Equilibria with coordination failures

This paper extends the literature on equilibria with coordination failures to arbitrary convex sets of admissible prices. This makes it possible to address coordination failures for cases with price indexation or more general price linkages between commodities. We introduce a new equilibrium concept, called quantity constrained equilibrium (QCE), giving a unified treatment to all cases considered in the literature so far. At a QCE the expected trade opportunities on supply and demand are completely determined by a rationing vector satisfying that the prevailing price system maximizes the value of the rationing vector within the set of admissible prices. When the set of admissible prices is compact, we show the existence of a connected set of QCEs. This set connects two trivial no-trade equilibria, one with completely pessimistic expectations concerning supply opportunities and one with completely pessimistic expectations concerning demand opportunities. Moreover, the set contains for every commodity a generalized Drèze equilibrium, being a QCE at which for that commodity no binding trade opportunities on both supply and demand are expected, and also a generalized supply-constrained equilibrium at which no binding constraints on demand opportunities are expected and for at least one commodity also not on supply. We apply this main result to several special cases, and also discuss the case of an unbounded set of admissible prices.     

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.     

Equilibrium turnpike theory with time-separable utility

The purpose of this paper is to show that under reasonably general conditions intertemporal competitive equilibrium has a turnpike property. The model is general because it permits (1) time-variant, time-separable utility functions, (2) heterogeneous rates of discount across consumers, and (3) matching flatness in utilities and production possibilities. The results rely on bounded marginal utility for all consumers and aggregate stationarity of utilities of the set of most patient consumers. Under these assumptions, the neighborhood turnpike result holds with (1) and (2) because of the eventual unimportance of the impatient consumer. Matching flatness requires the use of a two-sided Liapounov function and the growth theoretic methods of McKenzie.     

Competitive General Equilibrium with network externalities

We identify sufficient conditions for existence of competitive equilibrium with network externalities and indivisibilities. Such combination of externalities and indivisibilities is present in many goods and services with network effects, and it makes existence of equilibrium non-trivial. We provide an existence theorem in a model with a measure space of consumers. Key conditions for existence are anonymity of network effects and dispersion in the economy’s income distribution.     

Learning and coordination with dispersed information

We analyse adaptive learning in a model of incomplete and dispersed information, with externalities and strategic interactions. We build on the framework proposed by Angeletos and Pavan (2007a) and extend it to a dynamic multi-period setting where agents need to learn to coordinate. We derive conditions under which adaptive learning obtains in such setting and show that, when actions are strategic substitutes, the information structure affects the speed of convergence: while more precise private information is beneficial, better public information has negative effects. We also show that adaptive learning dynamics converge to the Bayesian Nash equilibrium, which means that agents can learn to act strategically by relying only on observable (exogenous) information.     

具有价格干预的单产品流网络均衡

研究了由具有产能约束的多个相互竞争制造商以及面临随机需求和商品限制性价格上限的多个相互竞争零售商组成的供应链网络均衡问题。借助变分不等式理论,刻画了制造商、零售商以及消费者的最优行为,建立了供应链网络均衡模型。结合数值算例,分析了产能约束和限制性价格上限对网络均衡的影响。结果表明当政府对竞争市场实行限制性价格上限时,将造成消费市场中的商品短缺,并导致制造商和零售商的总利润减少;当存在产能限制时,将导致无价格限制的商品均衡价格更高以及消费市场中商品短缺量更大。     

具有价格干预的单产品流网络均衡

研究了由具有产能约束的多个相互竞争制造商以及面临随机需求和商品限制性价格上限的多个相互竞争零售商组成的供应链网络均衡问题.借助变分不等式理论,刻画了制造商、零售商以及消费者的最优行为,建立了供应链网络均衡模型.结合数值算例,分析了产能约束和限制性价格上限对网络均衡的影响.结果表明当政府对竞争市场实行限制性价格上限时,将造成消费市场中的商品短缺,并导致制造商和零售商的总利润减少;当存在产能限制时,将导致无价格限制的商品均衡价格更高以及消费市场中商品短缺量更大.     

具有质量竞争的供应链网络均衡研究

文章研究了具有质量竞争的供应链网络均衡问题。借助Lagrange对偶理论和有限维变分不等式理论,刻画了供应市场、零售市场及供应链网络的均衡条件,并利用投影算法对模型进行求解。结合算例,讨论了质量标准、质量成本系数对网络均衡的影响。数值结果表明:当质量标准较低时,制造商存在一个高于质量标准的均衡质量水平;当行业质量标准超过该均衡质量水平时,随着行业质量标准的提高,制造商利润会降低,而零售商利润会增加;随着行业质量标准的增加,供应链网络总利润呈现出先增后减规律,因此从供应链网络整体来看,行业质量标准应当适当,不能定得过高。同时,具有质量成本优势的制造商,会提高均衡质量水平,而具有质量成本劣势的制造商,会降低均衡质量水平,目的是增加产品质量差异以增加利润。     

Equilibrium search unemployment with explicit spatial frictions

Assuming that job search efficiency decreases with distance to jobs, workers' location in a city depends on spatial elements such as commuting costs and land prices and on labour elements such as wages and the matching technology. In the absence of moving costs, we show that there exists a unique equilibrium in which employed and unemployed workers are perfectly segregated but move at each employment transition. We investigate the interactions between the land and the labour market equilibrium and show under which condition they are interdependent. When relocation costs become positive, a new zone appears in which both the employed and the unemployed co-exist and are not mobile. We demonstrate that the size of this area goes continuously to zero when moving costs vanish. Finally, we endogeneize search effort, show that it negatively depends on distance to jobs and that long and short-term unemployed workers coexist and locate in different areas of the city.     

Optimal investment with vintage capital: Equilibrium distributions

The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with vintage capital, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time but also by age. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable of ages. A general method is developed to compute and study equilibrium points of a wide range of infinite dimensional, infinite horizon, optimal control problems. We apply the method to optimal investment with vintage capital, for a variety of data, deriving existence and uniqueness of equilibrium distribution, as well as analytic formulas for optimal controls and trajectories in the long run. The examples suggest that the same method can be applied to other economic problems displaying heterogeneity. This shows how effective the theoretical machinery of optimal control in infinite dimension is in computing explicitly equilibrium distributions. To this extent, the results of this work constitute a first crucial step towards a thorough understanding of the behavior of optimal paths in the long run.     

Equilibrium unemployment with outsourcing under labour market imperfections

We study the effects of international outsourcing on equilibrium unemployment in a high-wage economy with labour market imperfections. We demonstrate, consistent with empirical results, that the wage elasticity of labour demand is increasing as a function of outsourcing. Furthermore, we show that a production mode with more outsourcing reduces the negotiated wage in a high-wage country with labour market imperfections if the relative bargaining power of the labour union is sufficiently high. Under such circumstances outsourcing reduces equilibrium unemployment. Finally, we characterize the optimal production mode showing that stronger labour market imperfections induce a production mode with more outsourcing.     

Equilibrium existence in Tullock contests with incomplete information

We prove an existence theorem for pure strategy Bayesian Nash equilibrium in Tullock contests where the information endowment of each contender is described by a countable partition.     

Equilibrium asset pricing with Epstein-Zin and loss-averse investors

We study multi-period equilibrium asset pricing in an economy with Epstein-Zin (EZ-) agents whose preferences for consumption are represented by recursive utility and with loss averse (LA-) agents who derive additional utility of gains and losses and are averse to losses. We propose an equilibrium gain-loss ratio for stocks and show that the LA-agents are more (less) risk averse than the EZ-agents if their degree of loss aversion is higher (lower) than this ratio. When all the agents have unitary relative risk aversion degree and elasticity of intertemporal substitution, we prove the existence and uniqueness of the equilibrium and the market dominance of the EZ-agents in the long run. Finally, we extend our results to the case in which the LA-agents use probability weighting in their evaluation of gains and losses.     

Equilibrium in a market with intermediation is Walrasian

We show that a profit maximizing monopolistic intermediary may behave approximately like a Walrasian auctioneer by setting bid and ask prices nearly equal to Walrasian equilibrium prices. In our model agents choose to trade either through the intermediary or privately. Buyers (sellers) trading through the intermediary potentially trade immediately at the ask (bid) price, but sacrifice the spread as gains. A buyer or seller who trades privately shares all the gains to trade with this trading partner, but risks costly delay in finding a partner. We show that as the cost of delay vanishes, the equilibrium bid and ask prices converge to the Walrasian equilibrium prices. Received: 2 February 1996 / Accepted: 28 March 1997     

Temporary Equilibrium,Full Equilibrium,and Elasticity of Cost

The result by Morrison (1985) and Morrison and Schwarzt (1994) that there is an one-to-one relationship between the rate of economic capacity utilization and ratio of cost elasticities at the temporary and the full equilibrium has been instrumental in past studies on measuring economic capacity utilization and on adjusting indexes of productivity growth for temporary equilibrium. In this paper, dynamic duality and comparative dynamics are employed to assess the behavior of cost elasticity along an optimal path to the steady state. The analysis suggests that no a priori relationship exists between economic capacity utilization and elasticity of cost. The absence of an a priori relationship between these two economic variables implies that theoretical and empirical results based on past notions about the dynamic behavior of cost elasticity may have to be reconsidered.     

Equilibrium with endogenous technological changes: Theory and applications

In this paper we use a continuous-time general equilibrium model to analyze the problem of evaluating new irreversible investment opportunities that take the form of technological changes. Being a new technology, by definition, not perfectly correlated with the existing ones, the traditional spanning assumption invoked by the Real Option literature is not applicable in this context and a general equilibrium approach provides a more suitable framework. We analyze the problem of optimal consumption and investment of the representative individual in the context of the Cox Ingersoll and Ross (1895) model. We characterize the solution of the model under different assumptions about the utility function of the representative individual and about the parameters describing the technologies in the economy. A major result obtained from the model is the possibility of jumps in the equilibrium rate of return at the time in which technological changes are implemented. This is particularly interesting considering the fact that such jumps are obtained endogenously from the solution of the optimization problem and not imposed by “ad hoc” assumptions on the evolution of some variables.

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Riassunto Un modello di equilibrio economico generale in tempo continuo è utilizzato per analizzare il problema di valutare una nuova, irreversibile, opportunità di investimento che si presenta sotto forma di innovazione tecnologica. Essendo, per definizione, la nuova tecnologia non perfettamente correlata con le tecnologie esistenti, la letteratura delle “opzioni reali” non è applicabile ed un modello di equilibrio economico generale fornisce un ambiente più adatto allo studio del problema. Facendo uso del modello di Cox Ingersoll and Ross (1985) si fornisce una soluzione sotto diverse ipotesi riguardanti la struttura delle preferenze e la natura dell'innovazione tecnologica. Un interessante risultato è la derivazione di possibili discontinuità nel tasso di interesse di equilibrio in corrispondenza dell'adozione della nuova tecnologia.

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I would like to express my gratitude to Vasant Naik, David Peterson, Raman Uppal and especially Burton Hollifield and Tan Wang for helpful discussions and suggestions.     

Two-period supply chain coordination strategies with ambidextrous sustainable innovations

This study considers a manufacturer with ambidextrous sustainable innovation capability selling products in environmentally conscious market through an independent retailer in a two-period game setting. We design a two-period game theoretic and dyadic supply chain (SC) model considering exploitative and exploratory nature of environmental innovations. We study five different contract types, namely, wholesale price contract, vertical Nash game structure, cost sharing contract, revenue sharing contract and two-part tariff contract. We demonstrate the impact of market sensitivity towards sustainable innovation and cost parameters on optimal level of decision parameters. The equilibrium results reveal that a suitably designed two-part tariff contract can be used to achieve coordination in a fragmented SC. The equilibrium results assist managers to optimise the SC based on the two-period contract model. The results obtained in this study can help the decision-makers to take decisions on investment in the ambidextrous sustainable innovation under different types of contract structures.     

经济学中一般均衡存在性问题理论述评

本文对经济学中一般均衡理论进行了概述。文中主要介绍了Arrow—Debreu经济模型、均衡存在性定理、存在性涸题在无穷维商品空间上的扩展以及相关工作。     

Equilibrium and arbitrage in incomplete asset markets with fixed prices

At arbitrary prices of commodities and assets, fix-price equilibria exist under weak assumptions: endowments need not satisfy an interiority condition, utility functions need only satisfy a very weak monotonicity requirement, and the asset return matrix allows for redundant assets. Prices of assets may permit arbitrage. At equilibrium, though restricted through endogenously determined trading constraints, arbitrage possibilities may persist; in an example, an individual holds an arbitrage portfolio.