Quasi-linear Preferences Research Articles

A new necessary condition for implementation in iteratively undominated strategies

Implementation in iteratively undominated strategies relies on permissive conditions. However, for the sufficiency results available, authors have relied on assumptions that amount to quasilinear preferences on a numeraire. We uncover a new necessary condition that implies that such assumptions cannot be dispensed with. We term the condition “restricted deceptionproofness.” It requires that, in environments with identical preferences, the social choice function be immune to all deceptions, making it then stronger than incentive compatibility. In some environments the conditions for (exact or approximate) implementation are more restrictive than previously thought.

A New Necessary Condition For Implementation in Iteratively Undominated Strategies

Implementation in iteratively undominated strategies relies on permissive conditions. However, for the sufficiency results available, authors have relied on assumptions that amount to quasilinear preferences on a numeraire. We uncover a new necessary condition that implies that such assumptions cannot be dispensed with. We term the condition “restricted deception-proofness.” It requires that, in environments with identical preferences, the social choice function be immune to all deceptions, making it then stronger than incentive compatibility. In some environments the conditions for (exact or approximate) implementation are more restrictive than previously thought.

Independence Axioms for Water Allocation

We consider the problem of sharing water among agents located along a river. Each agent has quasi-linear preferences over river water and money, where the benefit of consuming an amount of water is given by a continuous and concave benefit function. A solution to the problem efficiently distributes the river water over the agents and wastes no money. We introduce a number of (independence) axioms to characterize two new and two existing solutions. We apply the solutions to the particular case that every agent has constant marginal benefit of one up to a satiation point and marginal benefit of zero thereafter. In this case we find that two of the solutions (one existing and one new) can be implemented without monetary transfers between the agents.

‘Just one of us’: consumers playing oligopoly in mixed markets

Consumer cooperatives represent a highly successful example of democratic form of enterprises operating in developed countries. They are usually medium to large-scale companies competing with the profit-maximizing firms in the retail sector. This paper describes this situation as a mixed oligopoly in which consumer cooperatives maximize the utility of consumer-members and, in return, refund them with a share of the profits corresponding to the ratio of their individual spending to the cooperative’s total sales. We show that when consumers possess quasi-linear preferences over a bundle of symmetrically differentiated goods, and companies operate using a linear technology, the presence of consumer cooperatives positively affects total industry output, as well as welfare. The effect of cooperatives on welfare proves to be even more significant when goods are either complements or highly differentiated, and when competition is à la Cournot rather than à la Bertrand.

All but one free ride when wealth effects are small

Quasilinear preferences on a public good and a numeraire good are limits of preferences where both goods are normal. The set of equilibria of the voluntary contribution (or private provision) game is easily characterized under quasilinearity by: top valuators aggregately contribute their common stand-alone contribution, whereas non-top valuators contribute nothing. Because, as long as preferences are randomly selected, there will typically be a single top valuator, it follows that, typically, the equilibrium is unique, with all players but one contributing nothing, hence “free riding” in the sense of the ordinary English usage of the expression. The upper-hemicontinuity of the Nash equilibrium correspondence implies that this is also the case when both goods are strictly normal, but the wealth effects on the public good are small.

An existence result and a characterization of the least concave utility of quasi-linear preferences

Abstract This note shows that there exists a least concave utility function of a convex quasi-linear preference relation and that a utility function of a convex quasi-linear preference relation is least concave iff it is of the form u( x) + cy.

A public procurement combinatorial auction mechanism with quality assignment

This article focuses on mechanism design for quality assignment combinatorial procurement auctions. We model how the participants can maximize social surplus, the difference between gross utility and total cost in electronic procurement, while selecting appropriate quality standards for the procured items. In typical forward combinatorial auctions, the goal is to maximize the sum of all buyers' valuations. In our setting, however, to achieve high buyer utility with low supplier cost, the selected quality levels for the procured items from the suppliers must exceed some predetermined minimum threshold. So the identification of capable suppliers and the corresponding quality assignments are crucial, since buyer utility and supplier cost will be affected by the buyer's quality choice. We develop a novel mechanism to balance the interests of buyers and sellers. Our proposed quality assignment Vickrey–Groves–Clarke (QA-VCG) mechanism is incentive-compatible, provides constraints on partial participation, and is efficient in quasi-linear preferences. In consideration of the perspective of the buyer as a government auctioneer, we also propose a revised mechanism to implement the goal of achieving minimal procurement costs, and appropriate benefits for participating suppliers. We provide a numerical illustration of our QA-VCG mechanism, and an extension that addresses an iterative combinatorial auction mechanism design in our context.

International Trade and Volume Patterns under Quasilinear Preferences

We formally analyze the pattern and volume of trade by embedding quasilinear preferences in the standard perfectly competitive, two-factor, two-good, two-country trade model. Quasilinear preferences deliver a natural partition of the two goods into a luxury and a necessity, and preserve the validity of the Heckscher–Ohlin and Heckscher–Ohlin–Vanek theorems. In addition, the predicted factor content of trade under quasilinear preferences is smaller (larger) than the predicted factor content of trade under homothetic preferences if and only if the luxury good is capital (labor) intensive. This result offers a novel explanation for the “missing-trade” mystery.

Consumer Cooperatives and Welfare in a Mixed Oligopoly

Consumer co-operatives constitute a highly successful example of democratic forms of enterprises operating in developed countries. They are usually organized as medium or large-scale firms competing with profit seeking firms in retail industries. In this paper we model such a situation as a mixed oligopoly in which consumer co-operatives maximize consumer-members' utilities and distribute them a patronage rebate on their goods purchase. We show that when consumers possess quasilinear preferences over a bundle of symmetrically differentiated goods and firms operate with a linear technology, the presence of consumer co-operatives positively a¤ects all industries output and social welfare. The effect of Co-ops on welfare is shown to be more significant when goods are either complements or highly di¤erentiated and when competition is a la Cournot rather than a la Bertrand.

Are incentives against economic justice?

We consider the problem of fairly allocating a social endowment of indivisible goods and money when the domain of admissible preferences contains, but is not restricted to, quasi-linear preferences. We analyze the manipulability of the Generalized Money Rawlsian Fair (GMRF) solutions. (i) We show that the Nash and strong Nash equilibrium correspondences of the “preference revelation game form” associated with each GMRF solution coincide with the no-envy solution (in equilibrium, efficiency is preserved according to agents' true preferences). (ii) A corollary is that the GMRF solutions “naturally implement” the no-envy solution in Nash and strong Nash equilibria.

Tagging and Income Taxation: Theory and an Application

We derive a set of analytical results for optimal income taxation with tags using quasilinear preferences and a Rawlsian social welfare function. Secondly, assuming a constant elasticity of labor supply and log-normality of the skills distribution, we analytically identify the winners and losers of tagging. Third, we prove that if the skills distribution in one group first-order stochastically dominates the other, tagging calls for redistribution from the former to the latter group. Finally, we calibrate our model to the US workers using gender as tag. Welfare implications are dramatic. Only male high-wage earners lose. Everyone else gains, some substantially. (JEL H21, H23, H24)

Just One of Us: Consumers Playing Oligopoly in Mixed Markets

Consumer cooperatives constitute a highly successful example of democratic forms of enterprises operating in developed countries. They are usually organized as medium and large-scale firms competing with pro fit-maximizing firms in retail industries. This paper models such situation as a mixed oligopoly in which consumer cooperatives maximize the utility of consumer-members and distribute them a share of the profit equal to the ratio of their individual expenditure to the firm total sales. We show that when consumers possess quasilinear preferences over a bundle of symmetrically differentiated goods and firms operate with a linear technology, the presence of consumer cooperatives affects all industries output and social welfare positively. The effect of cooperatives on welfare proves more significant when goods are either complements or highly differentiated and when competition is a la Cournot rather than a la Bertrand.

On the uniqueness of Groves mechanisms and the payoff equivalence principle

Consider a standard mechanism design setting with quasi-linear preferences and private valuations. From Holmström (1979), we know that if the valuations are smooth with respect to types then any efficient, dominant strategy mechanism is in the class of Groves mechanisms. Here I show that, given regular assumptions on the primitives of the design problem, a weaker condition that includes the case of non-smooth valuations is sufficient and necessary for the uniqueness of Groves mechanisms among all efficient, dominant strategy mechanisms. This condition, which imposes a restriction on the behavior of the one-sided directional derivatives of the valuation functions with respect to individual types, is also shown to be sufficient and necessary to obtain the Payoff Equivalence principle for dominant strategy mechanisms whose choice rules are affine maximizers.

Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems

A set of agents with possibly different waiting costs have to receive the same service one after the other. Efficiency requires to maximize total welfare. Fairness requires to treat equal agents equally. One must form a queue, set up monetary transfers to compensate agents having to wait, and not a priori arbitrarily exclude agents from positions. As one may not know agents' waiting costs, they may have no incentive to reveal them. We identify the only rule satisfying Pareto-efficiency, equal treatment of equals in welfare or symmetry, and strategy-proofness. It satisfies stronger axioms, as no-envy and anonymity. Further, its desirability extends to related problems. To obtain these results, we prove that a rule, single-valued or not, satisfies queue-efficiency and strategy-proofness if and only if it always selects efficient queues and sets transfers à la Groves [Groves, T., 1973. Incentives in teams. Econometrica 41, 617–631]. This holds in other problems, provided the domain of quasi-linear preferences is rich enough.

Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness

Hedonic pricing with quasi-linear preferences is shown to be equivalent to stable matching with transferable utilities and a participation constraint, and to an optimal transportation (Monge-Kantorovich) linear programming problem. Optimal assignments in the latter correspond to stable matchings, and to hedonic equilibria. These assignments are shown to exist in great generality; their marginal indirect payoffs with respect to agent type are shown to be unique whenever direct payoffs vary smoothly with type. Under a generalized Spence-Mirrlees condition (also known as a twist condition) the assignments are shown to be unique and to be pure, meaning the matching is one-to-one outside a negligible set. For smooth problems set on compact, connected type spaces such as the circle, there is a topological obstruction to purity, but we give a weaker condition still guaranteeing uniqueness of the stable match.

Bailey's Measure of the Welfare Costs of Inflation as a General‐Equilibrium Measure

Lucas (2000) has shown that Bailey's formula for the welfare costs of inflation can be regarded as an approximation to the general‐equilibrium measures that emerge from the Sidrauski and the shopping‐time models. In this paper we show that Bailey's measure can be exactly obtained in the Sidrauski general‐equilibrium framework under the assumption of quasilinear preferences. The result, based on whether or not wealth effects are incorporated into the analysis, is also helpful in clarifying why Lucas' measure derived from the Sidrauski model turns out to be an upper bound to Bailey's. Two examples are used to illustrate the main conclusions.

Trade and Child Labor: A General Equilibrium Analysis

This paper augments the existing literature on trade and child labor by exploring the effects of terms of trade changes in the context of a three good general equilibrium model, where one of the goods is a non-traded good. We find that under quasi-linear preferences the effect of the terms of trade on child labor depends critically on the pattern of substitutability (or complementarity) in the excess demand functions between the export good and the non-traded good. We extend the analysis to the case of homothetic preferences and find that the basic result is somewhat modified in a context where the marginal utility of income is affected by the terms of trade. We also extend the analysis to the case where factors move freely between the three goods as in a Heckscher-Ohlin type framework. Finally, we show that a balanced budget policy of taxing the education of skilled families and subsidizing the education of unskilled families must reduce child labor without any impact on aggregate welfare.

Consumer' Surplus, Fundamental Welfare Theorems and Revealed Preference Approach

Modern mainstream economics teach us that Marshallian consumer surplus concept can be correctly applied only in the special case of quasilinear preferences (when price of numeraire is normalized to unity), which is never observed in reality. Our paper shows the opposite: we can every time correctly apply individual and aggregate Marshallian surplus approach for the general class of differentiable preferences along subset of monotonous and piecewise monotonous parameterizations. Aggregate generalized consumer surplus - change in the sum of all consumers' incomes and net surpluses - is identically equal to the change in efficient social welfare function, if level of efficient social welfare is changing (piecewise) monotonously along adjustment path. Fundamental welfare theorems are proposed to generalization for potential application of aggregate Marshallian surplus measures and the relation between aggregated revealed preference approach, Coase' theorem, fundamental welfare theorems and representative consumer' approach is discussed.

PUBLIC GOOD PROVISION AND THE COMPARATIVE STATICS OF OPTIMAL NONLINEAR INCOME TAXATION*

Comparative static properties of the solution to an optimal nonlinear income tax problem are provided for a model in which the government both designs an income tax schedule for redistributive purposes and provides a public good optimally. There are two types of individuals, distinguished by their skill levels, who have the same quasilinear preferences for labor supply and the consumption of a private and a public good. Comparative statics are obtained for the weights in a weighted utilitarian social welfare function, the prices of the two goods, a taste parameter that measures the onerousness of working, and the skill levels.

Optimal Insurance with Adverse Selection

We solve the principal-agent problem of a monopolist insurer selling to an agent whose riskiness (chance of a loss) is private information, a problem introduced in Stiglitz (1977)'s seminal paper. We prove several properties of optimal menus: the highest type gets full coverage (efficiency at the top), all other types are underinsured (downward distortions elsewhere), the contract is non-negative and there are always gains to trade. The main novelty here is that we prove these basic properties for an arbitrary type distribution using elementary arguments. We also prove a new comparative static result for wealth effects, showing that the principal always prefers an agent facing a larger loss, and a poorer one if the agent's risk aversion decreases with wealth. We then specialize to the case of a continuum of types distributed according to an smooth density. We give sufficient conditions for complete sorting, exclusion, and quantity discounts. Our most surprising result is that, under two mild assumptions-log-concavity of the density and decreasing absolute risk aversion for the agent-the optimal premium is backwards-S shaped in the amount of coverage, first concave, then convex (a shape consistent with global quantity discounts). We contrast our results with the standard monopoly model with private values and quasilinear preferences and with competitive insurance models. We calculate a closed form solution for the CARA case and use it to illustrate these differences. Although we focus on the monopoly insurance problem, our proofs can be adapted to other screening problems with wealth e ffects and common values.