Excess demand functions, equilibrium prices, and existence of equilibrium

Summary. For continuous aggregate excess demand functions of economies, the existing literature (e.g. Sonnenschein (1972, 1973), Mantel (1974), Debreu (1974), Mas-Colell (1977), etc.) achieves a complete characterization only when the functions are defined on special subsets of positive prices. In this paper, we allow the functions to be defined on a larger class of price sets, (allowing, for example the closed unit simplex, including its boundary). Besides characterizing excess demands for a larger class of economies, our extension provides a useful tool for proving other results. It allows us to characterize the equilibrium price set for a larger class of economies. It also permits extending Uzawa's observation (1962), by showing that Brouwer's Fixed-Point Theorem is implied by the Arrow-Debreu Equilibrium Existence Theorem (1954, Theorem I). Received: October 18, 1995; revised version June 28, 1996     

Nonstandard foundations of equilibrium search models

We develop an equilibrium sequential search model which includes most of the literature as special cases. In particular, the model can accommodate heterogeneity in buyers’ search costs and demand functions and firms’ cost functions, with general demand and cost functions. We identify conditions which ensure existence of equilibrium in pure strategies, utilizing recent progress in the theory of large games by Khan and Sun. These conditions elucidate the essential structure of equilibrium search models. Although we focus on sequential search, our methodology can be used for other classes of equilibrium search models as well.     

The empirical content of Cournot competition

We consider the testable implications of the Cournot model of market competition. Our approach is nonparametric in the sense that we abstain from imposing any functional specification on market demand and firm cost functions. We derive necessary and sufficient conditions for (reduced form) equilibrium market price and quantity functions to be consistent with the Cournot model. In addition, we present identification results for the corresponding inverse market demand function and the firm cost functions. Finally, we use our approach to derive testable restrictions for the models of perfect competition, collusion and conjectural variations. This identifies the conditions under which these different models are empirically distinguishable from the Cournot model. We also investigate empirical issues (measurement error and omitted variables) related to bringing our testable restrictions to data.     

Excess demand functions with incomplete markets—a global result

The purpose of this paper is to give a global characterization of excess demand functions in a two-period exchange economy with incomplete real asset markets. We show that continuity, homogeneity and Walras’ law characterize the aggregate excess demand functions on any compact price set which maintains the dimension of the budget set.     

Differentiable Technology,the Curvature of the Profit Function,and the Response of Supply to Own-Price Changes

The author establishes a property of supply for a competitive firm: Assuming differentiability of the production frontier, linearly independent price vectors have disjoint image sets under the supply mapping. This property supports the main results. First, the author drew a simple proof of McFadden's proposition that differentiability of the production frontier is necessary and sufficient for strict quasiconvexity of the profit function. This proposition rules out linearity of the profit function on any subset of price domain, in turn ruling out supply and input- demand functions that are constant and have zero values for all price effects. Second, for discrete price changes, own-price effects in supply are strictly positive, assuming a differentiable technology. In this context, strict convexity of the production set is irrelevant. The author indicates implications for cost and demand theory.     

Errors of aggregation and errors of specification in a consumer demand model: a theoretical note

Abstract .  Consumer demand models based on the concept of a representative or average consumer suffer from aggregation error. Misspecification of the underlying micro utility-maximizing model, which is virtually inevitable, also results in error. This note provides a theoretical investigation of the relationship between the two types of error. Misspecified expenditure support functions for demand systems at the micro level induce the same misspecified structure in the corresponding expenditure functions at the macro level, and the errors at the two levels are shown to be of similar order.     

Excess demand functions when new assets are introduced

We demonstrate that information on the aggregate excess demand function of an incomplete real asset market economy is not helpful toward predicting the equilibrium of a new economy to which unredundant assets are added. An innovation of assets can completely change the aggregate excess demand functions.     

A reformulation of the theory of demand by compensated demand functions

We present a formal approach to consumer demand by compensated demand functions. In accordance with the integrability theory or with the theory of revealed preference, we do not require the existence of a utility function, but we do assume certain hypotheses concerning functions describing rational behavior. In view of their properties, these functions can be interpreted as compensated demand functions. According to traditional neoclassical consumer theory, Shephard's lemma and the symmetry and negative semidefiniteness of the Slutsky-Hicks matrix can be shown. We shall also see that a convex, continuous, and monotonic preference ordering, which is representable by income compensation functions, can be introduced. It can also be shown that the existence of a compensated equilibrium can be derived within this approach by compensated demand functions. In order to obtain the existence of a compensated equilibrium under less stringent conditions we finally generalize the axioms assuming that a compensated demand correspondence is given.     

Effective global regularity and empirical modelling of direct, inverse, and mixed demand systems

Abstract .  This paper utilizes the notion of 'effective global regularity' and the intuition stemming from Cooper and McLaren (1996)'s General Exponential Form to develop a family of 'composite' (product and ratio) direct, inverse and mixed demand systems. Apart from having larger regularity regions, the resulting specifications are also of potentially arbitrary rank, which can better approximate non-linear Engel curves. We also make extensive use of duality theory and a numerical inversion estimation method to rectify the endogeneity problem encountered in the estimation of the mixed demand systems. We illustrate the techniques by estimating different types of demand systems for Japanese quarterly meat and fish consumption.     

Exit, sunk costs and the selection of firms

Summary. This paper aims to identify the cost characteristics of exiting firms whenever firms are playing an infinite horizon supergame with time-invariant cost and demand functions. With more than two firms, the problem of which firms exit is quite similar to a coalition formation one. Solving this coalition formation problem, we obtain that the exiting firms are those with higher average cost functions whenever reentry is costless while, whenever reentry is unprofitable, the exiting firms are those with lower marginal (and possibly average) cost functions. Since reentry costs are typically sunk, our analysis points out that the presence of sunk costs affects not only the size (as it is well known) but also the composition of the industry. Received: April 5, 1995; revised version: January 28, 1998     

Characterizing C2 aggregate excess demand functions

Summary. We integrate and sharpen two characterizations of aggregate excess demand functions: we obtain Mas-Colell's (1977) equilibrium invariance, and strengthen Geanakoplos' (1984) weakly concave utility functions to strictly concave ones. Our proofs modify and extend Geanakoplos' utility-construction. We note two applications: a sharper characterization of equilibrium price sets (cf. Mas-Colell (1977)), and a basis for the studies of computable economies (Richter and Wong (1996)). Received: July 29, 1996; revised version: February 20, 1997     

Dynamic properties of a Cournot–Bertrand duopoly game with differentiated products

In this paper we consider a Cournot–Bertrand duopoly model with linear demand and cost functions and with product differentiation. We propose a dynamic framework for the study of the stability properties of this kind of mixed oligopoly game, a rather neglected topic in the existing literature despite its relevance. In particular, in this paper we highlight the role of best response dynamics and of an adaptive adjustment mechanism for the stability of the equilibrium.     

Indirect addilog translation of indirect utility functions

Abstract .  The difficulty of specifying a set of consumer demand equations that can simultaneously display compatibility with rational economic behaviour (regularity) and have the capacity to represent a comprehensive spectrum of consumer behaviour (flexibility) is well known. A variety of approaches have been investigated in the literature, but scope for substantial improvement remains. The approach of this paper is to start from indirect utility functions producing globally regular, if inflexible, systems and to improve flexibility by adding parameters through a device termed 'indirect addilog translation.'     

Consumer preferences,the demand for Divisia money,and the welfare costs of inflation

This paper uses neoclassical demand theory to calculate the welfare costs of inflation. It considers the demand interactions between money, consumption goods, and leisure, relaxes the assumption of fixed consumer preferences, and addresses the inter-related problems of estimation of money demand functions, instability of money demand relations, and monetary aggregation. It makes full use of the relevant economic theory and econometrics and generates inference in terms of long-run welfare costs of inflation that is internally consistent with the data and models used.     

Disentangling the effects of process and product innovation on cost and demand

ABSTRACT

We explore in this note different structural models of the impact of process and product innovation on firms' demand and production cost functions. We find that the introduction of process and product innovations affects them differently as could be expected. Both product and process innovation shift forward the demand for the products of the firm. Process innovation reduces production marginal cost, but not always. A possibility, that we cannot prove or reject with the current specification of our models and available data, is that process innovation associated with product innovation raise marginal cost. Interestingly, we also find that advertising significantly augments demand but does not affect production marginal cost. To obtain broader conclusions, richer data will be needed allowing an enlargement of the model, in which process and product innovations could be specified distinctively and well identified.     

Asset price fluctuations without aggregate shocks

We analyze the pricing of a productive asset in a class of dynamic exchange economies with heterogeneous, infinitely-lived agents, and self-enforcing intertemporal trades. Individual incomes fluctuate and are correlated; preferences, dividends and aggregate income are fixed. Almost all economies in this class have a unique stationary Markovian equilibrium with fluctuations in asset prices. As the set of unrationed households changes over time and states, excess demand functions shift, asset returns fluctuate, and some households are shut out of asset markets. Examples suggest that the amplitude of these movements is negatively correlated with the productivity of the asset and with the penalty for default.     

Adaptive behavior,demand and preferences

This paper extends the work on endogenous change of tastes of Von Weizsäcker to the n-commodity framework and for a general adaptive behavior process. The paper examines the relation between the effect of taste changes to income and price changes. It provides sufficient conditions for stability of the underlying dynamic process, establishes uniqueness of the equilibrium demand vector and some useful relations between the long-run demand functions and the equilibrium short-run demand functions. It is also shown that the long-run demand functions can be rationalized by a utility function if and only if the short-run utility function is such that any good that experiences learning or taste change is separable from all other goods.     

Welfare from a benefit viewpoint

Summary Individual welfare is most naturally measured in terms of individual utility but this has the well-known disadvantage that utility levels of different consumers cannot be meaningfully compared. This difficulty is traditionally avoided by using various willingness-to-pay measures, such as compensating and equivalent variation. These measures are based on price changes. This paper develops alternative welfare measures using willingness-to-trade concepts as originally proposed by Dupuit (1844). These measures are based directly on commodity bundle changes. These welfare measures can be represented as integrals under certain inverse demand functions.An important property of the proposed welfare measures studied here is that they can be meaningfully aggregated to form overall welfare measures. These measures in turn directly quantify a compensation criterion. It is shown that competitive prices provide a first-order approximation to the welfare measures. Furthermore a second-order approximation can be found by forming a suitable aggregation of the individual second-order effects.Finally, it is shown that the representations for consumer welfare as integrals under inverse demand curves can be extended to the aggregate measures as well. This then provides a complete complement to traditional measures based on price changes.This research was supported by Grant SES-9022881 from the National Science Foundation. The author wishes to thank Andrew Yates for valuable suggestions on this paper.     

The Comparative Statics of Effective Demand

Keynes introduces the term ‘effective demand’ in Chapter 3 of the General Theory as designating the point of intersection of two functions: the ‘aggregate demand function’ (D) and the ‘aggregate supply function’ (Z). For the first time in the literature, I here use specific functional forms for the D and Z functions and run numerical simulations which allow study of the comparative statics of the model in the face of various ‘shocks’. The demonstration of how the D/Z model actually works will hopefully prove useful for future students of the economics of Keynes.     

国有股权、内部人掠夺与外部人约束——一个理论模型

上市公司的组织结构实际上是一个社会对于投资者保护水平需求的反应函数,而国有股权作为一种非标准的经济组织形式在特定的制度环境和历史阶段具有约束上市公司内部人的掠夺程度以及提高外部投资者参与程度的双重功能.