Analysis of the relationship between age and economic activities may be approached from the standpoint of the individual undergoing aging or from that of the manner in which the behavior of the older segment of the population differs from that of the younger segment. The former approach reveals how the economic behavior of an individual changes as he grows older. The latter approach directs attention to the collective economic behavior of older segments of a population, contrasts their behavior with that of younger segments of the population, and inquires into macroeconomic effects of population aging. In this chapter we deal with the former or life-cycle approach; in other chapters we deal with economic behavior characteristics of older segments of populations. Although the life-cycle approach concentrates upon stages in the life of an individual and the interrelation of these stages, information yielded by the life-cycle approach contributes to an understanding of the group behavior and characteristics of older segments of a population – that is, to macroeconomic aspects of population aging.

Economic stages of human development

During their lives, individuals pass through a series of economic, social, and physiological stages that both influence and reflect their consumption and labor-supply activities (Brennan et al.; Woytinsky). The economics of aging includes explicit recognition of effects associated with change in functional capacity as an individual matures and declines, together with its significance for the social framework of a population (e.g., see Botwinick). Moreover, income transfers and tax liabilities which constitute a significant proportion of lifetime income usually vary with age.

Applying labor supply models to older workers

Questions concerning the supply of labor by an individual have been fertile ground for economic researchers since Adam Smith (Spengler). The standard presentation of individual labor-supply decision making evolved through, among other studies, a paper by Lionel Robbins, John Hicks's explication of income-substitution effects in Value and Capital, and a family-context framework formulated by Marvin Kosters. This analysis presents an individual with a constrained maximization problem where, subject to a resource constraint, he attempts to maximize his utility function which includes income and leisure. (Graphic expositions can be found in Fleisher, pp. 38–51, and Rees, pp. 22–4; for a formal presentation, see Henderson and Quandt, pp. 29–37.) Becker provided a framework for examining the allocation of time between market work and home production (i.e., value is placed on hours away from market activity because of the home-produced goods that are generated). More recently, Heckman and Sadik and Johnson, have expanded the time-allocation model to include home production, market work, and investment in human capital over the life cycle.

The most appropriate framework in which to examine the retirement decisions in late life is the life-cycle concept. Many of the factors that influence the withdrawal from the labor force are a function of prior economic decisions. Thus, retirement should be viewed as one of the many resource-allocation decisions that an individual faces throughout life; however, only the most recent theoretical and empirical research has formulated the labor-supply choices of older workers in the life-cycle framework.

In Chapters 2–9 we have reviewed the literature bearing upon economic and related consequences of population aging and its causes – a phenomenon that, according to Sauvy, tended to escape notice despite its obviousness. The tendency toward population aging will be accentuated should fertility descend below the replacement level or should a “gerontic revolution” get under way. Whether a decline in a nation's fertility and eventually in its population in conjunction with further population aging constitutes a serious economic problem turns on “the capacity of our societal institutions to cope with the changes that can be anticipated” and realize the potential advantages of a longer life (see Myers).

Fertility is currently below the replacement level in a number of highly developed countries, according to the United Nations Demographic Yearbook. Among these countries in 1973–4, besides Canada, Japan, and the United States, were Austria, Belgium, Denmark, England and Wales, Finland, both Germanies, Netherlands, Scotland, Sweden, and Switzerland. Should fertility persist at these levels, the age composition will include more persons over 65 than would a corresponding stationary population.

Should life expectancy at higher ages increase, the fraction of the population 65 and over would increase somewhat. For example, in the ultimately stationary population projected for the United States made in 1975, the median age would be 37.8 years, with 17.05 percent 65 and over and 58.93 percent aged 18–64 years. As a result mainly of the upward adjustment of anticipated life expectancy in the stationary population, projections constructed in 1977 illustrate further population aging in the future stationary state (U.S. Bureau of the Census, July 1977, pp. 1–11).

Our concern here is how the economic behavior and productivity of an economy respond to population aging; that is, to increases in the relative number of older persons – those 65 and over. As a population ages owing to the decline of fertility and its approach to the replacement level, both the relative number of persons aged 18–64 and that of those over 64 increase, the latter more rapidly (in the absence of echo effects), until the age composition becomes stable and the ratio of those 65 and over to those aged 18–64 becomes stationary. With the population stationary and stable, the ratio of those aged 18–64 to the total population will fall roughly within a range of 0.58 to 0.6, and, given entry into the labor force at age 18 and withdrawal at age 65, per capita potential productivity will be in the neighborhood of a maximum. Of course, given considerable deferment of retirement beyond 64, potential productivity will be higher.

Even given fertility slightly below the replacement level, the fraction of a population aged 18–64 may remain little affected. Under these circumstances, however, two adverse effects may be experienced. First, dependency cost per capita increases insofar as cost per dependent over 65 exceeds that per dependent under 18. Second, output per person aged 18–64 will be somewhat lower if productivity per worker is lower among those over 55 or 60 than among those younger. This decline occurs because a larger fraction of those 18–64 will be over 55 or 60 in a population based on fertility below the replacement level than in a stationary or growing population.

The economic well-being of the elderly has been the focus of considerable public debate during the past two decades in most developed countries. The standard of living attainable by the aged differs from country to country and is determined in part by the national per capita income, government transfers to the elderly, and the propensity and ability of older persons to continue to work. The international commitment to the income support of the elderly through social security systems is noted in Chapter 8, whereas the following discussion outlines the absolute and relative economic position of older Americans through an examination of currently available data and research assessing the economic status of the aged. This analysis should be considered as illustrative of worldwide changes in the sources and patterns of income of the elderly. Although the American experience is not fully comparable to that of other nations, this examination does indicate the effects of a maturing national pension system and the decline in labor-force participation of the elderly. Of course, many problems such as inflation transcend institutional frameworks and international boundaries.

Income of the aged

The number of individuals 65 and over with incomes below the Social Security Administration's poverty level declined from 5.5 million in 1959 to 3.3 million in 1976, a reduction in the proportion of the nation's elderly below this poverty index from 35.2 to 15.0 percent. The decline in the poverty rate of the aged families was even more pronounced, falling from 27 to 8 percent during this period (U.S. Bureau of the Census Series P-60, No. 106, p. 21; also No. 107, p. 20).

The economics of population aging is essentially a new concern for economists as well as other social scientists. Individual aging, of course, has always been a concern of man, both as an observer and as an individual undergoing the process of aging. Belletristic and other literature relating to man is replete with references to aging concerning its incidence among individuals and within the family. Of this we find representative evidence, for example, in Simone de Beauvoir's The Coming of Age, in relevant articles in the July–September 1977 Educational Gerontology, and in many interpretations of individual aging and its treatment by poets, novelists, and philosophers.

Even so, important research on aging is of relatively recent vintage. Don C. Charles writes (pp. 237–8) that “research (other than medical) on old persons is almost exclusively a phenomenon of the post–World War II period, although some work began prior to that – as early as the 1920s. Philosophers did, of course, give some thought to what we today call man's life cycle (e.g., see Cyril P. Svoboda's account of “Senescence in Western Philosophy,” pp. 219–35). Svoboda reports, for example, that Aristotle, one of the classical world's most careful observers, “posited that it is natural for the body to reach its prime around age 35 and to ‘advance’ until about age 50,” and then begin to decline (p. 223). The “soul,” he said, reached its perfection at age 50.” Some authors mentioned the functional usefulness of older persons and their experience, but without always correlating this aspect closely with specific age. At the other extreme, we find descriptions such as that of mythological Tithonus or Jonathan Swift's “Struldbrugs.”

Introduction

This paper is primarily devoted to a study of the (static) optimality properties (e.g., Pareto-optimality of the equilibria) of certain resource allocation mechanisms. It is shown that one such mechanism (the “greed process”) is optimal in a class of economic environments much broader than the class for which perfect competition is optimal. More specifically, the greed process has the desired optimality properties for all environments from which so-called external economies or diseconomies are absent; unlike perfect competition, the greed process does not presuppose the absence of indivisible goods, of discontinuities, or of increasing returns. However, the greed process lacks the dynamic (stability) properties known to hold for perfect competition, at least in certain special cases.

That the greed process does have certain optimality properties would be of little interest, were it not for the fact that it belongs to a class of informationally decentralized processes and hence shares with perfect competition a feature that has been extolled as one of the main virtues of the classical market mechanism. Still, just because it is designed to cover a broader class of environments, the greed process calls for more information (is informationally less efficient) than the competitive mechanism. To illustrate this, a variant of the latter (called “quasi-competitive”) is constructed and is shown to have the desired optimality properties when the environment satisfies the usual divisibility and convexity assumptions, while requiring less information than does the greed process.

Formulation of the problem

Introduction

In this paper, we wish to discuss the bearing of some recent developments in mathematical economics on the problem of the optimal allocation of resources. We will confine attention here to an economy whose aims are well defined. That is, we assume that the preferences of the economic system can be embodied in a utility function which depends upon the outputs of commodities. For a given technology, the possibilities of different output combinations are restricted by the availabilities of primary resources. The problem of optimal resource allocation is to choose among all the feasible combinations of production processes that combination which maximizes the utility achieved by the economy.

Since the discussion is at a fairly high level of abstraction, the economy being studied may be a nation or some smaller economic system, including a single firm. The assumption that a single utility function represents the objectives of the economy fits best the case of a firm. For a nation, the assumption is less justified, but it provides an introduction, at least, to the more complex problem raised by the presence of many individuals, each of whom judges the workings of the economic system in light of his own utility function. We also avoid the subtle problems involved in defining optimality in the more general case.

The problem of choosing the allocation of primary resources among different productive processes so as to maximize a prescribed utility function is a mathematical one, and its solution in any concrete case can be regarded as a matter of computation.