On the complexity of simultaneous price-quantity adjustment processes

While the Walrasian price tâtonnement represents the traditional dynamic process in the general equilibrium context with and without production, Walras and other classics designed the process exclusively for pure exchange economies. In productive economies, the short-run output adjustment of existing firms and the entry/exit of firms should be modeled as well. So-called cross-dual processes which represent the classical approach to the dynamics of productive economies are discussed and extended. Complex motion can emerge in a discrete-time version of the original two-dimensional system when the aggregate demand function has a non-standard shape. A simultaneous process of price and short-run quantity adjustment with free entry and exit of competitive firms in a single market with a continuum of firms can generate closed orbits via a Hopf bifurcation when the slope of the demand function is positive at equilibrium. When the continuum economy is replaced by an economy with a finite number of firms, noisy limit cycles and complicated behavior can be observed.     

Risk-neutral economy and zero price of risk

The paper investigates the equilibrium in an economy in which all participants are indifferent to risk. The mechanism of asset and derivative pricing in such economy is identified. It is shown that no economy in equilibrium with stochastic interest rates can be simultaneously risk-neutral and have zero market price of risk. On the other hand, there exist equilibrium economies with risk-averse participants and zero prices of risk.     

Continuity and Uniqueness of Equilibria for Linear Exchange Economies

The purpose of this paper is to study the continuity and uniqueness properties of equilibria for linear exchange economies. We characterize the sets of utility vectors and initial endowments for which the equilibrium price is unique and respectively the set for which the equilibrium allocation is unique. We show that the equilibrium allocation correspondence is continuous with respect to the initial endowments and we characterize the set of full measure where the equilibrium allocation correspondence with respect to the initial endowments and utility vectors is continuous.     

Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

Exchanges and measures of risks

When investors or reinsurers measure economic risk in monetary terms, they operate as though utility were transferable. A main purpose of this paper is to show that transferability largely facilitates attainment, analysis, computation and modelling of equilibrium in exchange economies. To wit, under reasonable and weak assumptions, it is shown that duality delivers an equilibrium price, and that simple bilateral barters may ensure market clearing. If, however, underlying beliefs about future states are strictly incompatible, equilibrium cannot generally exist.     

Split equilibrium problems for related games and applications to economic theory

ABSTRACT

In this paper we introduce the concept of split Nash equilibrium problems associated with two related noncooperative strategic games. Then we apply the Fan-KKM theorem to prove the existence of solutions to split Nash equilibrium problems of related noncooperative strategic games, in which the strategy sets of the players are nonempty closed and convex subsets in Banach spaces. As an application of this existence to economics, an example is provided that studies the existence of split Nash equilibrium of utilities of two related economies. As applications, we study the existence of split Nash equilibrium in the dual (playing twice) extended Bertrand duopoly model of price competition.     

Nonlinear Prices in Nonconvex Economies with Classical Pareto and Strong Pareto Optimal Allocations

The paper is devoted to applications of modern tools of variational analysis to equilibrium models of welfare economics involving generally nonconvex economies with infinite-dimensional commodity spaces. The main results relate to the so-called generalized/extended second welfare theorem ensuring an equilibrium price support at Pareto optimal allocations. Based on advanced tools of variational analysis and generalized differentiation, we establish refined results of this type with the novel usage of nonlinear prices at the three types to optimal allocations: weak Pareto, Pareto, and strong Pareto. We pay a special attention to strong Pareto optimal allocations in economies with ordering commodity spaces showing that enhanced results for them do not require, in contrast to the classical types of weak Pareto and Pareto optimality, any net demand qualification conditions. Mathematics Subject Classifications (2000): 91B50, 49J52 Dedicated to the memory of Yuri Abramovich     

An investigation of stock price dynamics in emerging markets

The emergence of stock markets in former centrally planned economies poses a significant problem to financial economists and policy makers in that price movements in these markets are not well explained by conventional capital theory. The opening of stock markets brings about a new equilibrium value P̂ for the firm. Shares are floated on an estimate of P̂, and buyers of these shares and individuals trading in the secondary market are also obliged to do so on the basis of their estimates of this magnitude. At any time, the market price of the firm's shares then reflects the market's best guess of what its value would be in the new equilibrium, and information on which to calculate estimates become more readily available as the stock market matures. This paper presents a stochastic price model which takes all of these factors into consideration. The model also provides a theoretical foundation underlying the pronounced trends of prices in emerging stock markets, and explains why they appear to be so volatile. © 1998 John Wiley & Sons, Ltd.     

Semi-Lagrangean approach for price discovery in markets with non-convexities

From standard economic theory, the market clearing price for a commodity is set where the demand and supply curves intersect. Convexity is a property that economic models require for a competitive equilibrium, which is efficient and well-behaved and provides equilibrium prices. However, some markets present non-convexities due to their cost structure or due to some operational constraints that need to be addressed. This is the case for electricity markets where the electricity producers incur costs for shutting down a generating unit and then bringing it back on. Non-convex cost structures can be a challenge for the price discovery process, since the supply and demand curves may not intersect, or if they intersect, the price found may not be high enough to cover the total cost of production. We apply a Semi-Lagrangean approach to find a price that can be applied in the electricity pool markets where a central system operator decides who produces and how much they should produce. By applying the model to an example from the literature, we found prices that are high enough to cover the producer’s total costs, and follows the optimal solution for achieving mining cost in production. The prices are an alternative solution to the price discovery problem in non-convexities economies; in addition, they provide nonnegative profits to all the generators without the use of side-payments or up-lifts, and closes the integrality gap.     

On a New Class of Systems of Generalized Quasi-Variational Inequalities

We introduce new types of systems of generalized quasi-variational inequalities and we prove the existence of the solutions by using results of pair equilibrium existence for free abstract economies. We consider the fuzzy models and we also introduce the random free abstract economy and the random equilibrium pair. The existence of the solutions for the systems of quasi-variational inequalities comes as consequences of the existence of equilibrium pairs for the considered free abstract economies.     

A Fixed-Point Theorem and Equilibria of Abstract Economies with Weakly Upper Semicontinuous Set-Valued Maps

The main purpose of this paper is to introduce the notion of weakly upper semicontinuous set-valued maps and to establish a new fixed-point theorem. The set-valued maps with an approximating upper semicontinuous selection property are also defined. Next, we use our fixed-point result to obtain equilibrium existence in abstract economies with two constraints, which provide a natural scenario for potential applications of our approach to general equilibrium theory. In this regard, we set models of economies with asymmetric informed agents, who are able to improve their initial information through market signals. These economies offer examples in which the informational feasibility requirement represents an additional constraint.     

有偿付约束的无限期资产经济均衡的存在性

本文通过一个简单的模型证明了有偿付约束的无限期资产经济均衡存在性,所用条件与已有文献相比更加简明．这一研究可望为我们今后研究无限期经济提供方向：同时也可以更好地理解偿付约束（或保证金制度）在资本市场中的作用     

带交易费用的无限期资产市场预期均衡的存在性

本文通过一个简单的模型证明了带交易费用的无限期资产经济预期均衡存在性，所用条件与已有文献相比更加简明     

带交易费用的可数无限态两期经济的均衡存在性

To some two-period economies with countable infinite state spaces,the existence of expectation equilibrium of real asset economies with transaction costs is given. This work extends the researches of Zame in 1993.     

EXISTENCE OF EXPECTATION EQUILIBRIUM OF REAL ASSET ECONOMIES WITH TRANSACTION COSTS

Abstract. To some two period economies with countable infinite state spaces, the existence of expectation equilibrium of real asset economies with transaction costs is given. This work extends the researches of Zame in 1993.     

On the uniqueness of Bertrand equilibrium

We introduce product differentiation in the model of price competition with strictly convex costs in which firms have to supply all of the forthcoming demand. We find that although a continuum of equilibria exists in a homogeneous product market, the competitive price equilibrium is the only robust one. Specifically, as long as the equilibrium correspondence is nonempty, the equilibrium price converges to the competitive price when the degree of product differentiation shrinks to zero.     

基于最优让步均衡协调策略的供应链差价补偿机制研究

制造商为了激励零售商订购更多数量的产品,会在产品零售价下调时提供给零售商一定的补偿,如何制定最优补偿机制是提高供应链收益的关键问题.为此,建立了两阶段销售差价补偿机制下制造商与零售商的博弈模型,分析了纳什均衡解和Stackelberg均衡解下制造商对零售商的差价补偿机制的决策行为,导出了在最优让步均衡策略下差价补偿机制...     

Incomplete financial markets model with nominal assets: Variational approach

We deal with the analysis of the general equilibrium model with incomplete financial markets and nominal assets. We assume that there are 2 periods of time, say today and tomorrow. We define a consumption, portfolio holding, commodity and asset price vector as an equilibrium vector associated with a given economy if at those prices and economies households maximize utility under a budget constraints and markets clear. While the path breaking proofs of existence by Cass [6] and Werner [25] use a fixed point argument, we provide an independent existence proof in terms of variational inequalities (about the variational approach for the analysis of general equilibrium models see for example [9] and [10]). The analysis presented in this paper indicates that the variational inequality approach promises to be applicable in many specifications of the incomplete market model.     

Gradients,subgradients, and economic equilibria

Two concepts of differentiability are shown to underlie two concepts of equilibrium for nonatomic economies. The weaker concept of subdifferentiability corresponds to Walrasian equilibrium and the stronger concept of Fréchet differentiability to product-exhaustion. Product-exhaustion is shown to be equivalent to a definition of economic equilibrium in terms of the rationality of price-taking.     

价格歧视下四种市场的均衡产量和价格

在线性需求函数条件下,对1个垄断厂商市场情形用微分法,对,1个厂商市场情形用完全信息静态博弈的方法,对实施二度价格歧视时均衡产量和价格的确定进行了研究,给出了市场均衡歧视产量,均衡歧视价格和均衡歧视总收益的统一的计算公式,并分析了其性质.