Coalition-enhancing fiscal policies in an open economy: A CES framework of Gale’s transfer paradox

The motivation of our paper comes from David Gale’s seminal work in 1974. He constructed an example of the “transfer paradox” based on three Leontief functions. The transfer paradox is that when there is a set of agents in the home country and that the home country is trading with other countries, then certain public lump-sum tax transfer plans could make all agents in the home country better off. Our contributions are as follows. First, we show that such an example can be constructed with three smooth CES utility functions. Second, we establish the three crucial conditions for the existence of the transfer paradox: (1) the donor (a taxpayer) has stronger preference for the foreign good than the recipient; (2) the donor is ex-ante wealthier than the recipient; (3) the elasticity of substitution of the foreign country’s preference is strictly less than one.     

CALIBRATION OF CES FUNCTIONS FOR REAL-WORLD MULTISECTORAL MODELING

We show how to calibrate CES production and utility functions when indirect taxation affecting inputs and consumption is present. These calibrated functions can then be used in computable general equilibrium models. Taxation modifies the standard calibration procedures since any taxed good has two associated prices and a choice of reference value units has to be made. We also provide an example of computer code to solve the calibration of CES utilities under two alternate normalizations.     

Bilateral redistribution

We explore the implications of three basic and intuitive axioms for income redistribution problems: continuity, no transfer paradox and stability. The combination of the three axioms characterizes in the two-agent case a large family of rules, which we call threshold rules. For each level of total income in society, a threshold is considered for each agent. It is impossible for both agents to be below their respective thresholds. If an agent’s income is below the threshold, the difference is redistributed from the other agent; otherwise, the rule imposes laissez-faire.     

An Exact Index for the CES Function with Unobservable Prices

Introduction of new products into the market place poses a difficult problem for the calculation of a cost-of-living (COL) index. The problem is that the reservation prices of new products in the periods before their introduction are unobservable. This paper introduces a new index number formula that overcomes the problem. It is exact for the constant-elasticity-of-substitution (CES) function. Unlike the one introduced to the literature by Feenstra (1994), for which the elasticity of substitution has to be estimated using a separate econometric model, the new index can be computed by simply substituting available prices and quantities into a known exact functional form. The new index number formula is illustrated with the data used in Feenstra (1994).     

Proper preferences and quasi-concave utility functions

It is shown that preferences which are continuous, convex and uniformly proper [Mas-Colell (1983)] on the positive cone of a Banach lattice can be represented by a quasi-concave utility function which is defined on a larger domain with non-empty interior. This utility function may be chosen to be either upper or lower semi-continuous on its domain, and continuous at each point of the positive cone. Conversely, any preference relation on the positive cone which is monotone and arises from such a utility function is shown to satisfy a condition which is slightly weaker than uniform properness but which (in the presence of appropriate compactness assumptions) is sufficient to establish the existence of quasi-equilibria. An example is presented to illuminate the role played by the uniformity requirement.     

Universal Pareto dominance and welfare for plausible utility functions

We study Pareto efficiency in a setting that involves two kinds of uncertainty: Uncertainty over the possible outcomes is modeled using lotteries whereas uncertainty over the agents’ preferences over lotteries is modeled using sets of plausible utility functions. A lottery is universally Pareto undominated if there is no other lottery that Pareto dominates it for all plausible utility functions. We show that, under fairly general conditions, a lottery is universally Pareto undominated iff it is Pareto efficient for some vector of plausible utility functions, which in turn is equivalent to affine welfare maximization for this vector. In contrast to previous work on linear utility functions, we use the significantly more general framework of skew-symmetric bilinear (SSB) utility functions as introduced by Fishburn (1982). Our main theorem generalizes a theorem by Carroll (2010) and implies the ordinal efficiency welfare theorem. We discuss three natural classes of plausible utility functions, which lead to three notions of ordinal efficiency, including stochastic dominance efficiency, and conclude with a detailed investigation of the geometric and computational properties of these notions.     

Efficient provision of public goods with endogenous redistribution

We study a balanced mechanism that is capable of implementing in Nash equilibrium all the Pareto-efficient individually rational allocations for an economy with public goods. The Government chooses a set of weights directly related to the Lindahl prices corresponding to the Pareto-efficient allocation to be implemented. The mechanism then guarantees that initial endowments are re-allocated so that the chosen vector of Lindahl prices is indeed a Lindahl equilibrium, and implements the corresponding Lindahl allocation. Finally, besides being balanced, our mechanism is simple. Each agent has to declare a desired increase in the amount of public good, and a vector of redistributive transfers of initial endowments (across other agents).Received: 9 May 2003, Accepted: 22 October 2003, JEL Classification: C79, H21, H30, H41We wish to thank Jeremy Edwards, Andrew Postlewaite and Emanuela Sciubba for helpful comments. Of course, any remaining errors are our own.     

Turnpike property and convergence rate for an investment model with general utility functions

In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high levels of wealth: one is whether the turnpike property still holds for a general utility that is not necessarily differentiable or strictly concave, the other is whether the error and the convergence rate of the turnpike property can be estimated. We give positive answers to both questions. To achieve these results, we first show that there is a classical solution to the HJB equation and give a representation of the solution in terms of the dual function of the solution to the dual HJB equation. We demonstrate the usefulness of that representation with some nontrivial examples that would be difficult to solve with the trial and error method. We then combine the dual method and the partial differential equation method to give a direct proof to the turnpike property and to estimate the error and the convergence rate of the optimal policy when the utility function is continuously differentiable and strictly concave. We finally relax the conditions of the utility function and provide some sufficient conditions that guarantee the turnpike property and the convergence rate in terms of both primal and dual utility functions.     

A microfoundation for normalized CES production functions with factor-augmenting technical change

Based on a tractable “endogeneous technology choice” framework, we provide a microfoundation for aggregate normalized constant elasticity of substitution (CES) production functions with non-neutral, factor-augmenting technical change. In this framework, firms are allowed to choose unit productivities of capital and labor optimally from a technology menu constructed under the assumption that unit factor productivities (UFPs) are independently Weibull-distributed. The Weibull distribution itself is also microfounded here: based on extreme value theory, it is found to be an accurate and robust approximation of the true UFP distribution if technologies consist of a large number of complementary components.     

Maxmin expected utility with additivity on unambiguous events

This paper provides a model of beliefs representation in which ambiguity and unambiguity are endogenously distinguished in the maxmin expected utility model of Gilboa and Schmeidler (1989). Specifically, I first extend it by getting a representation of beliefs such that the probabilistic beliefs over each ambiguous event are represented by a nondegenerate interval, while the ones over each unambiguous event are represented by a number. I then suggest a behavioral definition of ambiguity. It provides a choice theoretical foundation for the Knightian distinction between ambiguity and unambiguity.     

Expected utility with uncertain probabilities theory

This paper introduces a model of decision making under ambiguity by extending the Bayesian approach to uncertain probabilities. In this model, preferences for ambiguity pertain directly to probabilities such that attitude toward ambiguity is defined as attitude toward mean-preserving spreads in probabilities—analogous to the Rothschild–Stiglitz risk attitude toward mean-preserving spreads in outcomes. The model refines the separations between tastes and beliefs, and between risk and ambiguity. These separations are crucial for the measurement of the degree of ambiguity and for the elicitation and characterization of attitudes toward ambiguity, thereby providing an empirically and experimentally applicable framework.     

Explicit characterizations of financial prices with history-dependent utility

The present paper demonstrates how explicit representations of financial prices and returns can be derived in economies with history-dependent utility. While the techniques are applicable to a wide range of economies, they are applied to a representative consumer economy where (i) the consumer’s preferences exhibit habit formation, and (ii) purchases of the consumption good also gives rise to a flow of services. Solutions are computed for the case of multiplicative or nonlinear habit formation, and additive service flows. Other applications are also indicated.     

A new axiomatization of rank-dependent expected utility with tradeoff consistency for equally likely outcomes

This paper provides a new axiomatization of rank-dependent expected utility by relaxing tradeoff consistency to hold only when the involved outcomes are equally likely. The resulting weakened variant of tradeoff consistency is considerably simpler and intuitively more appealing than the original condition. Consequently, an improved tool for empirical studies and the elicitation of utilities is provided. It turns out that in the presence of weak ordering, simple-continuity, and stochastic dominance, the new tradeoff consistency for equally likely outcomes is sufficient to derive rank-dependent expected utility for general lotteries.     

On rankings and top choices in random utility models with dependent utilities

Different aggregate preference orders based on rankings and top choices have been defined in the literature to describe preferences among items in a fixed set of alternatives. A useful tool in this framework is constituted by random utility models, where the utility of each alternative, or object, is represented by a random variable, indexed by the object, which, for example, can capture the variability of preferences over a population. Applications are derived in diverse research fields, including computer science, management science and reliability. Recently, some stochastic ordering conditions have been provided for comparing alternatives by means of some aggregate preference orders in the case of independent random utility variables by Joe (Math Soc Sci 43:391–404, 2002). In this paper we provide new conditions, based on some joint stochastic orderings, for aggregate preference orders among the alternatives in the case of dependent random utilities. We also provide some examples of application in different research fields.