Revelation of preferences for public goods: Aggregation by Abelian operations

When the utility functions for the public and private goods are additively separable, in the two-public-alternative situation, a new class of incentive compatible mechanisms is presented, and some of its properties are explored. If there are more than two public alternatives and if the utility functions remain separable according to a generalized addition (called an abelian operation), it is also possible to construct incentive compatible mechanisms. Such mechanisms are similar to those of Groves but they do not involve maximizing a sum of utilities.     

Notes on separable preferences

Examples are constructed to show that Gorman's important basic theorem for overlapping strictly separable sectors does not hold if the sectors are only nonstrictly separable. This is done with the help of a new definition for the notion of nonstrict separability of utility preferences. The new definition is equivalent to that of Bliss; but it clarifies the relationship between the geometry and representation of preferences with separable sectors. The gained geometric insight leads to the conjecture that if all sectors are strictly essential, then Gorman's Basic Theorem would hold.     

The progressivity of equalization payments in federations

We investigate the conditions under which an inequality averse and additively separable welfarist central government would choose to set up a progressive equalization payments scheme in a federation with local public goods. A progressive equalization payments scheme is a list of per capita net (possibly negative) subsidies – one such net subsidy for every jurisdiction – that are decreasing with respect to jurisdictions per capita wealth. We examine this question in a setting where the case for progressivity is a priori the strongest, namely: all citizens have the same utility function, inhabitants of a given jurisdiction have the same wealth and are not able to move across jurisdictions and there is no cross-jurisdiction competition in the setting of tax rates. We show that the central government favors a progressive equalization payments scheme for all distributions of wealth and population sizes if and only if its objective function is additively separable between each jurisdiction's per capita wealth and number of inhabitants. When interpreted for a mean of order r social welfare function, and assuming the absence of congestion in the local public good, this condition is shown to be equivalent to the requirement that the individual indirect utility function be additively separable between wealth public good price and be raised at the power 1/r before its agregation by means of the mean-of-order r social welfare function. Some implications of this restriction to the case where the individual's direct utility function is additively separable are also derived.     

Equilibrium existence in infinite horizon economies

In sequential economies with finite or infinite-lived real assets in positive net supply, we introduce constraints on the amount of borrowing in terms of the market value of physical endowments. We show that, when utility functions are either unbounded and separable in states of nature or separable in commodities, these borrowing constraints not only preclude Ponzi schemes but also induce endogenous Radner bounds on short-sales. Therefore, we obtain existence of equilibrium. Moreover, equilibrium also exists when both assets are numéraire and utility functions are quasilinear in the commodity used as numéraire.     

Alternative perspectives on connections in economic systems

This paper explores the significance of Potts’s (2000) claim that the key difference between orthodox and heterodox economics lies in the former viewing the economy as a mathematical field in which everything is connected to everything else, and the latter viewing it as a complex system in which only some elements are connected. It focuses on the types of connections in economic systems that different economists have identified and the significance of the degree of connectivity for how economic systems function. Topics explored include separable consumer networks, separable utility functions, checklist-based decision rules, lifestyles, goodwill, the nature of business strategies and evolution.     

The separability axiom and equal-sharing methods

A quasi-linear social choice problem is defined as selecting one (among finitely many) indivisible public decision and a vector of monetary transfers among agents to cover the cost of this decision. This decision is based upon individual preferences, which are assumed to be additively separable and linear in money. The Separability axiom is a consistency property for choice methods on societies with variable size: the decision is not affected if we remove an arbitrary agent under the condition that he be guaranteed his original utility level and the cost to the remaining agents is modified accordingly. Thus the utility level assigned by the social choice function to agent i is the price at which the other agents are unanimously willing to buy agent is share of the decision power. A general characterization of choice methods satisfying this axiom is provided. Three subclasses of particular interest are characterized by additional milder axioms. Those are: (i) equal sharing of the surplus left over some reference utility (e.g., the utility at a status quo decision), (ii) utilitarian methods that merely select the efficient public decision and perform no monetary transfers, and (iii) equal allocation of nonseparable costs, which divides equally the surplus left over from the utility derived from the pivotal mechanism (also known as the Vickrey-Clarke-Groves mechanism).     

Optimal growth and cycles in overlapping generations models

Summary This paper investigates the dynamical properties of optimal paths in one-sector overlapping generations models without assuming that the utility function of the representative agent is separable. When the utility function is separable, the optimal growth paths monotonically converges toward the modified golden rule steady state. In the non-separable case, we show that the optimal growth path may be oscillating and optimal two-period cycles may exist. Applying these results to the model with altruism, we show that the condition of operative bequest is fully compatible with endogeneous fluctuations provided that the discount factor is close enough to one. All our results are illustrated using Cobb-Douglas utility and production functions.We thank C. Blackorby, J. Blot, P. Cartigny and one anonymous referee for helpful comments and suggestions which generally improved the exposition of the paper. We would also like to thank the participants of the Population and demography session of the European Economic Association 10th Annual Congress (Prague, The Czech Republic, September 1–4, 1995).     

Intertemporal price discrimination and consumer demand

Under a particular class of utility functions, intertemporal price discrimination (IPD) is not feasible. That is, customers cannot be made to pay different prices for a durable good at different points in time. Other factors such as falling costs, and differing discount rates between buyers and sellers have been found to make intertemporal pricing schemes feasible, or even profitable. None of these factors, however, were fundamental demand differences which give rise to static price discriminations. In this paper we argue that IPD is indeed feasible and sometimes profitable, if only we allow for a nondurable good in the utility function. A simple additively separable utility is examined first, which is then extended to a nonseparable utility function which allows richer substitution/complementary relations between the durable and the nondurable goods. This may help us to better understand the similarities between static and intertemporal price discriminations.     

Preferences and normal goods: A sufficient condition

This note contains a sufficient condition for all goods to be normal, in the case of differentiable individual demand. This condition appears as a relationship between the first and second partial derivatives of the utility function. But it is shown that this condition is independant of the utility function chosen and, then, is a characteristic of the preference order.     

基于高斯冲击和习惯形成的资产定价模型

在卢卡斯提出的资产定价模型中,消费增长率是独立同分布的和投资者效用函数是可分的。卢卡斯模型无法解释著名的股票溢价之谜和无风险利率之谜,对卢卡斯模型做的两个修改是:消费增长率服从一阶高斯自回归随机过程和投资者偏好是具有习惯形成的效用函数,修改后的模型,一是存在资产定价的显示解;二是可以解释股票溢价之谜和无风险利率之谜。     

A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game

It is well-known that a transferable utility game has a non-empty core if and only if it is balanced. In the class of non-transferable utility games balancedness or the more general π-balancedness due to Billera (SIAM J. Appl. Math. 18 (1970) 567) is a sufficient, but not a necessary condition for the core to be non-empty. This paper gives a natural extension of the π-balancedness condition that is both necessary and sufficient for non-emptiness of the core.     

Production Efficiency and the Direct-Indirect Tax Mix

In the design of the optimal direct/indirect tax mix, the canonical view was laid by Atkinson and Stiglitz (1976) who showed that commodity taxes are unnecessary in an economy in which there is an optimal nonlinear income tax provided that commodities are separable from labor in the utility functions of all taxpayers, that the aggregators over these commodities are ordinally equivalent and that wages are fixed. When wages are endogenous, Naito (1999) showed that this result may not hold and in addition that production efficiency may not be Pareto optimal. Given an optimal nonlinear income tax, we show that production inefficiency is Pareto optimal if the aggregate technology set is strictly concave. The Atkinson–Stiglitz condition is neither necessary nor sufficient for zero commodity taxation and commodity taxes are part of almost all Pareto optima.     

Bilateral Search and Vertical Heterogeneity

Just like perfect (frictionless) matching models, a search model is proposed that is characterized by bilateral search and vertical heterogeneity. It allows for a generally specified utility function. The equilibrium allocation is unique and exists in iterated strict dominance. The model is robust with the perfect matching model as frictions disappear. Nonetheless, the equilibrium allocations are surprisingly odd. For multiplicatively separable preferences, the distributions are partitioned endogenously. And for a wide range of preferences, matching sets are naturally disconnected.     

A note on risk aversion and multivariate,state-dependent preferences

Within the multivariate, state-dependent utility framework, a full insurance specification of risk aversion places severe restrictions on preferences. In particular, the von Neumann-Morgenstern utility function must be separable, and state-dependent only for consumption of the insured good.     

Adaptive behavior and the existence of Weizsäcker's long-run indifference curves

Suppose that past consumptions of the first r commodities (r < n) influence present consumption. Then, the long-run demand function to which demand converges maximizes the equilibrium short-run utility function only under very restrictive conditions. The long-run demand functions can be rationalized by a utility function, different from the equilibrium short-run utility function, if and only if the short-run utility function is such that past consumptions of any good that experience, learning, or taste changes is separable from all other goods. The class of such utility functions has been found.     

Quasiconcavity and the kernel of a separable utility

Summary. In this paper I prove that a quasiconcave separable utility function defined on an atomless space is concave. Received: August 11, 1997; revised version: October 2, 1997     

Simple mechanisms and preferences for honesty

We consider full implementation in complete-information environments when agents have an arbitrarily small preference for honesty. We offer a condition called separable punishment and show that when it holds and there are at least two agents, any social choice function can be implemented by a simple mechanism in two rounds of iterated deletion of strictly dominated strategies.     

ON THE SUSTAINABILITY OF GOVERNMENT BORROWING IN A DYNAMIC GENERAL EQUILIBRIUM

Abstract.  This paper constructs a dynamic general equilibrium model with money in consumers' utility functions and investigates the equilibrium dynamics of government's debt. The limitation level of the government borrowing for which a dynamic equilibrium and the no Ponzi Game condition are compatible with each other is explicitly derived. The critical level depends on the long-run interest rate, primary balance, money supply etc.