Aggregation and the existence of a social utility function

In a well-known paper Gorman (Econometrica21 (1953)) established that the necessary and sufficient condition for the existence of an aggregate, or social, utility function, independent of the distribution of income, is that all individuals' income consumption paths be parallel straight lines. Recently Chipman (J. Econ. Theory8 (1974)), building on the paper of Hurwicz and Uzawa (in “Preference Utility and Demand”) has shown that if the distribution of income is proportional and individual preferences are homothetic, aggregate consumption behavior obeys the necessary integrability conditions. It is shown here that the consistency of aggregate behavior can be derived from more general conditions than the ones used by Chipman and Gorman. Examples of demand systems from which aggregate behavior implies a social utility function are provided. It is then shown that if individual demand functions are linear in income—a form employed by both Gorman and Chipman—it is not necessary that the distribution of income be fixed.     

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.     

Modelling the demand for housing over the life cycle

We model individual demand for housing over the life cycle, and show the aggregate implications of this behaviour. Individuals delay purchasing their first home when incomes are low or uncertain. Higher house prices lead households to downsize, rather than to stop being owners. Fixed costs (property transactions taxes) have important impacts on welfare (a wealth effect) and house purchase decisions (substitution effect). In aggregate, positive house price shocks lead to consumption booms among the old but falls in consumption for the young, and reduced housing demand; positive income shocks lead to consumption booms among the young and increased housing demand.     

Testable implications of transferable utility

Although the Transferable Utility (TU) assumption is widely used in micro theory, little is known about its testable consequences, and in particular how one can, from the observation of a group's demand, test whether the TU assumption is satisfied within this group. We derive a set of necessary and sufficient conditions on demand that characterize the TU context. The conditions are of two types. First, TU requires the group to behave as a single decision maker. Secondly, within the unitary setting, the representative utility generated by a TU framework must be of the Generalized Quasi-Linear (GQL) form. We derive testable properties of the demand function that fully characterize GQL utilities. These additional restrictions only involve specific prices - namely, those of the goods that are publicly consumed within the group.     

An Afriat Theorem for the collective model of household consumption

We provide a nonparametric ‘revealed preference’ characterization of rational household behavior in terms of the collective consumption model, while accounting for general individual preferences that can be non-convex. Our main result is the Collective Afriat Theorem, which parallels the well-known Afriat Theorem for the unitary model. First, it provides a characterization of collectively rational consumption behavior in terms of collective Afriat inequalities. Next, it implies the Collective Axiom of Revealed Preference (CARP) as a testable necessary and sufficient condition for data consistency with collective rationality. Finally, the theorem has some interesting testability implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.     

Mechanism design with side payments: Individual rationality and iterative dominance

We investigate the collective decision with incomplete information and side payments. We show that a direct mechanism associated with the social choice function that satisfies budget balancing, incentive compatibility, and interim individual rationality exists for generic prior distributions. We consider the possibility that a risk-averse principal extracts full surplus in agency problems with adverse selection. With regard to generic prior distributions, we show that there exists a modified direct mechanism associated with the virtual social choice function, which satisfies budget balancing and interim individual rationality, such that truth telling is the unique three times iteratively undominated message rule profile.     

Demand Aggregation and the Weak Axiom of Stochastic Revealed Preference

We address the problem of aggregating demand across a group of consumers, who are identical in terms of wealth and face identical price vectors, but vary in their chosen consumption bundles. We show that, when a stochastic demand function is constructed to aggregate a number of deterministic demand functions, satisfaction of the weak axiom of stochastic revealed preference by this stochastic demand function is weaker than the restriction that every underlying deterministic demand function satisfy Samuelson's weak axiom of revealed preference. Journal of Economic Literature Classification Number: D11.     

Effective Demand: Securing the Foundations

Abstract

This paper is one of three contributions to a symposium commenting on papers previously published by the other authors. Allain (Allain, O. (2009) Effective demand and short-term adjustments in the General Theory, Review of Political Economy, 21, pp. 1–22) argues that Keynes elides a distinction between aggregate demand and global expenditure that is necessary to explain the formation of price expectations by individual entrepreneurs. Allain's conclusions depend upon redefinitions of aggregate and effective demand and the consumption function. Hartwig (Hartwig, J. (2007) Keynes vs. the Post Keynesians on the principle of effective demand, European Journal of the History of Economic Thought, 14, pp. 725–739) argues that entrepreneurs must take into account the state of the economy as a whole, in order to form price expectations independently and not as a market equilibrium determined by aggregate supply and demand. This leaves demand price expectations to be determined outside the principle of effective demand. Neither author does full justice to Keynes's own treatment. We still need to agree by what mechanism individual entrepreneurs form a collective and mutually consistent state of expectation in The General Theory.     

The communication requirements of social choice rules and supporting budget sets

The paper examines the communication requirements of social choice rules when the (sincere) agents privately know their preferences. It shows that for a large class of choice rules, any minimally informative way to verify that a given alternative is in the choice rule is by verifying a “budget equilibrium”, i.e., that the alternative is optimal to each agent within a “budget set” given to him. Therefore, any communication mechanism realizing the choice rule must find a supporting budget equilibrium. We characterize the class of choice rules that have this property. Furthermore, for any rule from the class, we characterize the minimally informative messages (budget equilibria) verifying it. This characterization is used to identify the amount of communication needed to realize a choice rule, measured with the number of transmitted bits or real variables. Applications include efficiency in convex economies, exact or approximate surplus maximization in combinatorial auctions, the core in indivisible-good economies, and stable many-to-one matchings.     

Afriat's theorem for general budget sets

Afriat proved the equivalence of a variant of the strong axiom of revealed preference and the existence of a solution to a set of linear inequalities. From this solution he constructed a utility function rationalizing the choices of a competitive consumer. We extend Afriat's theorem to a class of nonlinear, nonconvex budget sets. We thereby obtain testable implications of rational behavior for a wide class of economic environments, and a constructive method to derive individual preferences from observed choices. We also show that by increasing in a regular way the number of observed choices from our class of budget sets one can fully identify the underlying preference relation.     

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.     

Rebate rules in threshold public good provision

This paper considers how six alternative rebate rules affect voluntary contributions in a threshold public-good experiment. The rules differ by (1) whether an individual can receive a proportional rebate of excess contributions, a winner-takes-all of any excess contributions, or a full rebate of one's contribution in the event the public good is provided and excess contributions exist, and (2) whether the probability of receiving a rebate is proportional to an individual's contribution relative to total contributions or is a simple uniform probability distribution set by the number of contributors. The paper adds to the existing experimental economics literature on threshold public goods by investigating both aggregate and individual demand revelation under the winner-take-all and random full-rebate rules. Half of the rules (proportional rebate, winner-take-all with uniform probability among all group members, and random full-rebate with uniform probability) provide total contributions that nearly equal total benefits, while the rest (winner-take-all with proportional probability, winner-take-all with uniform probability among contributors only, and random full-rebate with proportional probability) exceed benefits by over 30%. Only the proportional rebate rule is found to achieve both aggregate and individual demand revelation. Our experimental results have implications for both fundraisers and valuation practitioners.     

Within‐Subject Intra‐ and Inter‐Method Consistency of Two Experimental Risk Attitude Elicitation Methods

We compare the consistency of choices in two methods used to elicit risk preferences on an aggregate as well as on an individual level. We ask subjects to choose twice from a list of nine decisions between two lotteries, as introduced by Holt and Laury 2002, 2005 ) alternating with nine decisions using the budget approach introduced by Andreoni and Harbaugh ( 2009 ). We find that, while on an aggregate (subject pool) level the results are consistent, on an individual (within‐subject) level, behaviour is far from consistent. Within each method as well as across methods we observe low (simple and rank) correlations.     

THE (AGGREGATE) DEMAND FOR STATE‐LOTTERY TICKETS: WHAT HAVE WE REALLY LEARNED?

Lottery‐demand models using aggregate data are often used to make inferences regarding individual behavior, the most important being the distributional burden of lottery‐ticket expenditures. It is shown here that estimates for the income elasticity and the cross‐price elasticity will only be representative of individual behavior under extremely restrictive assumptions. In fact, estimation of aggregate‐demand models presupposes that the income elasticity is equal to one. Cross‐sectional analyses using microlevel data face similar restrictions on consumer behavior. Remedies are discussed, but more conclusive evidence on the distributional burden of lotteries will remain elusive until better individual‐level data become available. (JEL D11, H71, H22)     

Exact aggregation and Generalized Slutsky Conditions

This article indicates a natural connection between Generalized Slutsky Conditions and demand structures of the exact aggregation form. It is shown that Generalized Slutsky Conditions are assured when the number of consumers is greater than or equal to the number of goods, if and only if demands are of a generalized exact aggregation form. This result provides some understanding of the properties of aggregate demand and allowable differences between consumers, as well as naturally generalizing W. M. Gorman's (Econometrica21 (1953), 63–80) famous conditions for the integrability of aggregate demand.     

Inflation and the Exchange Rate: The Role of Aggregate Demand Elasticity

This paper examines the effect of aggregate demand elasticity on the exchange rate when inflation occurs. We discover that both the source of the inflation, whether demand-pull or cost-push, and the elasticity of aggregate demand with respect to the price level, are of consequence for the exchange rate. We obtain two primary conclusions. First, the effect on the exchange rate of cost push inflation is ambiguous and is partially determined by the price level elasticity of aggregate demand. In particular, and assuming that the two examined countries have equivalent aggregate supply elasticities, we conclude that the nation with the less elastic aggregate demand function will see its currency appreciate relative to the other. Second, demand-pull inflation results in an unambiguous increase in the exchange rate but the size of that increase is partially a function of aggregate demand elasticity. Assuming again that two countries have equivalent aggregate supply elasticities, that country with the more elastic aggregate demand will experience currency appreciation.     

On some global properties of Gorman class demand systems

This letter explores some global properties of the Gorman class of demand functions. We find that generalizing the homothetic preferences case to non-homotheticity gives rise to an unexpected global problem. In particular, interaction of the bounded budget share condition with either Slutsky symmetry or with homogeneity reduces the set of admissible Gorman class demand functions to but one — the polar form.     

Time inconsistency and retirement planning

We quantify the welfare gains from better retirement planning using a model in which retirement planning is time inconsistent. A modest increase in a household’s planning horizon by just a few years generates large aggregate and individual welfare gains.     

MODELING INTERNATIONAL CONSUMPTION PATTERNS

This article addresses a number of key problems commonly confronted in the literature on international demand analysis. These include data issues and requirements, multistage budgeting, outliers, group heteroskedasticity, and model selection. A two-stage demand system is fit to International Comparison Programme data for 114 countries for nine aggregate categories and eight food sub-categories of goods. Outliers are identified and omitted from the sample. Parameter estimates for the two stages are obtained with a maximum-likelihood procedure that corrects for group heteroskedasticity. Country-specific income and own-price elasticities are calculated and indicate that poor countries are more responsive to changes in income and prices than rich countries. We also find evidence for the strong version of Engel's law; when income doubles, the budget share of food declines by approximately 0.10.     

Pigouvian pricing and stochastic evolutionary implementation

We study the implementation of efficient behavior in settings with externalities. A planner would like to ensure that a group of agents make socially optimal choices, but he only has limited information about the agents’ preferences, and can only distinguish individual agents through the actions they choose. We describe the agents’ behavior using a stochastic evolutionary model, assuming that their choice probabilities are given by the logit choice rule. We prove that there is a simple price scheme with the following property: regardless of the realization of preferences, a group of agents subjected to the price scheme will spend the vast majority of time in the long run behaving efficiently. The price scheme defines a game that may possess multiple equilibria, but we are able to obtain a unique and efficient selection from this set because of the stochastic nature of the agents’ choice rule. We conclude by comparing the performance of our price scheme with that of VCG mechanisms.