Utilitarian Welfare Function Research Articles

Life is too short to be small: an experiment on mortality salience and prosocial behavior

We study the impact of mortality salience on altruistic giving using a laboratory experiment. We primed subjects in treatment group with grid tasks and made mortality salient. We found that it made them think of things “bigger” than themselves, and therefore behaved more like maximizers of utilitarian (Coasian) welfare function. We also found that temporal discounting factor acted as the mediating variable, particularly when the price of giving was high. Furthermore, we established a structural model of the dictator game and estimated the preference parameters for each group. The significant parametric differences confirmed preference alteration as the second channel. Finally, our findings were strengthened by showing that the priming did not change subjects’ mood while it indeed alter their awareness of mortality. This paper provides implications for several research topics such as the impact of catastrophe, function of religion, and implementations of anti-corruption.

Trading Off Consumption and COVID-19 Deaths

This note develops a framework for thinking about the following question: What is the maximum amount of consumption that a utilitarian welfare function would be willing to trade off to avoid the deaths associated with COVID-19? The answer depends crucially on the mortality rate associated with the coronavirus. If the mortality rate averages 0.81%, as projected in one prominent study, our answer is 41% of one year’s consumption. If the mortality rate instead averages 0.44% across age groups, as suggested by a recent seroprevalence study, our answer is 28%.

Earthquake risk and inter-temporal fairness: An economic assessment of the national land-use structure

Population concentration in metropolitan areas is recognized not only as a factor in earthquake disaster risk, but also as a factor in economic efficiency. In other words, with regard to the geographic concentration of urban functions, there is a trade-off between a reduction in earthquake disaster risk and increased economic efficiency. This suggests that we need a coherent assessment method to enable the development of a better national land-use structure incorporating inter-temporal fairness in the context of earthquake disaster risk.In this study, the impact of the national land-use structure on social welfare is assessed while considering earthquake risk and inter-temporal fairness. The results suggest that a decentralized national land-use structure cannot be justified under the risk-neutral and utilitarian welfare function, but can be justified using a welfare function incorporating inter-temporal fairness.

Perception-theoretic Foundations of Weighted Utilitarianism

We provide a microfoundation for a weighted utilitarian social welfare function that reflects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopt utilitarian welfare functions, assuming that comparable utility functions can be calibrated, using information beyond consumer choice data. We show that consumer choice data alone are sufficient. As suggested by Edgeworth (1881), just noticeable differences (JNDs) provide a common unit of measure for interpersonal comparisons of utility differences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual JNDs.

Majority Vote on Educational Standards

The direct democratic choice of an examination standard, i.e., a performance level required to graduate, is evaluated against a utilitarian welfare function. It is shown that the median preferred standard is inefficiently low if the marginal cost of reaching a higher performance reacts more sensitively to ability for high than for low abilities, and if the right tail of the ability distribution is longer than the left tail. Moreover, a high number of agents who choose not to graduate may imply that the median preferred standard is inefficiently low even if these conditions fail.

Foundations of Weighted Utilitarianism

We provide a microfoundation for a weighted utilitarian social welfare function that reflects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are sufficient. As suggested by Edgeworth (1881), just noticeable differences provide a common unit of measure for interpersonal comparisons of utility differences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's.

INTEGRATING MARKET ALTERNATIVES INTO THE ECONOMIC THEORY OF OPTIMAL DETERRENCE

Leading economic models of crime assume that potential criminals achieve their ends by criminal means or not at all. We develop a framework in which potential criminals can also attain their objectives through voluntary trade. Our framework helps explain several features of the legal system that have proven to be problematic for the canonical approach: why optimal sanctions should be increasing in an individual's criminal history, and why necessity may be a partial defense in some situations. Finally, the inclusion of a voluntary trade option makes the maximization of a utilitarian welfare function identical to minimizing the costs of crime, implying that a long‐standing controversy in the literature is, in part, an artifact of the assumption that criminals face a binary choice set. (JEL K42, D60, H00)

The Rotten Kid Theorem and Almost Transferable Utility

We assume like Bergstrom (1989) and Dijkstra (2007) that each child's utility is treated as a normal good in the altruistic head's utility function, and show that if utility functions lead to Almost Transferable Utility children can manipulate the tradeoff between their own utility and the parent's utility through their own actions, but they have an incentive to maximize the altruistic head's utility if the altruistic head also considers children's utilities as Hicksian substitutes and hence the rotten kid theorem holds. A special class of such altruistic utility functions that treat utilities of children as normal and Hicksian substitutes are the Generalized Utilitarian Welfare functions.

Stochastic National Income

Abstract: How can national income be adjusted to indicate welfare improvement if the future is uncertain? The present paper extends the definition of national income to stochastic settings on the basis of discounted utilitarian welfare function. Real interest rate of consumption is redefined so that real national income can be interpreted as the expected present value of real interest on future national consumption. A stochastic one-good model is used to illustrate the application of the stochastic real national income. It turns out that under uncertainty real national income may be decreasing even though captial stock is constant or increasing over time.

Social Welfare and the Benefits to Crime

There exists a large literature on the optimal deterrence of crime. Within the literature, however, there exists a controversy over what the appropriate criterion to determine optimality should be. While the most popular method is that of maximization of a utilitarian welfare function, another criterion sometimes used is that of cost minimization. The controversy stems from the question of whether the benefits to crime enjoyed by criminals ought to be included in the welfare analysis. This paper argues that the controversy is an artifact of the fact that the standard model restricts a potential criminal's choice to one of committing a crime or doing nothing. We show that when potential criminals are given the additional choice of achieving their ends through voluntary methods that maximizing the sum of utilities is in fact equivalent to minimizing the costs of crime. The model developed also provides explanations for sanctions that increase in one's criminal history and why necessity may be a partial defense.

Stochastic National Income

How can national income be adjusted to indicate welfare improvement if the future is uncertain? The present paper extends the definition of national income to stochastic settings on the basis of discounted utilitarian welfare function. Real interest rate of consumption is redefined so that real national income can be interpreted as the expected present value of real interest on future national consumption. A stochastic one-good model is used to illustrate the application of the stochastic real national income. It turns out that under uncertainty real national income may be decreasing even though captial stock is constant or increasing over time.

INTERGENERATIONAL EQUITY AND THE DISCOUNT RATE FOR POLICY ANALYSIS

For two independent principles of intergenerational equity, the implied discount rate equals the growth rate of real per capita income, say, 2%, thus falling right into the range suggested by the U.S. Office of Management and Budget. To prove this, we develop a simple tool to evaluate small policy changes affecting several generations, by reducing the dynamic problem to a static one. A necessary condition is time invariance, which is satisfied by any common solution concept in an overlapping-generations model with exogenous growth. This tool is applied to derive the discount rate for cost–benefit analysis under two different utilitarian welfare functions: classical and relative. It is only with relative utilitarianism, and assuming time-invariance of the set of alternatives (policies), that the discount rate is well defined for a heterogeneous society at a balanced growth equilibrium, is corroborated by an independent principle equating values of human lives, and equals the growth rate of real per-capita income.

Social Planning with Partial Knowledge of Social Interactions

In his article, Charles F. Manski (Manski [2009]) elaborates on a topic that is familiar to economists, namely the normative question concerning which policy a social planner should implement to maximize welfare. Suppose a benevolent planner has a set of available policies 7' of which he can implement a particular policy t. Each policy affects individual outcomes for the members of society. The effectiveness of policies, the treatment response, is therefore characterized by a mapping of policies t e Τ into outcomes y(t) e Y for the different members j of the population (or the society at large), yjs(·): Τ -» Y. The treatment response can, in general, differ across the members of the population, and can also depend on the particular state of the world, s e S. Given a measure of welfare, such as a utilitarian welfare function, the planner can evaluate the effect of a policy on the population at large. Of course, in this canonical model the planner should choose the policy that maximizes social welfare and that implements the first-best allocation under the given environment.

Optimal unemployment policy in a matching equilibrium

This paper considers optimal unemployment policy in a matching equilibrium with risk averse workers and unobserved job search effort. The Planner chooses unemployment benefits, taxes and job creation subsidies to maximise a Utilitarian welfare function. Optimal policy involves a trade-off between higher employment taxes (which finance more generous unemployment benefits) and greater market tightness (which reduces the average unemployment spell). Optimal UI implies the initial UI payment equals the wage, thus ensuring consumption is smooth across the job destruction shock, and UI payments then fall with duration.

Conditional Grants, Grant-Seeking and Welfare when There is Government Failure on the Subordinate Level

The paper addresses the welfare implications of conditional grants if government failure leads to inefficiencies in the production of regional public goods and services. Conditional grants may improve welfare by setting incentives for regions to improve efficiency. At the same time, resources are wasted in the process of grant-seeking. This paper provides a theoretical model to assess the net effect on welfare. A three-stage game-theoretic context is developed and simulations are performed to derive the optimal grant-distribution scheme. We found conditional grants to be welfare-enhancing in the vast majority of simulated scenarios under a classical utilitarian welfare function. Once distributional concerns are accounted for, the scope for conditional grants becomes limited.

Designing a linear pension scheme with forced savings and wage heterogeneity

This paper studies the optimal linear pension scheme when society consists of rational and myopic individuals. Myopic individuals have, ex ante, a strong preference for the present even though, ex post, they would regret not to have saved enough. While rational and myopic persons share the same ex post intertemporal preferences, only the rational agents make their savings and labor supply decisions according to these preferences. Individuals are also distinguished by their productivity. The social objective is “paternalistic”: the utilitarian welfare function depends on ex post utilities. We examine how the presence of myopic individuals affects both the size of the pension system and the degree of redistribution it operates, with and without liquidity constraints. The relationship between proportion of myopic individuals and characteristics of the pension system turns out to be much more complex than one would have conjectured. Neither the impact on the level of pensions nor the effect on their redistributive degree is unambiguous. Nevertheless, we show that under some plausible assumptions adding myopic individuals increases the level of pension benefits and leads to a shift from a flat or even targeted scheme to a partially contributory one. However, we also provide an example where the degree of redistribution is not a monotonic function of the proportion of myopic individuals.

Designing a Linear Pension Scheme with Forced Savings and Wage Heterogeneity

This paper studies the optimal linear pension scheme when society consists of rational and myopic individuals. Myopic individuals have, ex ante, a strong preference for the present even though, ex post, they would regret not to have saved enough. While rational and myopic persons share the same ex post intertemporal preferences, only the rational agents make their savings decisions according to these preferences. Individuals are also distinguished by their productivity. The social objective is paternalistic: the utilitarian welfare function depends on ex post utilities. We examine how the presence of myopic individuals affects both the size of the pension system and the degree of redistribution it operates. The relationship between proportion of myopic individuals and characteristics of the pension system turns out to be much more complex than one would have conjectured. Neither the impact on the level of pensions nor the effect on their redistributive degree are unambiguous. Nevertheless, we show that under some plausible assumptions adding myopic individuals increases the level of pension benefits and leads to a shift from a flat or even targeted scheme to a partially contributory one. However, we also provide an example where the degree of redistribution is not a monotonic function of the proportion of myopic individuals.

Intergenerational Equity and the Discount Rate for Cost-Benefit Analysis

For two independent principles of intergenerational equity, the implied discount rate equals the growth rate of real per-capita income, say 2%, thus falling right into the range suggested by the U.S. Office of Management and Budget. To prove this, we develop a simple tool to evaluate small policy changes affecting several generations, by reducing the dynamic problem to a static one. A necessary condition is time-invariance, which is satisfied by any common solution concept in an overlapping generations model with exogenous growth. This tool is applied to derive the discount rate for cost-benefit analysis under two different utilitarian welfare functions: classical and relative. It is only with relative utilitarianism that the discount rate is well-defined for a heterogeneous society, is corroborated by an independent principle equating values of human lives, and equals the growth rate of real per-capita income.

Disability insurance and optimal income taxation

This paper studies the design of disability insurance scheme when agents differ in their privately known productivity. We extend the Diamond and Mirrlees (1978) two period model to allow for agents differing ex-ante in their productivity and characterize the optimal nonlinear tax transfer that maximizes a utilitarian welfare function when per-period earnings and age are observable while individuals’ productivity and health status are not observable. We show that the induced tax/benefit scheme should exhibit a marginal income tax that decreases with age for some agents. A marginal subsidy on the young high productive income may be desirable. While the disability scheme always involves the old low productive agents to be indifferent between working and claiming disability benefits, this result is not always true for the old high productive agents.

Social security, retirement age and optimal income taxation

It is often argued that implicit taxation on continued activity of elderly workers is responsible for the widely observed trend towards early retirement. In a world of laissez-faire or of first-best efficiency, there would be no such implicit taxation. The point of this paper is that, when first-best redistributive instruments are not available, because some variables are not observable, the optimal policy does imply a distortion of the retirement decision. Consequently, the inducement of early retirement may be part of the optimal tax-transfer policy. We consider a model in which individuals differ in their productivity and their capacity to work long and choose both their weekly labor supply and their age of retirement. We characterize the optimal non-linear tax-transfer that maximizes a utilitarian welfare function when weekly earnings and the length of active life are observable while individuals' productivity and health status are not observable.