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.     

On the structure of the set of fixed price equilibria

Working in the framework suggested by Drèze, this paper studies the number of fixed price equilibria and their continuity with respect to the price system. In an exchange economy, the concept of a rationing scheme is introduced, which specifies how shortages are shared among agents. For given utility functions and a given rationing scheme, under standard assumptions, an existence theorem is recalled, and it is shown that the graph of the equilibrium correspondence, when prices and initial endowments vary, is a piecewise continuously differentiable manifold. Moreover, generically, the number of equilibria for an economy, at given prices, is finite and the set of equilibria varies continuously with the price system and the initial endowments.     

Constrained suboptimality when prices are non-competitive

The paper addresses the following question: how efficient is the market system in allocating resources if trade takes place at prices that are not competitive? Even though there are many partial answers to this question, an answer that stands comparison to the rigor by which the first and second welfare theorems are derived is lacking. We first prove a “Folk Theorem” on the generic suboptimality of equilibria at non-competitive prices. The more interesting problem is whether equilibria are constrained optimal, i.e. efficient relative to all allocations that are consistent with prices at which trade takes place. We discuss an optimality notion due to Bénassy, and argue that this notion admits no general conclusions. We then turn to the notion of p-optimality and give a necessary condition, called the separating property, for constrained optimality: each constrained household should be constrained in each constrained market. If the number of commodities is less than or equal to two, the case usually treated in the textbook, then this necessary condition is also sufficient. In that case equilibria are constrained optimal. When there are three or more commodities, two or more constrained households, and two or more constrained markets, this necessary condition is typically not sufficient and equilibria are generically constrained suboptimal.     

Existence and uniqueness of price equilibria: Theory and application to discrete choice models

Continuous excess demand systems which do not obey homogeneity of degree zero or Walras's Law are proved to have equilibria if they satisfy certain mild regularity conditions when prices tend to the extremes of a price domain which need not be closed or bounded. A straightforward generalization of Brouwer's theorem is used. Systems also obeying a weak balance condition (of which Walras's Law is a special case) and homogeneity are treated as corollaries to the main theorem. Sufficient conditions for differentiable excess demand systems to have unique equilibria are developed in three separate theorems. The usefulness of these general existence and uniqueness theorems is demonstrated by applying them to three specific models constructed from discrete choice theory: (1) a competitive rental housing market, (2) a regulated rental housing market with fixed rents and rationing and (3) an interregional labor market in which laborers can choose among regions for employment (or voluntary unemployment) as well as the work hours they will supply.     

Space–time economies under free mobility:: Competitive Equilibria and efficiency

In this paper, a space–time sequence economy with money, storage and transaction /transportation costs of mobile commodities will be considered. Conditions on technologies and households′ characteristics will be derived to establish the existence of competitive equilibria under locational choice. The notion of Pareto efficiency under costly trading will be discussed and the question of (in-)efficiency of equilibria examined using a separation theorem. The model extends earlier work of the author [Karmann (1981), Karmann (1982)] and others [see Schweizer et al. (1976), Castello-Ruiz (1978)] to include time and extends also the model in Kurz (1974) to include space.     

Existence of equilibria in economies with externalities and non-convexities in an infinite-dimensional commodity space

We prove an equilibrium existence theorem for economies with externalities, general types of non-convexities in the production sector, and infinitely many commodities. The consumption sets, the preferences of the consumers, and the production possibilities are represented by set-valued mappings to take into account the external effects. The firms set their prices according to general pricing rules which are supposed to have bounded losses and may depend upon the actions of the other economic agents. The commodity space is L_∞(M,M,μ), the space of all μ-essentially bounded M-measurable functions on M.As for our existence result, we consider the framework of Bewley (1972). However, there are four major problems in using this technique. To overcome two of these difficulties, we impose strong lower hemi-continuity assumptions upon the economies. The remaining problems are removed when the finite economies are large enough.Our model encompasses previous works on the existence of general equilibria when there are externalities and non-convexities but the commodity space is finite dimensional and those on general equilibria in non-convex economies with infinitely many commodities when no external effect is taken into account.     

Real indeterminacy of equilibria and manipulability

In this paper, we analyze the indeterminacy of equilibria in financial markets and propose a selection mechanism. We suggest that there is one equilibrium that prevails over the others, as a result of the market power of the agents that some states of nature become monopolists of certain commodities. Given a financial assets model, we define a price game and show the existence of mixed strategies equilibria. Then we purify these equilibria by considering a price game with incomplete information.     

Price and interest rate dynamics induced by multiperiod contracts

This paper suggests a mechanism by which nominal price rigidities can create a transmission mechanism for monetary shocks through relative price distortions in an economy with both spot and contract markets. The globally unique equilibrium time path of interest rates and prices following an impulse shock to the money supply is characterized. The model predicts that prices and interest rates cycle around the new steady state, with real interest rates initially falling and prices overshooting in the case of a positive shock. The volatility of spot prices and interest rates exceeds that of contract prices.     

Price Equilibria in Pure Strategies for Homogeneous Oligopoly

For a homogeneous product oligopoly market, possibilities for pure strategy Nash equilibria in prices are studied. Consumers, who each nonstrategically purchase one unit up to a common reservation price, are hypothesized to be more concerned with large price differences (and therefore buy from the cheapest firm) than slightly different prices. For the duopoly case, existence, uniqueness, and characterization results are provided. Linear examples are given with 2 and n firms.     

Equilibrium in incomplete markets: I : A basic model of generic existence

This paper demonstrates the generic existence of general equilibria in incomplete markets. Our economy is a model of two periods, with uncertainty over the state of nature to be revealed in the second period. Securities are claims to commodity bundles in the second period that are contingent on the state of nature, and are insufficient in number to span all state contingent claims to value, regardless of the announced spot commodity prices. Under smooth preference assumptions, equilibria exist except for an exceptional set of endowments and securities, a closed set of measure zero. The paper includes partial results for fixed securities, showing the existence of equilibria except for an exceptional set of endowments.     

Multiproduct price competition with heterogeneous consumers and nonconvex costs

This paper extends the oligopolistic model of price competition to environments with multiple goods, heterogeneous consumers, and arbitrary continuous cost functions. A Nash equilibrium in mixed strategies with an endogenous sharing rule is proven to exist. It is also shown that, in environments with fixed costs and constant marginal costs, all (symmetric and asymmetric) equilibria exhibit price dispersion across stores. Furthermore, the paper identifies scenarios in which prices will necessarily be random. In these markets, stores keep each other guessing because, given the fixed costs, they would incur a loss if their price strategies were anticipated and beaten by competitors. This is interpreted as an important economic feature that is possibly behind random price promotions such as weekly specials.     

Spatial market equilibria with flow-dependent supply and demand: The single commodity case

Existence and uniqueness of spatial price equilibria are analyzed for a single commodity market network in which supply and demand levels are allowed to depend on commodity flows as well as market prices. This framework makes possible the explicit incorporation of flow-dependent shipment costs into market supply and demand functions. Moreover, since many quantity signals are also expressible as flow-dependent variables, it is possible to incorporate a number of recent models of supply and demand behavior which allow for quantity signals as well as price signals. In this context, the main result of the paper is to establish the existence of spatial price equilibria for such market networks under quite general conditions. In addition, certain uniqueness results are established for the case of arc-generated networks.     

Pure and randomized equilibria in the stochastic von Neumann–Gale model

The paper examines the problem of the existence of equilibrium for the stochastic analogue of the von Neumann–Gale model of economic growth. The mathematical framework of the model is a theory of set-valued random dynamical systems defined by positive stochastic operators with certain properties of convexity and homogeneity. Existence theorems for equilibria in such systems may be regarded as generalizations of the Perron–Frobenius theorem on eigenvalues and eigenvectors of positive matrices. The known results of this kind are obtained under rather restrictive assumptions. We show that these assumptions can be substantially relaxed if one allows for randomization. The main result of the paper is an existence theorem for randomized equilibria. Some special cases (models defined by positive matrices) are considered in which the existence of pure equilibria can be established.     

Note on the optimality of unemployment equilibria

An equilibrium concept for an economy with rigid prices has been given by Drèze (1975). He formulated a model where for some commodity, either the supplies or the demands are rationed. In this note we discuss ‘unemployment equilibria’, i.e., fixed price equilibria for which the quantity rationing affects the supplies only. It can be proved that there exists a set of unemployment equilibria. Therefore we consider the question whether it is possible to characterize the set of undominated unemployment equilibria.     

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.     

Stationary Markov equilibria on a non-compact self-justified set

The existence of stationary processes of temporary equilibria is examined in an OLG model, where there are finitely many commodities and consumers in each period, and endowments profiles and expectations profiles are subject to stochastic shocks. A state space is taken as the set of all payoff-relevant variables, and dynamics of the economy is captured as a stochastic process in the state space. In our model, however, the state space does not necessarily admit a compact-truncation consistent with the intertemporal restrictions because distributions over expectations profiles may have non-compact supports. As shown in Duffie et al. [Duffie, D., Geanakoplos, J., Mas-Colell, A., McLennan, A., 1994. Stationary Markov equilibria. Econometrica 62, 745–781), such a compact-truncation, called a self-justified set, is essential for the existence of stationary Markov equilibria. We extend their existence theorem so as to be applicable to our model.     

涨跌停板制度对期货市场价格发现过程及波动性的影响--基于上海期货交易所的实证研究

本文通过检验在出现涨跌停板之后一个交易日的期货价格及其波动性的变化情况，研究了涨跌停板制度对上海期货交易所期货价格变动的影响。研究结果显示，对不同的期货品种，涨跌停板制度的影响存在一定的差异，但总体而言，涨跌停板制度并没有起到防范价格过度反应和降低市场波动性的作用。相反，在一定程度上延缓了期货市场价格发现功能的发挥，增大了市场的波动性。     

Learning quality through prices and word‐of‐mouth communication

This paper studies the effect of word‐of‐mouth communication on the optimal pricing strategy for new experience goods. I consider a dynamic monopoly model with asymmetric information about product quality, in which consumers learn in equilibrium from both prices and other consumers. The main result is that word‐of‐mouth communication is essential for the existence of separating equilibria, wherein the high‐quality monopolist signals high quality through a low introductory price (lower than the monopoly price), and the low‐quality one charges the monopoly price. The intuition is simple: low prices are costly, and will only be used by firms confident enough that increased experimentation (and therefore communication among consumers) will yield good news about quality and increased future profits. Additional results are the following: for the high‐quality seller, the expected price (quantity) is increasing (decreasing) over time; whereas for the low‐quality one, the opposite is true. Moreover, signaling becomes more difficult when consumers pay less attention to their peers' reports and more attention to past prices. Finally, word‐of‐mouth communication improves consumer welfare.     

Dividend paying assets,the unit root property,and suboptimality

We consider the stationary equilibria of one good overlapping generations (OLG) economies with a sequence of possibly incomplete asset markets and prove two results. First, we show that if some asset always pays a nonnegative dividend, then its price changes sign across states if and only if the Perron root of every agent’s matrix of intertemporal rates of substitution exceeds one. Second, we provide sufficient conditions in terms of dividends and asset prices such that, keeping asset prices fixed, a conditionally Pareto improving allocation is induced by a stationary reassignment of a single asset. When taken together the results show that when for some agent the Perron root exceeds one, the existence of an asset that pays a strictly positive dividend in every state is sufficient to induce an improvement.     

Determinants of Relative Sectoral Prices: The Role of Demographic Change

Demographic change raises demand for non‐tradable old‐age related services relative to tradable commodities. This demand shift increases the relative price of non‐tradables and thereby causes real exchange rates to appreciate. We claim that the change in demand affects prices via imperfect intersectoral factor mobility. Using a sample of 15 OECD countries, we estimate a robust increase of relative prices. According to our main estimate, up to one fifth of the average increase in relative prices between 1970 and 2009 can be attributed to population ageing. Further findings confirm the relevance of imperfect factor mobility: Countries with more rigid labour markets experience stronger price effects.