On the non-existence of equilibria in differentiated product models

It is sometimes suggested that the non-existence of an equilibrium in the Hotelling spatial model pointed out by d'Aspremont, Gabszewicz and Thisse (1979) is due to demand discontinuity. In this paper we first show that demand continuity is a natural property in general spatial or differential product markets. However, we also claim that the non-existence of an equilibrium is also a general property of these models. Further the assumption of no mill-price undercutting suggested by Eaton and Lipsey (1978) and Novshek (1980) is shown to be not sufficient to restore existence.     

On the non-existence of oligopolistic equilibria in differentiated products spaces

In a large class of product differentiation models á la Hotelling, the firms' payoffs in the game involving location in the differentiated products space exclusively depends on the distance to their neighbouring firms, rather than on the firms' locations proper. This leads to a degeneracy on the firms' strategy space. Using alternative equilibrium concepts, this is shown to be the reason for the non-existence of non-cooperative equilibria, especially if the firms' technologies are not identical.     

Environmental depletion,defensive consumption and negative externalities

This paper analyses economic dynamics in a context in which the production and consumption choices of economic agents generate environmental degradation. Agents can defend themselves from environmental degradation by increasing the production and consumption of output, which is assumed to be a (perfect) substitute for environmental quality. We consider the cases in which agents can coordinate their actions or not, and we show that if the dynamics is conditioned by negative externalities (so that there is no coordination), then a self-reinforcing mechanism may occur leading to production and consumption levels higher than the socially optimal ones. A complete analysis of the dynamics and of the welfare properties of the stationary states is provided.     

Existence of marginal pricing equilibria in economies with externalities and non-convexities

We consider a general equilibrium model with externalities and non-convexities in production. The consumption sets, the preferences of the consumers and the production possibilities are represented by set-valued mappings to take into account possibility of external effects. There is no convexity assumption on the correspondences of production. We propose a definition of the marginal pricing rule, which generalizes the one used in the model without externality and, which satisfies a continuity assumption with respect to the external effect.We prove the existence of general equilibria under assumptions which allow us to encompass together the works on economies with externalities and convex conditional production sets, and those on marginal pricing equilibria in economies without externalities. We provide examples to illustrate the definition of the marginal pricing rule and to show the difference with the standard case.     

The hybrid equilibria and core selection in exchange economies with externalities

This paper introduces a hybrid equilibrium concept that combines the elements of cooperative and non-cooperative behaviors in an exchange economy with externalities. For a fixed coalition structure (or a partition of traders), the hybrid equilibrium is a price and consumption bundle such that each coalition chooses a core solution from its budget set and the consumption bundles are feasible. It becomes the competitive equilibrium when the position is the finest, and it selects a core allocation when the partition is the coarsest. The paper provides sufficient conditions for the existence of a hybrid equilibrium for any coalition structure.     

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.     

Chaos and sector-specific externalities

Benhabib and Farmer [1996. Indeterminacy and sector specific externalities. Journal of Monetary Economics 37, 397–419] explore the possibility of local indeterminacy in a two-sector model with sector-specific externalities. They find that very small sector-specific externalities are sufficient for local indeterminacy. In this case, it is possible to construct sunspot equilibria where extrinsic uncertainty matters. In this paper, I provide a global analysis of their model revealing the existence of Euler equation branching. This branching allows for regime switching equilibria with cycles and chaotic behavior. These equilibria occur whether the “local dynamics” are determinate or indeterminate.     

Global analysis and economics IV : Finiteness and stability of equilibria with general consumption sets and production

Among other things a global version of the fundamental theorem of welfare economics is proved. One starts with a pure exchange economy with fixed total resources where hypotheses of differentiability, convexity, and monotonicity are made on the utility functions. Let be the set of price equilibria where the initial allocation coincides with the final one. Then the map which assigns to such a price equilibrium, the corresponding allocation is a diffeomorphism (a complete correspondence) between and the set of Pareto Optima.     

Groves mechanisms and communication externalities

We put forward a model of private goods with externalities. Agents derive benefit from communicating with each other. In order to communicate they need to operate on a common platform. Adopting new platforms is costly. We first provide an algorithm that determines the efficient outcome. Then we prove that no individually rational and feasible Groves mechanism exists. We provide sufficient conditions that determine when an individually rational Groves mechanism runs a deficit and we characterize the individually rational Groves mechanism that minimizes such deficit whenever it occurs. Moreover, for 2-agent economies, we single out the only feasible and symmetrical Groves mechanism that is not Pareto dominated by another strategy-proof, feasible and symmetrical mechanism.     

Vertical externalities and control of politicians

A major role of (repeated) elections is to create incentives for politicians to act in the interests of voters. This paper considers the disciplining role of elections in countries with either one or two levels of government. Simple retrospective voting strategies which are based on cut-off levels with respect to expenditure and tax rates are considered. It is shown that the power of voters is weakened if a second independent level of government is added. However, voters can partially reinforce their power by making politicians not only liable for their own policy, but also for the policy carried out at each other level of government. Received: June 30, 2000 / Accepted: April 4, 2001     

需求依赖价格的服务性商品在提前期的定价

研究了服务商根据消费者的预定情况给服务性商品的定价问题。模型建立在消费需求依赖商品价格及考虑违约两种情况的基础上，然后求出最优解，最后进行数值分析。     

The non-existence of a universal topological type space

The concept of types was introduced by Harsányi (1967–1968). In the literature there are two approaches for formalizing types, type spaces: the purely measurable and the topological models. In the former framework Heifetz and Samet (1998) showed that the universal type space exists and later Meier (2001) proved that it is complete. In this paper we examine the topological approach and conclude that there is no universal topological type space in the category of topological type spaces.     

The non-existence of smooth demand in general banach spaces

We study the questions of existence and smoothness of demand functions with an infinite number of commodities. The main result obtained, under some hypothesis, is: if a C¹ demand exists in a commodity space B, then B can be given an inner product structure. For example, if B is L_p, 1p∞, and if there exists a C¹ demand function defined on B then p must be 2. Another result is: if a demand function exists, defined for all prices p and income, then the commodity space must be reflexive. For example, if B is L_p and a demand function exists on B, defined for all prices and incomes then 1<p<∞. We also study the cases L_∞ and L₁ with weaker assumptions. We finish the paper proving that the demand function is always defined for a dense set of prices and convenient incomes.     

Risk externalities and the problem of wildfire risk

Homeowners living in the wildland–urban interface must decide whether or not to create a defensible space around their house in order to mitigate the risk of a wildfire destroying their home. Risk externalities complicate this decision; the risk that one homeowner faces depends on the risk mitigation decisions of neighboring homeowners. This paper models the problem as a game played between neighbors in a wildland–urban interface. The model explains why sub-optimal investment in defensible space is likely and provides insights into the likely effectiveness of programs designed to encourage households to increase their defensible space. Data from Boulder County, Colorado confirm that a household's defensible space decision depends on the defensible space outcomes at neighboring sites.     

Industry evolution and R&D externalities

R&D externalities can imply ranges of aggregate increasing returns to scale in R&D. As a consequence several equilibria can exist involving different numbers of firms and different R&D investment levels. In a theoretical model the equilibrium dynamics are analyzed, showing that cyclical fluctuations of the number of firms and R&D investment may be expected, and that the long-run equilibrium is highly sensitive to investors' initial beliefs. The model is tested empirically using a unique database comprising competing firms in various R&D races.     

The effects of public spending externalities

We conduct a positive analysis on the effects of ‘externalities’ produced by government spending. To this effect, we estimate, using U.S. data, an RBC model with two salient features. First, we allow government consumption to directly affect the marginal utility of consumption. Second, we allow public capital to shift the productivity of private factors. We provide an identification analysis that supports the strategy adopted for estimating the parameters governing these two channels. On one hand, private and government consumption are robustly estimated to be substitute goods. Because of substitutability, labor supply reacts little to a government consumption shock, so the estimated output multiplier is much lower than in models with separabilities. On the other hand, our results point towards public investment being ‘unproductive’.     

Delay,multiplicity, and non-existence of equilibrium in unanimity bargaining games

We consider a class of perfect information bargaining games with unanimity acceptance rule. The proposer and the order of responding players are determined by the state that evolves stochastically over time. The probability distribution of the state in the next period is determined jointly by the current state and the identity of the player who rejected the current proposal. This protocol encompasses a vast number of special cases studied in the literature. We show that subgame perfect equilibria in pure stationary strategies need not exist. When such equilibria do exist, they may exhibit delay. Limit equilibria as the players become infinitely patient need not be unique.     

Spatial externalities and agglomeration in a competitive industry

We introduce spatial spillovers as an externality in the production function of competitive firms operating within a finite spatial domain under adjustment costs. Spillovers may attenuate with distance and the overall externality could contain positive and negative components with the overall effect being positive. We show that when the spatial externality is not internalized by firms, spatial agglomerations may emerge endogenously in a competitive equilibrium. The result does not require increasing returns at the private or the social level, increasing marginal productivity of private capital with respect to the externality, or location advantages. In fact agglomerations may emerge with decreasing returns to scale, declining marginal productivity of private capital with respect to the externality, and no location advantage. The result depends on the interactions between the structures of production technology and spatial effects as shown in the paper. No agglomerations emerge at the social optimum when spillovers are internalized and diminishing returns both from the private and the social point of view prevail. Numerical experiments with Cobb–Douglas and CES technologies and an isoelastic demand confirm our theoretical predictions.     

Industrialization and environmental externalities in a Solow-type model

In this paper we examine the role played by environmental externalities in shaping the dynamics of an economy with two sectors (a farming sector and an industrial one), free inter-sectoral labor mobility and heterogeneous agents (workers/farmers and industrial entrepreneurs). We find that, in the presence of the environmental pressure of the economic activity of the industrial sector, the stability properties of the equilibria and their features in terms of environmental preservation, welfare outcomes and sectoral allocation of labor are sensitive to the level of carrying capacity. We show that an endogenous process of industrialization associated with a reduction in farmers/workers׳ welfare can emerge.     

The general equilibrium effects of congestion externalities

This is the second in a series of three articles on the topic of congestion externalities. We use an urban general-equilibrium model to compute two types of cities: the market-equilibrium city, in which congestion externalities occur, and the optimum city. The optimum city has a more dispersed distribution of employment, and a more concentrated distribution of residence. If the population of the city is fixed, the optimum pricing of transportation generates a per capita welfare gain of $3.78 per week. If the population of the city is endogenous, the internalization of congestion externalities causes the city to grow.