Optimal population size and endogenous growth

"Many applications in economics require the selection of an objective function which enables the comparison of allocations involving different population sizes. The two most commonly used criteria are the Benthamite and the Millian welfare functions, also known as classical and average utilitarianism, respectively. The former maximizes total utility of the society and thus represents individuals, while the latter maximizes average utility and so represents generations. Edgeworth (1925) was the first to conjecture, that the Benthamite principle leads to a larger population size and a lower standard of living.... The purpose of this paper is to examine Edgeworth's conjecture in an endogenous growth framework in which there are interactions between output and population growth rates. It is shown that, under conditions that ensure an optimum, the Benthamite criterion leads to smaller population and higher output growth rates than the Millian."     

Recognizing progeny in the value of life

This note generalizes the value of life to incorporate the preferences for descendants of a dynastically altruistic decision-maker. It derives the value of progeny and shows how it depends on the Benthamite vs. Millian nature of dynastic altruism.     

Millian Efficiency with Endogenous Fertility

Should governments implement policies that affect fertility decisions on efficiency grounds? What is the correct notion of efficiency to use? To address these issues, this paper develops an extension of the notion of Pareto efficiency, referred to as Millian efficiency , to evaluate symmetric allocations in an overlapping generations setting with endogenous fertility. This extension is based on preferences of those agents who are actually alive, and exclusively allows for welfare comparisons of symmetric allocations. First, we provide necessary and sufficient conditions to determine whether an allocation is Millian efficient or not, and we show that the sufficient conditions for dynamic efficiency offered by Cass (1972) and Balasko and Shell (1980) cannot be directly applied when fertility decisions are endogenous. Second, we characterize Millian efficient allocations as the equilibria of a decentralized price mechanism, and we present a sufficient condition for dynamic efficiency that uses the sequence of prices associated to such decentralized equilibria. Finally, we analyse how intergenerational policies should be designed to restore efficiency and achieve net welfare gains in two different settings in which markets yield inefficient allocations: dynamic inefficiencies and financial market incompleteness regarding human capital. In the former, a pay-as-you-go social security system eliminates dynamic inefficiencies, provided pensions are explicitly linked with fertility decisions. In the latter, a specific link between social security and public education becomes a necessary condition for Millian efficiency.     

Optimal Taxation with a Trade-off Between Income and Children

This paper explores the implications of endogenous fertility for optimal redistributive taxation in the presence of a trade-off between labour income and children. The labour supply is a decreasing function of the desired quantity and quality of children. Since children enter into the parent's budget constraint in a nonlinear form, their shadow prices are directly distorted by the income tax rate. It is shown that the substitution effects of the income tax rate on the quantity and quality of children cannot be signed uniquely although the effect on labour supply is negative. The aggregate substitution effect of the income tax rate on the quantity of children plays an important role in the determination of the signs of the income tax and child subsidy rates at a Rawlsian or Benthamite social welfare optimum.
JEL Classification Numbers: H21, J13, J22     

The optimum population and growth: a new look; a modification to include a preference for children in the welfare function

An econometric model is proposed whereby optimum population levels can be defined. An optimum population is less than the maximum and varies according to several factors. The static optimum population which determines optimum solely by per capita income is inadequate since any level of welfare can always be increased by merely reducing the population. Other conditions for figuring social welfare must be used. A dynamic optimum population must be figured on the basis of such factor s as a preference for leisure or for open spaces. The prediction of optimum population levels is useful for the formulation of social policy.     

On the impossibility of complete Non-Interference in Paretian social judgements

We study a principle of ‘Non-Interference’ in social welfare judgements. Non-Interference captures aspects of liberal approaches (particularly a Millian approach) to social decision making. In its full generality, Non-Interference produces an impossibility result: together with Weak Pareto Optimality, it implies that a social welfare ordering must be dictatorial. However, interesting restricted versions of Non-Interference are compatible with standard social welfare orderings.     

Optimal Income Taxation and International Labour Mobility

This paper considers how a linear income tax should be set optimally when individuals are internationally mobile. The optimum tax analysis is founded on a social welfare function where each individual counts in the social welfare according to residence time in the home country. The discussion of the optimal income tax is organized from two perspectives. The first relates to the optimum income tax when a uniform lump sum transfer is used, while the second concerns the optimal rate of tax when a transfer is used which depends on time of residence in the taxing jurisdiction.     

Equitable and Efficient Federal Structures with Decentralized Leadership,Spillovers, and Attachment of Heterogeneous Labor

Relying on differentiability assumptions and on conditions that guarantee interior solutions, we show that a federation featuring decentralized leadership, interregional spillovers, and labor attachment allocates resources efficiently under two sets of circumstances. The first is when the center is Rawlsian. The second is when individual utilities are quasi‐linear, regional welfare functions are Benthamite, and the center's objective function is a Bergson–Samuelson transformation of regional welfare levels, which also satisfies conditions needed for the center to view regional welfare levels as normal goods. In both sets of circumstances, efficient behavior follows from incentive equivalence promoted by the center's egalitarian transfers.     

The trend of welfare disparity among subgroups of population in Australia 1983-1984 - 1993-1994

The aim of this paper is to estimate the trend of social welfare for Australia using 1983–1984, 1988–1989 and 1993–1994 Household Expenditure Survey data. The functional form of the Social Welfare Function (SWF) was derived by Sen, Degum, Yitzhaki and Shesinski (all independently). Since the function contains the Gini coefficient as the inequality parameter, it could not be formally disaggregated by subgroups of population. This paper, using a method of subgroup decomposition of the Gini coefficient developed by Podder, attempts to disaggregate the SWF. With this method it is now possible to identify disadvantaged groups by their relative shares in total welfare. In addition the method is used to determine effect of economic growth on specific subgroups, and in turn, on total social welfare. This study is based on the Australian economy. Distribution of relative shares of total social welfare among various regional groups are identified, groups determined by occupational status and groups determined by country of birth. The effect on society's welfare for a percentage change in income of a group and the trend of relative welfare of a specific group are also computed. This information can be used in a variety of social decision making situations, including cost benefit analysis.     

On Welfare Criteria and Optimality in an Endogenous Growth Model

In this paper, we explore the consequences for optimality of a social planner adopting two different welfare criteria. The framework of analysis is an overlapping generations model with physical and human capital. We first show that, when the social welfare function is a discounted sum of individual utilities defined over consumption per unit of natural labor, the precise cardinalization of the individual utility function becomes crucial for both the characterization of the social optimum and the policies that support it. Also, decentralizing the social optimum requires an education subsidy that is definitely positive, but its size depends in a determinant way on the aforementioned cardinalization. In contrast, when the social welfare function is a discounted sum of individual utilities defined over consumption per unit of efficient labor, the precise cardinalization of preferences becomes irrelevant. More strikingly, along the optimal growth path, the education subsidy is negative, i.e., the planner should tax rather than subsidize investments in human capital.     

Intergenerational transfers and the social discount rate

This paper investigates the relationship between intergenerational asset transfers and the choice of the discount rate for use in cost-benefit analysis in a model of a competitive overlapping generations economy constrained by a socially managed exhaustible resource. Provided that there are no distortions in capital markets and that all agents hold perfect foresight, cost-benefit techniques will result in a Pareto efficient resource allocation if the discount rate is set equal to the market rate of interest. But since the path of the interest rate depends on the level of intergenerational transfers, cost-benefit techniques do not ensure a socially desirable distribution of welfare between generations; a social optimum will result only if intergenerational transfers are properly chosen and enforced. Decentralized private altruism may result in intergenerational transfers that both present and future individuals would agree are too small if members of the present generation attach positive weight to the general welfare of future generations, not simply their personal descendants. In a world where intergenerational transfers are non-optimal, second-best policy-making may imply a constrained optimum that is inefficient. Together, these findings suggest that cost-benefit analysis is at best a partial criterion to policy formulation that should be used only in conjunction with ethical principles that define the proper distribution of welfare between present and future generations.     

Locational choice of AFDC recipients within California: a conditional logit analysis

This paper examines factors that influence migration of AFDC recipients within California. A county level conditional logit model is used to analyze the impact of cost adjusted benefits on intrastate moves during recipients’ first year of welfare participation. Costs of living, particularly housing costs, differ considerably across counties of California, yet the welfare benefit is set at the state level. This creates the potential for variation in the purchasing power of the welfare benefit if a family chooses to move. Variation in cost of living is shown to have a significant effect on migration patterns of AFDC recipients. Estimates suggest that a $150 decrease in fair market rent results in 15% more migration to the county. Recipients’ migration is more responsive to cost of living than migration of the general population.     

Labor Mobility, Trade, and Social Capital

Labor market integration raises welfare in the absence of distortions. This paper examines labor and goods market integration in a general‐equilibrium model with social capital. The findings are: (i) labor market integration has an ambiguous impact on welfare, and raises it if the goods and labor skills are sufficiently different; (ii) compared to Pareto optimum, labor mobility (social capital) is excessively large (depleted); (iii) trade is superior to labor market integration if trading costs are no higher than private migration costs, otherwise the outcome is ambiguous; and (iv) the creation of new institutions in response to labor market integration has an ambiguous impact on welfare.     

Allowing disagreement in evaluations of social welfare

There is no consensus on how to measure interpersonally comparable, cardinal utility. Despite of this, people repeatedly make welfare evaluations in their everyday lives. However, people do not always agree on such evaluations, and this is one important reason for political disagreements. Thus, to keep in control of the normative premises, decision makers may prefer information which can be used as input to an arbitrary social welfare function to information which is the output from a social welfare function specified by the analyst. In this paper we try to identify and simplify sufficient welfare indicators; information which enables decision makers to arrive at welfare evaluations of social states or projects, according to their own ethical beliefs. Our conclusion is that providing factual information about different population groups, their social state, size, and characteristics, may be better for this purpose than the more traditional approach of focusing on ordinal utility information.     

On the concept of optimum population

The economic welfare of a community is affected by policies that determine both the rate of capital accumulation and the rate of growth of population. The optimum size of population at any point is time will depend on the size of the existing capital stock and the optimum rate of savings will depend on the existing number of people. Consequently, in this sense, a population policy cannot be developed without a concurrent savings policy. The criterion of optimality that will be used is the ma ximization of the total discounted welfare of all generations from now to infinity. The problem will be to select that rate of savings and that size of population at every moment which will achieve this maximum welfare if, in fact, a maximum exists. An inquiry is made into the existence of an optimum policy under various circumstances. An attempt is made to evaluate the consequences of various ethical beliefs.     

Sharing the Cost of a Public Good without Subsidies

We study the construction of a social ordering function for the case of a public good financed by contributions from the population. We extend the analysis of Maniquet and Sprumont (2004) to the case when cost shares cannot be negative, i.e., agents cannot receive subsidies from others. We adapt the Maniquet–Sprumont defense of public good welfare egalitarianism to this context. Weakening their Free Lunch Aversion axiom and adding a continuity requirement allows us to characterize the public good welfare maximin social ordering function.     

Fair welfare maximization

We consider the general problem of finding fair constrained resource allocations. As a criterion for fairness we propose an inequality index, termed “fairness ratio,” the maximization of which produces Lorenz-undominated, Pareto-optimal allocations. The fairness ratio does not depend on the choice of any particular social welfare function, and hence it can be used for an a priori evaluation of any given feasible resource allocation. The fairness ratio for an allocation provides a bound on the discrepancy between this allocation and any other feasible allocation with respect to a large class of social welfare functions. We provide a simple representation of the fairness ratio as well as a general method that can be used to directly determine optimal fair allocations. For general convex environments, we provide a fundamental lower bound for the optimal fairness ratio and show that as the population size increases, the optimal fairness ratio decreases at most logarithmically in what we call the “inhomogeneity” of the problem. Our method yields a unique and “balanced” fair optimum for an important class of problems with linear budget constraints.     

Discounting and welfare evaluation of policies

We start with the premise that if policy discounting is to have any welfare relevance, one has to accept it being a derivative of a social welfare function (SWF). We show that if that derivative is to have a net present value (NPV) form, then the baseline allocation must be stationary. In addition, we show that at a stationary baseline in an overlapping generations growth economy, the intergenerationally fair discount rate equals the growth rate of per‐capita consumption, which is, roughly, 2% for the United States. This differs from the interest rate, even in the golden rule equilibrium, unless population growth is null. The last result is based on the main theorem in Mertens and Rubinchik (2012) and is demonstrated for a policy space that might naturally arise in applications.     

The theory of reform and indian indirect taxes

Given a set of value judgements, an initial state, and a model of the economy, one can ask whether some feasible tax change would increase welfare. We do this by defining the marginal cost in terms of welfare of raising an extra rupee from the ith good. The inverse optimum problem is the calculation of non-negative welfare weights on households which imply that the initial state is optimum. If no such welfare weights exist, then a Pareto improvement is possible. We illustrate the concepts and results using data from the Indian economy for 1979–1980. Directions of tax reform for a number of specific social welfare functions and for Pareto improvements are presented.     

Immigration and remittances in a two-country model of growth with labor market frictions

We present a North-South model with labor market frictions and labor migration to study the dynamic implications of workers mobility on employment, capital accumulation and welfare. In the baseline model, the Northern country is able to control immigration flows by setting a cap on the number of foreign workers. We find that, despite an increase in migration displaces native employment in the short-run, a permanent raise of the migration cap stimulates capital accumulation, improves labor market conditions and increases social welfare in the long run. In an extension of the model, we also test the long-run effects of a pro-employment protectionist policy consisting in imposing a distortionary tax on immigrant employment. We find that the protectionist policy in North, while increasing national welfare, damages the macroeconomic performance of the domestic economy and is not effective in improving native employment.