Locally stable price mechanisms

This paper develops necessary conditions for a price adjustment mechanism to achieve local stability at regular competitive equilibria. Two principal questions are: how closely must a locally stable mechanism be tailored to particular excess demand functions, and can any such mechanism be interpreted as a market adjustment process. In response to the first question, a variant of the (local) Newton method, termed the ‘orthogonal Newton method’ is shown to require, in a dimensional sense, the minimal information about excess demand functions. The second question is answered in the negative by proving the non-existence of any locally stable mechanism with the property that the price of any given commodity is not changed when its own market is in equilibrium. These and other results are obtained by using convergent price paths to generate a homotopy between the adjustment dictated by the mechanism and the actual direction of the equilibrium.     

Financial market equilibria with cumulative prospect theory

The paper first shows that financial market equilibria need not to exist if agents possess cumulative prospect theory preferences with piecewise-power value functions. This is due to the boundary behavior of the cumulative prospect theory value function, which might cause an infinite short-selling problem. But even when a non-negativity constraint on final wealth is added, non-existence can occur due to the non-convexity of CPT preferences, which might cause discontinuities in the agents’ demand functions. This latter observation also implies that concavification arguments which has been used in portfolio allocation problems with CPT preferences do not apply to our general equilibrium setting with finite many agents. Existence of equilibria is established when non-negativity constraints on final wealth are imposed and there is a continuum of agents in the market. However, if the original prospect theory is used instead of cumulative prospect theory, then other discontinuity problems can cause non-existence of market equilibria even in this case.     

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.     

Asymptotic stability of a general equilibrium under perfect and monopolistic competition

This study examines the asymptotic stability of a general equilibrium for an economy under perfect and monopolistic competition in which delays in a production process arise. Crucially, we find that the sufficient conditions for the stability of the equilibrium in each model differ markedly. For the stability of the equilibrium under perfect (monopolistic) competition, it is favorable that the slope of every demand curve is gradual (steep).     

Perturbed utility and general equilibrium analysis

We study general equilibrium theory of complete markets in an otherwise standard economy with each household having an additive perturbed utility function. Since this function represents a type of stochastic choice theory, the equilibrium of the corresponding economy is defined to be a price vector that makes its mean expected demand equal its mean endowment. We begin with a study of the economic meaning of this notion, by showing that at any given price vector, there always exists an economy with deterministic utilities whose mean demand is just the mean expected demand of our economy with additive perturbed utilities. We then show the existence of equilibrium, its Pareto inefficiency, and the upper hemi-continuity of the equilibrium set correspondence. Specializing to the case of regular economies, we finally demonstrate that almost every economy is regular and the equilibrium set correspondence in this regular case is continuous and locally constant.     

Existence of equilibrium in a differential game of spatial competition with advertising

We investigate a differential duopoly game with horizontal product differentiation and advertising efforts aimed at increasing market demand, to show that the standard approach to spatial competition fails to produce a pure-strategy price equilibrium in a dynamic game framework. This holds independently of the shape of the transportation cost function. Then, we introduce an endogenous cost associated with the choice of location and characterise the feedback equilibrium, identifying the necessary and sufficient condition for the existence of the pure-strategy (stationary) price equilibrium. The same condition is singled out for the static game where consumer population is constant. Finally, we show that the static game cannot be viewed as a special case of the dynamic one.     

The economics of property taxes and land values: The elasticity of supply of structures

Land values are explained by diminishing returns to a variable factor, structure, added to fixed land. The total cost minimizing structural density determined by land value, occurs where the marginal cost of increased density equals the average cost of structure plus land. Structural demand prices equal marginal costs in equilibrium determining land demands. A general equilibrium land price establishes the uses, prices and densities of structures. A simple method of calculating structure supply elasticity and the incidence and deadweight loss of property taxes is developed. Differing property tax rates are found to be efficient.     

Endowment-regarding preferences

We consider a general equilibrium model of pure exchange economies with endowment externalities. Consumers’ behaviors depend not only on their own consumption but also on the endowments of the other consumers. Applying the same method of analysis in Balasko (2015) about wealth concerns, we first show that almost all properties of equilibrium, including smooth equilibrium manifold and genericity of regular economies, can be directly extended to the economy where the demand function depends on the endowments of others and wealth of only one consumer. Next, we clarify the sufficient conditions under which those properties remain true in the economy with the most general form of endowment externalities. Finally, we generalize the above sufficient conditions to derive generic regularity results in the economy with both consumption and endowment externalities.     

Isomorphic multiclass spatial price and multimodal traffic network equilibrium models

In this paper, we first show that a multiclass spatial price equilibrium model can be formulated as an equivalent multimodal traffic network equilibrium model with special structure. This connection allows us to obtain, for the multiclass spatial price equilibrium model, in a routine manner, any information that is currently available in the well developed theory of the general multimodal network equilibrium model, and moreover, to strengthen a number of these results taking advantage of the special structure of the equivalent multimodal traffic network model.     

Product differentiation,monopolistic competition and city size

Traditionally, the formation of cities has been explained by such supply-side phenomena as scale economies in production or such demand-side phenomena as public goods. This paper presents an integrated demand and supply approach to the formation of cities in spatial economy. Demand considerations, in the form of consumer agglomeration economies (i.e., product variety), are presented as a major cause of urban agglomeration. On the supply side, scale economies are introduced. Both aspects are examined by using the Dixit-Stiglitz model of monopolistic competition to characterize the equilibrium and optimum city size. We also discuss a subsidy scheme that produces an equilibrium city size corresponding to a first-best optimum. Then we analyze the distribution of population in a system of two cities.     

Evaluating spatial service and layout efficiency of municipal Wi-Fi facilities for SmartCity planning: A case study of Wuhan city,China

This paper explores an approach to evaluating spatial service and layout efficiency of municipal Wi-Fi facilities for cyber infrastructure planning in the construction of a smart city. Based on the equilibrium principle that Wi-Fi services supply should meet the spatial demand for recreation, urgency, and security, two evaluation models were built. In the first model, the spatial service efficiency of Wi-Fi facilities is measured by a mean ratio of three types of demand spaces covered by Wi-Fi service. In the other model, spatial layout efficiency of each Wi-Fi facility is calculated by a demand load indicator - the sum of the three types of demand space's ratios of served quantity to the average quantity it should carry, and then assessed by relationship with its adjacent facilities. Corresponding statistical methods and analysis processes were also designed using the function modules found in ArcGIS software. The approach was applied to Wuhan city in 2016. After overlaying influence areas of 688 Wi-Fi facilities with demand spaces of 137 access points for recreation, 1200.99 km roads for urgency, 121.54 km² regions for security, the results show that there exists a spatial disequilibrium between supply and demand of Wi-Fi service in Wuhan due to lack of comprehensive planning. Specifically, there are 67 points, 700.76 km roads, and 42.59 km² regions of demand spaces covered by Wi-Fi service, with service efficiencies of 48.91%, 58.35%, and 35.04% respectively and an overall spatial service efficiency of 47.43%. Among all the Wi-Fi facilities, there are 481 carrying saturated demand, 3 straying from the centre of demand space, and 204 redundant. The overall spatial layout efficiency of Wi-Fi facilities is 43.01%. The conclusion is that the dense and massive redundant Wi-Fi facilities should be optimized, especially in the centre areas along the confluence of Yangtze and Han rivers and new Wi-Fi facilities supplemented in other ill-equipped areas. Since many metropolitan cities experience the same problem, this novel approach will find wide application in the future and offer improved evaluation strategies for researchers and policymakers.     

A new look at static spatial price equilibrium models

In this paper we propose a new view and more general formulations of static single commodity spatial equilibrium models, that lead to simpler and more efficient algorithms than those previously employed for solving models of this type. The proposed formulations incorporate general transportation networks and may be extended to allow for multiple commodities. Solution algorithms are suggested for the problem with multiple commodities, when there exists an equivalent optimization problem. We show that the multiple commodity problem may be cast in the form of a variational inequality, when there does not exist an equivalent optimization problem and propose algorithms to solve this version of the problem as well.     

Energy balance climate models and general equilibrium optimal mitigation policies

In a general equilibrium model of the world economy, we develop a two-dimensional energy balance climate model featuring heat diffusion and anthropogenic forcing driven by global fossil fuel use across the sphere of the Earth. This introduces an endogenous location dependent temperature function, driving spatial characteristics, in terms of location dependent damages resulting from local temperature anomalies into the standard climate-economy framework. We solve the social planner's problem and characterize the competitive equilibrium for two polar cases differentiated by the degree of market integration. We define optimal taxes on fossil fuel use and how they may implement the planning solution. Our results suggest that if the implementation of international transfers across latitudes is not possible then optimal taxes are in general spatially non-homogeneous and may be lower at poorer latitudes. The degree of spatial differentiation of optimal taxes depends on heat transportation. By employing the properties of the spatial model, we show by numerical simulations how the impact of thermal transport across latitudes on welfare can be studied.     

Uncertain availability,spatial location and regulation: An application to the airline industry

This paper presents an analysis of industries characterized by both uncertain availability and spatial location of the product. The analyis is applied to the US airline industry and is used to analyze the differential effect of price regulation on different markets and firms. From this analysis we obtain insights into which firms and markets may have benefited most from the deregulation of the industry in 1978. Previous works on the regulation of the airline industry implicitly assume that markets have the same demand structure. If airline services are of homogeneous quality, men we do not expect the unregulated solution to depend on demand structures. If on the other hand airline services vary in their quality component, then different markets may have different equilibrium price-quality combinations depending on the characteristics of demand. This paper explores the implication of different demand structures on the impact of (de)regulation.     

Estimating models of complex FDI: Are there third-country effects?

The recent general equilibrium theory of trade and multinationals emphasizes the importance of third countries and the complex integration strategies of multinationals. Little has been done to test this theory empirically. This paper attempts to rectify this situation by considering not only bilateral determinants, but also spatially weighted third-country determinants of foreign direct investment (FDI). Since the dependency among host markets is particularly related to multinationals’ trade between them, we use trade costs (distances) as spatial weights. Using panel data on U.S. industries and host countries observed over the 1989–1999 period, we estimate a “complex FDI” version of the knowledge-capital model of U.S. outward FDI by various recently developed spatial panel data generalized moments (GM) estimators. We find that third-country effects are significant, lending support to the existence of various modes of complex FDI.     

PRACTICAL TOOLS FOR POLICY ANALYSIS IN DSGE MODELS WITH MISSING SHOCKS

In this paper we analyze the propagation of shocks originating in sectors that are not present in a baseline dynamic stochastic general equilibrium (DSGE) model. Specifically, we proxy the missing sector through a small set of factors that feed into the structural shocks of the DSGE model to create correlated disturbances. We estimate the factor structure by either matching impulse responses of the augmented DSGE model to those generated by an auxiliary model or by using Bayesian techniques. We apply this methodology to track the effects of oil shocks and housing demand shocks in models without energy or housing sectors. Copyright © 2014 John Wiley & Sons, Ltd.     

General equilibrium analysis of the benefits of large transportation improvements

This paper considers three benefit measures of a large transportation improvement in a general equilibrium framework, i.e., the Marshall-Dupuit consumer's surplus, the. compensating variation, and the compensating surplus. First, we examine whether or not the measures can be reduced to the area to the left of a suitably defined transportation demand curve. Second, the measures are expressed as functions of various price and income elasticities which can be empirically estimated and we analyze factors affecting the magnitudes of the general equilibrium benefit measures. Third, the general equilibrium measures are compared with the partial equilibrium measures.     

Oligopolistic and competitive behavior of spatially separated markets

We examine the connection between Cournot oligopoly and perfect competition by showing that a fairly general oligopoly model with spatially separated markets generates a general spatial price equilibrium model as an extreme, limiting case. Our analysis depends crucially on the fact that the governing equilibrium conditions of both the oligopoly and the spatial price equilibrium problem can be formulated as variational inequalities.     

Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty

We provide new results for two-stage games in which firms make capacity investments when demand is uncertain, then, when demand is realized, compete in prices. We consider games with demand rationing schemes ranging from efficient to proportional rationing. In all cases, there is a subgame perfect equilibrium outcome coinciding with the outcome of the Cournot game with demand uncertainty if and only if (i) the fluctuation in absolute market size is small relative to the cost of capacity, or (ii) uncertainty is such that with high probability the market demand is very large and with the remaining probability the market demand is extremely small. Otherwise, equilibria involve mixed strategies. Further, we show under efficient rationing that condition (i) is sufficient for the unique equilibrium outcome to be an equilibrium outcome of the Cournot game with demand uncertainty.