The genuine savings criterion and the value of population

Summary. In any dynamic model of the economy with changing population, the latter should properly be one of the state variables of the system. It enters both in the maximand, at least under total utilitarianism, and into the production function in one way or another. If population growth is exponential and constant returns prevails, then a simple transformation to per capita variables can be used to eliminate one state variable, but this ceases to be true if growth is not exponential, as it obviously is not and cannot be. If the growth of population is exogenous, then introducing it into the system does not affect the optimal policy. However, if one asks whether the system is sustainable, in the sense of at least maintaining total welfare (integral of discounted utilities), then the criterion is that that the value of the rates of change of the state variables is non-negative, so that the shadow price of population becomes relevant. In this paper, we derive explicit formulas in a simple model, showing that the rate of growth of per capita capital is not the correct formula but must have another terms added to it. We also study the question under an alternative criterion of long-run average utilitarianism. Received: June 1, 2002; revised version: September 27, 2002 RID="*" ID="*"Research support was provided by the William and Flora Hewlett Foundation. An earlier version of this paper was presented at a celebration of Mordecai Kurz's 66th birthday at Stanford University, 1–3 August 2002. Correspondence to: K.J. Arrow     

Infinite-horizon competitive programs are optimal

For infinite-horizon optimal-growth problems the standard result in the literature says that a program is optimal if and only if associated with it is a sequence of present-value prices at which the program satisfies (i) a set of myopic competitive conditions, and (ii) an asymptotic transversality condition. The principal result of this paper points out the interesting and surprising fact that at least for a class of multisector models where the production side is described by a simple linear model, and there are some limiting primary factors, the competitive conditions alone characterize an optimal program.     

Patterns of Trade and Growth Under Increasing Returns: Escape from the Poverty Trap—a Comment

The paper generalizes a two-sector model of trade and growth in which the investment good sector exhibits an initial phase of increasing returns. It dispenses with the restriction that the utility function be of the isoelastic type. Allowing for general concave utility functions, it demonstrates that the qualitative properties of optimal growth and trade patterns are robust with respect to a wide choice of functional forms.
JEL Classification Numbers: O41, F12.     

Population, consumption and resources: ethical issues.

This article offers several models that test concepts of optimum population and consumption: classical or utilitarian models, contractual models, and generation-relative ethical models. This article is based on a lecture presented in August 1995, at a conference organized by the Swedish Collegium for Advanced Study in the Social Sciences. It is posited that classical utilitarianism casts the optimum population and consumption problem as a Genesis Problem. The authors argue that the Genesis problem is the wrong problem to study because there are no actual people. The Genesis problem asks how many people there ought to be ideally at what living standards. The unborn are not a class of people, just as mud on a river bank is not a mud hut. Actual persons and potential persons are categorically different. Actual persons have a claim that potential persons do not have. An overall ethical ordering over alternatives can only be conceived for each generation of actual people. The ethical point of view inevitably changes over time. For example, a generation in the first period consumes what they are given to consume by the older generation. In the second period, the younger generation is now the older generation who decide how many children to have and how to share nonstorable, all purpose consumption goods among themselves and future generations. Procreation is a means of making one's values durable. Human development is unfair. Those who live later benefit from the labor of their predecessors without paying the same price. Procreation and ecological preservation are a matter of ethics.     

Consistent firm choice and the theory of supply

Summary. This paper analyzes the problem of deriving predictions, regarding supply behavior of a competitive firm, from prior consistency postulates about input-output choices made by such a firm. It extends the literature by introducing a consistency postulate for firm choice, which is weaker than profit-maximization. This consistency postulate is nevertheless both necessary and sufficient for supply responses predicted by the standard theory of firm choice based on the postulate of profit-maximization. Furthermore, our rationality postulate, in conjunction with another condition, is shown to be equivalent to firm choice behavior that can be rationalized in terms of profit maximization.Received: 11 April 2003, Revised: 26 April 2004, JEL Classification Numbers: D21.Indraneel Dasgupta: I thank Bhaskar Dutta and two anonymous referees for helpful comments on earlier versions.     

Contents Volume 24 2003

Volume Contents

Contents Volume 24 2003     

Managerial risk-taking incentives, product market competition and welfare

Managers’ compensation may increase with the variance of the firm's profits. This paper investigates how this affects their choice of strategic variables, and how that affects managerial compensation. The social welfare aspects of this interaction are analyzed in a duopoly setting with uncertain linear demand and linear marginal cost. Compared to a situation in which the managers’ compensation does not depend on the variance of profits, social welfare may be either higher, lower, or remain unaffected, depending on the slope of the marginal cost curve and whether the competing firms produce goods that are demand substitutes or complements.     

Lindahl Pricing, Nonrival Infrastructure, and Endogenous Growth

The paper constructs a model of endogenous growth where infrastructure is an accumulable stock generating a nonrival input service. A typical market economy cannot attain the socially optimum steady state path, since nonrivalry precludes competitive pricing of infrastructure. However, there exist agent specific prices for the infrastructural service, a price for the infrastructural stock, a rate of interest, and a subsidy for the representative household that can sustain the optimal path as a dynamic Lindahl equilibrium. The rates of return from physical and infrastructural capital equal the rate of interest. Investment programs are socially optimum. The government's budget is balanced.