On the characterization of excess demand functions

Summary. In this paper, we give the necessary and sufficient conditions that characterize the individual excess demand function when it depends smoothly on prices and endowments. A given function is an excess demand function if and only if it satisfies, in addition to Walras law and zero homogeneity in prices, a set of first order partial differential equations, its substitution matrix is symmetric and negative semidefinite. Moreover, we show that these conditions are equivalent to the symmetry and negative semidefiniteness of Slutsky matrix, Walras law and zero homogeneity of Marshallian demand functions.Received: 25 November 2002, Revised: 11 March 2004, JEL Classification Numbers: D11.Marwan Aloqeili: I would like to thank an anonymous referee for helpful comments.     

The aggregated excess demand function and other aggregation procedures

Summary Two theorems are given; the first extends the Sonnenschein-Mantel-Debreu theorem characterizing aggregate demand functions from the set ofn2 commodities to all of the 2 ⁿ –(n+1) subsets of two or more commodities. The second theorem concerns spatial voting models for k2 candidates over a space of n2 issues. The theorem characterizes the sincere elecion rankings of thek candidates over all of the 2 ⁿ –1 subsets of one or more issues. Both theorems have the same kind of conclusion; anything can happen. By demonstrating the mathematical reasons for these conclusions and by recalling related, recent results from statistics, voting, and economics, it is argued that this anything can happen conclusion is the type one must anticipate for aggregation procedures; particularly for the processes commonly used in economic models where the procedure is responsive to changes in agents' preferences, changes in data, etc.I am pleased to acknowledge conversations with L. Hurwicz, A. Mas-Colell and C. Simon about this material. In particular, I want to thank J. Jordan for his several helpful suggestions. Also, I benefited from comments made at meetings and seminars where these results were presented; this includes a June, 1990, conference in Stockholm, Sweden. Some stylistic suggestions were made by Arvid and Padon Kalinen. This research was supported, in part, by NSF Grant IRI-8803505.     

A note on implicit inventory behavior in cyclical macroeconomic models with excess demand

The paper is concerned with dynamic models that allow for non-zero excess demand on goods markets but abstain from considering possible feedback effects of stock-piling. That is, inventories are only implicitly determined. Consistency requires that they do not fall below zero and, relative to output, do not grow beyond all bounds. With respect to periodic motions, conditions for consistency as well as for inconsistency are derived. It is indicated that a priori, in particular in the presence of long-run growth, inconsistency may not be an exception.     

Ticket pricing and the impression of excess demand

If willingness to pay depends on characteristics of other attendees, a monopolist will use a lineup as a screening mechanism only if a consumer's characteristic is inversely related to her cost of lining up. No capacity constraint is necessary.     

On the disaggregation of excess demand functions when prices and aggregate income vary independently

Under the assumption that prices and aggregate income can vary independently and that the income distribution scheme is known and homogeneous of degree 1 in prices and aggregate income, I raise the question of the restrictions on aggregate excess demand behavior implied by the postulate of rationality of individual agents. If the number of agents is at least as high as the number of commodities, aggregate excess demand need not satisfy, at a point, any restrictions other than homogeneity of degree 0 and Walras' law. Furthermore, if the number of agents, m, is less than the number of commodities, l, aggregate excess demand can be locally arbitrary when projected on an m-dimensional subspace of the commodity space.     

Measuring capacity utilization and excess demand

This paper investigates the usefulness of qualitative data on capacity utilization (CU) in approximating various macroeconomic variables which are not covered by direct statistical measurement. By help of a model of demand distribution over firms, the relation between a qualitative CU measure, an ‘ideal’ CU measure, and excess demand, is studied for changing levels of aggregate demand. The model is then used to derive time series for capacity, utilization and excess demand from a qualitative CU index and an index of production. Results suggest that qualitative data may provide better measurement of capacity and utilization than, e.g., the Wharton index, and may also perform well in the measurement of excess demand.     

Marginal and conditional probabilities of excess demand

This note compares and illustrates two criteria for classifying observations on a non-clearing market, namely the marginal probability of excess demand and the probability of excess demand conditional on the observed quantity.     

Disaggregation of excess demand under additive separability

A differentiable function satisfying Walras' law and homogeneity of degree zero can be disaggregated, at a point, into excess demand functions, each derived by the maximization of a regular and additively separable utility function subject to the budget constraint.     

Homothetic preferences and community excess demand functions

It has recently been shown that microeconomic theory imposes almost no restriction on community excess demand functions besides Walras' Law, if the economy contains no more commodities than consumers.It is shown that the same result is true if the preferences of the consumers are further restricted by the seemingly strong requirement that they be homothetic, even when the distribution of initial endowments is a set of independent points in commodity space fixed in advance except for a scaling factor which is common to all consumers.     

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     

Optimal taxation theory and excess demand functions

A class of individual excess demand functions found in optimal taxation theory is shown to restrict the set of possible community excess demand functions.     

A method for finding the maximal set in excess demand

We present a polynomial time method for identifying the maximal set in excess demand at a given payoff vector. This set can be used in “large” partnership formation problems to identify the minimum element in the set of individually rational payoff vectors at which there is no overdemanded set of agents. This minimum element corresponds to the minimum Walrasian equilibrium price vector in a special case of the partnership formation problem.     

The excess demand for subsidized child care in Germany

The extension of publicly provided or subsidized child care is currently one of the priorities of the political agenda in many European countries. In this article, the excess demand for subsidized child care slots in Germany is estimated using a partial observability model. The results show that there is considerable excess demand for child care for children aged less than 3 years in East and West Germany, even among children with working mothers.     

Leakages from the money demand function

The performance of alternative scale variables is explored in a simple demand function for narrow money. Sequential test establish consumers' expenditure as the preferred measure. The implications for fiscal policy and the paradox of thrift are outlined.     

On the demand for information

Most previous research on the economics of information has been based on the expected utility hypothesis and Bayesian learning. Yet there is experimental evidence that decision makers do not always maximize expected utility and that human learning is not always consistent with Bayes' rule. Using a two-period model, this paper examines the valuation of information as well as the demanf for information in the broader context of a state preference approach under an ordinal representation of preferences. In particular, it is not assumed that the decision maker is Bayesian, nor that he behaves in a way consistent with the expected utility hypothesis. In this general framework, the value of information is defined and analysed. Also, under active learning, the optimal allocation of information gathering activities is discussed. Behavioural properties of the demand for information are derived making use of a compensation function. Implications of the results for measuring the value of information and for the economic analysis of learning activities are discussed.     

Estimating the import demand function for China

This paper estimates the import demand elasticity for China using three fully efficient cointegrating regressions and the autoregressive distributed lag (ARDL) method. This paper is the first to accommodate the perception of global risk in an investigation of the information transmission mechanism between the relationship import demand and its determinants in China. The empirical results show that real imports are cointegrated with domestic economic activity, real effective exchange rate, and the perception of global risk. Domestic income is found to have a significantly positive effect on imports. Contrary to theory, the real effective exchange rate carries negative coefficients, which suggests that a decrease in external competitiveness (appreciation) will decrease the level of imports in the case of China. One of the reasons for this may be the tied anti-dumping duty on some import items. Since the perception of global risk adversely affects China's aggregated imports, policy-makers should consider the degree to which the perception of global risk affects the implementation of trade policies.