Utilitarian Optimum Research Articles

Fair and Truthful Giveaway Lotteries

We consider a setting where a large number of agents are all interested in attending some public resource of limited capacity. Attendance is thus allotted by lottery. If agents arrive individually, then randomly choosing the agents – one by one - is a natural, fair and efficient solution. We consider the case where agents are organized in groups (e.g. families, friends), the members of each of which must all be admitted together. We study the question of how best to design such lotteries. We first establish the desired properties of such lotteries, in terms of fairness and efficiency, and define the appropriate notions of strategy proofness (providing that agents cannot gain by misrepresenting the true groups, e.g. joining or splitting groups). We establish inter-relationships between the different properties, proving properties that cannot be fulfilled simultaneously (e.g. leximin optimality and strong group stratagy proofness). Our main contribution is a polynomial mechanism for the problem, which guarantees many of the desired properties, including: leximin optimality, Pareto-optimality, anonymity, group strategy proofness, and adjunctive strategy proofness (which provides that no benefit can be obtained by registering additional - uninterested or bogus - individuals). The mechanism approximates the utilitarian optimum to within a factor of 2, which, we prove, is optimal for any mechanism that guarantees any one of the following properties: egalitarian welfare optimality, leximin optimality, envyfreeness, and adjunctive strategy proofness.

Behavioural utilitarianism and distributive justice

What are the distributive implications of utilitarianism? Is it compatible with a concern for equality, as many utilitarians have argued? We analyse these questions in the context of a pure allocation problem. We consider an infinitely-lived economy and, drawing on the behavioural literature, assume that individuals have reference-dependent preferences: agents’ utility is a function of current consumption and a reference point which captures consumption habits, or the agents’ upbringing. Assuming a history of inequalities in consumption, we show that the utilitarian allocation is equalising: starting from an unequal distribution, inequalities decrease over time at the utilitarian optimum. However, even though agents are in a relevant sense identical, equality does not obtain at any finite time.

Voting over selfishly optimal tax schedules: Can Pigouvian tax redistribute income?

AbstractThis paper studies pairwise majority voting over selfishly optimal nonlinear income tax schedules proposed by a continuum of individuals who differ in privately observable skills and make consumption comparisons, which creates a negative positional externality. It shows that the tax schedule preferred by the median skill type will win the voting contest. Given a reference consumption defined as the average consumption in the population, all skills face the same Pigouvian tax rate in the utilitarian optimum, whereas in selfish optima high skills face a Pigouvian tax rate larger than that facing low skills, generating a novel income redistributive effect. Under a constant elasticity of labor supply, two more results are obtained. First, for Pareto, Champernowne, Weibull, and lognormal skill distributions, the selfishly optimal tax schedule facing high (low) skills tends to be more progressive when the bottom‐skill's (top‐skill's) status concern intensifies. Second, it identifies the conditions under which, in the voting equilibrium, high skills face higher marginal tax rates while low skills face lower ones than what they face in the utilitarian optimum.

Voting for Experimentation: A Continuous Time Analysis

This paper uses a laboratory experiment to analyze how a group of voters experiment with a new reform. The experiment implements the continuous time Strulovici (2010) collective experimentation model. I analyze a subset of data where groups and single decision makers should eventually prefer to stop experimentation and abandon the reform. I find three results that are consistent with the modeled experimentation incentives. In this subset of data, groups stop experimentation earlier than single decision makers, wait longer to stop experimentation as the number of revealed winners increases, and stop experimentation earlier than the utilitarian optimum predicts. However, I also find that both groups and single decision makers stop experimentation earlier than predicted. Additional treatments show that this result is unlikely to be explained by standard explanations such as incorrect belief updating or risk aversion.

Rawlsian versus Utilitarian: Teachers' Incentives and the Distribution of Student Performance

By using the test score of the least able student in a classroom as the objective function (Rawlsian optimum), this paper examines the implications for teachers' incentives and compares them with the objective that uses the average test score of all the students in a classroom (utilitarian optimum). We show that for certain human-capital production functions and teachers' effort cost functions, the Rawlsian optimum yields at least the same average human capital as the utilitarian optimum, but that the resulting distribution of human capital under the former is more equitable than that under the latter.

Pollution, unequal lifetimes and fairness

This paper characterizes the optimal level of pollution in a two-period OLG economy where pollution deteriorates survival conditions. We compare two long-run social optima: on the one hand, the average utilitarian optimum, where the long-run average well-being is maximized, and, on the other hand, the ex post egalitarian optimum, where the realized well-being of the worst-off at the stationary equilibrium is maximized. It is shown that the ex post egalitarian optimum involves, under weak conditions, a higher level of pollution in comparison with the utilitarian optimum. This result is robust to introducing health expenditures in the survival function. Finally, we examine the decentralization of those two social optima, and we compare the associated optimal taxes on capital income aimed at internalizing the pollution externality.

Resource conservation across generations in a Ramsey–Chichilnisky model

The Chichilnisky criterion is an explicit social welfare function that satisfies compelling conditions of intergenerational equity. However, it is time inconsistent and has no optimal solution in the Ramsey model. By investigating stationary Markov equilibria in the game that generations with Chichilnisky preferences play, this paper shows how, nevertheless, this criterion can be practically implemented in the Ramsey model, leading to attractive consequences. The time-discounted utilitarian optimum is the unique equilibrium path with a high-productive initial stock, implying that the weight on the infinite future in the Chichilnisky criterion plays no role. However, this part of the Chichilnisky criterion may lead to more stock conservation than the time-discounted utilitarian optimum with a low-productive initial stock. Based on the notion of von Neumann–Morgenstern abstract stability, we obtain uniqueness by assuming that each generation coordinates on an almost best equilibrium and takes into account that future generations will do as well.

Optimal Margins and Equilibrium Prices

We study the interaction between contracting and equilibrium pricing when risk- averse hedgers purchase insurance from risk-neutral investors subject to moral hazard. Moral hazard limits risk-sharing. In the individually optimal contract, margins are called (after bad news) to improve risk-sharing. But margin calls depress the price of investors' assets, affecting other investors negatively. Because of this fire-sale externality, there is too much use of margins in the market equilibrium compared to the utilitarian optimum. Moreover, equilibrium multiplicity can arise: In a pessimistic equilibrium, hedgers who fear low prices request high margins to obtain more insurance. Large margin calls trigger large price drops, confirming initial pessimistic expectations. Finally, moral hazard generates endogenous market incompleteness, raises risk premia, and induces contagion between asset classes.

The Political Economy of Migration Enforcement: Domestic Versus Border Control

We study migration policy enforcement by an elected government. The policy-maker faces uncertainty on the supply of migrants, but has more information than the public on its preferences and the extent and effectiveness of its enforcement activities. We show that a utilitarian government preferring more migrants than the majority may find it optimal to set a restrictive target to please the median voter, while relaxing its enforcement to admit more foreigners in a concealed way. Lax enforcement may be achieved either by deploy- ing inadequate resources on cost–effective activities (domestic enforcement) or by allocating a larger budget on less effective tools (border enforcement). The attractiveness of one in- strument over the other depends on the size of the immigrant flow: if the supply is large, border enforcement might be preferred because, although more costly, it brings the number of migrants closer to the utilitarian optimum. Hence, re–election concerns might provide a rationale for the widespread use of less a effective enforcement tool, such as border control.

Collective action and the common enemy effect

How is collective defence by players affected when they face a threat from an intelligent attacker rather than a natural threat? This paper analyses this question using a game-theoretic model. Facing an intelligent attacker has an effect if players move first and visibly set their defence strategies, thereby exposing any players who do not defend, and if the attacker is, moreover, not able to commit to a random attack. Depending on the parameters of the game, the presence of an intelligent attacker either increases the probability that players jointly defend (where such joint defence either does or does not constitute a utilitarian optimum), or decreases the probability that players jointly defend (even though joint defence is a utilitarian optimum).

'Pay for Percentile': Rawlsian vs. Utilitarian

This paper compares the Rawlsian and the Utilitarian optimums in the Barlevy and Neal (2012) model. Our results suggest that, while both the Rawlsain optimum and the Utilitarian optimum yield the same average human capital, the resulting distribution of human capital under Rawlsian optimum is more equitable than that under the Utilitarian optimum. Furthermore, we show that a modi fied tournament-based incentive payment scheme is incentive compatible and can induce the teachers to allocate Rawlsian socially optimal levels of e ffort to all students.

Fair Accumulation under Risky Lifetime

AbstractIndividuals save for their old days, but not all of them enjoy the old age. This paper characterizes the optimal capital accumulation in a two‐period OLG model where lifetime is risky and varies across individuals. We compare two long‐run social optima: (1) the average utilitarian optimum, where steady‐state average welfare is maximized; (2) the egalitarian optimum, where the welfare of the worst‐off at the steady‐state is maximized. It is shown that, under plausible conditions, the egalitarian optimum involves a higher capital and a lower fertility than the utilitarian optimum. Those inequalities hold also in a second‐best framework where survival conditions are exogenously linked to the capital level.

Intergenerational externalities, sustainability and welfare—The ambiguous effect of optimal policies on resource depletion

This paper studies an endogenous growth model with exhaustible resources, overlapping generations and human capital externalities. In the competitive equilibrium, selfish behavior and inefficient skills accumulation may prevent sustained growth. Implementing the utilitarian optimum likely induces sustainability via increased knowledge formation, but resource depletion may be faster or slower than under laissez-faire depending on the social discount rate. Heavy (modest) social discounting delays (anticipates) the achievement of net welfare gains for newborn agents and successors. The reason is that human capital accumulation magnifies the positive growth effects of policies that lower the rate of resource destruction, preserving the welfare of newborn agents. Resource-depleting policies, instead, hamper growth and reduce lifetime welfare of early-in-time generations—the first loser being the currently young.

Optimal linear taxation under endogenous longevity

This paper studies the optimal linear tax-transfer policy in an economy where agents differ in productivity and in genetic background and where longevity depends on health spending and genes. If agents internalize imperfectly the impact of health spending on longevity, the utilitarian optimum can be decentralized with type-specific lump-sum transfers and Pigouvian taxes correcting for agents’ myopia and for their misperception of health spending’s effects on the economy’s resources. The second-best problem is examined under linear taxation instruments. It may be optimal to tax health spending, especially under complementarity of genes and health spending in the production of longevity.

Optimal tax policy and expected longevity: a mean and variance utility approach

This paper studies the normative problem of redistribution between agents who can influence their survival probability through private health spending, but who differ in their attitude towards the risks involved in the lotteries of life to be chosen. For that purpose, a two-period model is developed, where agents’ preferences on lotteries of life can be represented by a mean and variance utility function allowing, unlike the expected utility form, some sensitivity to what Allais (Econometrica 21(4), 503–546, 1953) calls the ‘dispersion of psychological values’. It is shown that if agents ignore the impact of health spending on the return of their savings, the decentralization of the first-best utilitarian optimum requires intergroup lump sum transfers and group-specific positive taxes on health spending. Under asymmetric information, a differentiated taxation across agents is still required, but subsidizing health spending may be optimal as a way to solve the incentive problem.

Long-standing influenza vaccination policy is in accord with individual self-interest but not with the utilitarian optimum.

Influenza vaccination is vital for reducing infection-mediated morbidity and mortality. To maximize effectiveness, vaccination programs must anticipate the effects of public perceptions and attitudes on voluntary adherence. A vaccine allocation strategy that is optimal for the population is not necessarily optimal for an individual. For epidemic influenza, the elderly have the greatest risk of influenza mortality, yet children are responsible for most of the transmission. The long-standing recommendations of the Centers for Disease Control follow the dictates of individual self-interest and prioritize the elderly for vaccination. However, preferentially vaccinating children may dramatically reduce community-wide influenza transmission. A potential obstacle to this is that the personal utility of vaccination is lower for children than it is for the elderly. We parameterize an epidemiological game-theoretic model of influenza vaccination with questionnaire data on actual perceptions of influenza and its vaccine to compare Nash equilibria vaccination strategies driven by self-interest with utilitarian strategies for both epidemic and pandemic influenza. Our results reveal possible strategies to bring Nash and utilitarian vaccination levels into alignment.

Constant savings rates and quasi-arithmetic population growth under exhaustible resource constraints

In the Dasgupta–Heal–Solow–Stiglitz (DHSS) model of capital accumulation and resource depletion we show the following equivalence: if an efficient path has constant (gross and net of population growth) savings rates, then population growth must be quasi-arithmetic and the path is a maximin or a classical utilitarian optimum. Conversely, if a path is optimal according to maximin or classical utilitarianism (with constant elasticity of marginal utility) under quasi-arithmetic population growth, then the (gross and net of population growth) savings rates converge asymptotically to constants.

Constant Savings Rates and Quasi-Arithmetic Population Growth Under Exhaustible Resource Constraints

In the Dasgupta-Heal-Solow-Stiglitz model of capital accumulation and resource depletion we show the following equivalence: If an efficient path has constant (gross and net of population growth) savings rates, then population growth must be quasi-arithmetic and the path is a maximin or a classical utilitarian optimum. Conversely, if a path is optimal according to maximin or classical utilitarianism (with constant elasticity of marginal utility) under quasiarithmetic population growth, then the (gross and net of population growth) savings rates converge asymptotically to constants.

An Overlapping Generations Model of Climate‐Economy Interactions

A numerically calibrated overlapping generations model of climate change and the world econommy is examined in this paper. In the absence of intergenerational transfers, efficient rates of greenhouse gas emissions abatement rise from 16% in the present to 25% in the long run, while mean global temperature increases by 7.4°C relative to the preindustrial norm. A utilitarian optimum, which attaches equal weight to each generation's life‐cycle utility, yields abatement rates that rise from 48% to 89%, with a long‐run temperature increase of 3.4°C. A second‐best utilitarian path, in which intergenerational transfers are by assumption institutionally infeasible, also supports stringent abatement measures.

Incremental Cost in the Convention on Biological Diversity

The Convention on Biological Diversity stipulates the principle of incremental cost for the international financing of biodiversity conservation. The international debate about the exact meaning of the concept and about its practical application focuses on the issues of baseline determination and treatment of incremental domestic benefits. This paper uses some standard tools of partial equilibrium demand analysis to illustrate theoretical solutions to the indeterminacy of the Convention. The allocation of resources resulting from an incremental cost scheme is compared with a 'domestic optimum', and with a hypothetical 'global optimum'. Regarding the behaviour of the country hosting biodiversity, a distinction is proposed between 'quantity-' and 'transfer-' taking behaviour. The issue of price distortions in the baseline is also addressed. It is shown that both the host country (H) and the Rest of the World (ROW) will have incentives for agreeing on a transfer of resources that entails only partial deduction of domestic incremental benefits. This transfer, despite failing to reach the utilitarian global optimum, still represents a Pareto improvement over the pre-convention status quo. By imposing a particular multiplicative functional form on the utility of both host and ROW, additional results can be obtained. In particular, the optimal transfer implies a clawback factor decreasing with relative income differentials, and incremental cost financing dominates the domestic optimum even when price distortions are present in the host country. If removal of price distortions is a precondition for incremental cost funding, the analysis illustrates the magnitude of incentives necessary for the host to give up the distorted baseline.