty measures (VIX, VIX-oil and FSI) to examine the patterns of volatility transmission across the resource, major and safe haven currencies The results with and without the uncertainty variables generally identify three patterns of volatility transmission: interdependence, spillover and comovement. They reveal the dominance of interdependence over spillovers and comovements when the uncertainty variables are excluded, highlighting the significance of mutual reciprocity of individual market shocks over common shocks across the selected assets. Within portfolios of a two-variable framework (two variables representing two minimum variance portfolios (à la Markowitz), containing a weighted combination of the currencies and of the commodities, respectively), we find interdependence between the two portfolios with and without the VIX, a spillover from commodities to currencies in the case when the FSI is included and independence between the two portfolios in the case when the oil-VIX is accounted for. The implications of the results are important for the portfolio managers in selecting portfolios’ components during high oil volatility periods.