In Part I, we saw how the theory of choice, initially developed for application to the allocation of a fixed total expenditure over a number of goods, could be extended to deal with labor supply, the allocation of income between saving and consumption, and the purchase of durable goods. So far, we have looked at these extensions as separate problems, but in principle, each consumer has to deal with all of them simultaneously. At any given time, current assets and current and future income must be allocated over nondurable and durable goods for current and future periods, while for consumers who are free to do so, plans must be made for allocating time between work and leisure in the present and the future. There are also the complications of choosing types of real and financial assets as well as the problems of dealing with uncertainty. All of the parts of this allocation problem may interact: changes in future wage rates may alter retirement plans with important consequences for durable good purchases now; an anticipated increase in asset values three years hence may cause an elated investor to buy more of his favorite dinner, and so on. Such interactions pose formidable problems, not only for the consumer but also for the economist who attempts to describe consumer behavior. If making today's purchases requires knowledge of the price of bootlaces 30 years from now, daily living is close to impossible. Nor is there much hope of predicting behavior if all such possible interactions must be allowed for.

The quality of goods and household production theory • Labor supply • The consumption function and intertemporal choice • The demand for durable goods • Choice under uncertainty

Restrictions on preferences • The theory of market demand

We have already discussed, in Chapter 4, the straightforward extension of the neoclassical utility maximizing model to problems involving choice over consumption in different time periods. In this chapter, we extend the analysis in several directions. Section 12.1 considers various aspects of intertemporal planning, especially in the context of the individual's life cycle. First, the model is extended to allow simultaneous choice of consumption and labor supply, and we discuss how, given freedom of choice, we might expect consumers to vary their work and consumption levels in response to variations over the life cycle in prices and wages. We then turn to the more conventional case of constrained labor supply as discussed in Chapter 4, and illustrate the derivation of the consumption function with a model based on the AIDS of Chapter 3. The relationship between the consumption function and systems of demand equations is also briefly considered. Liquidity constraints in the form of borrowing restrictions or different rates of interest on borrowing and lending are then discussed, and their influence in raising the marginal propensity to consume is emphasized. Finally, we discuss the implications of the analysis for the relationship between the aggregates of consumption, income, and wealth. Section 12.2 considers the dynamics of the link between income and consumption, not only within the full intertemporal model but also taking into account other explanations and the econometric evidence. Section 12.3 is concerned with questions of imperfect information.

Inflation and capital gains

The taxation of capital gains has always created difficulties for experts and governments. An economic definition of income of the Schanz-Haig-Simons type, which is the most accepted one for taxation, would call for the inclusion of capital gains in taxable income on an accrual basis, inasmuch as the ability to pay of the taxpayer is clearly enhanced by these gains. In practice, however, various difficulties have prompted most countries to either exempt them or tax them only when they are realized. Even then, only part of the gains are generally included in taxable income; or, alternatively, they are taxed at lower rates than other incomes. In the absence of inflation, this preferential tax treatment definitely favors those who receive these gains.

When inflation is present, capital gains will be distorted and, as normally measured, will no longer conform to the Schanz-Haig-Simons definition of income. As Goode has put it, “Appreciation in the price of an asset that reflects only a general rise in prices is a fictitious gain because it gives the investor no increased command over goods and services.” The tax laws generally do not make a distinction between gains that reflect an actual real increased command over economic resources (real gains) and those that do not (fictitious gains). Thus, during inflationary periods, at least part of the capital gains tax will inevitably become a tax on wealth, rather than income, because it will be levied on the fictitious gains.

The preceding two chapters have been concerned with the analysis and measurement of the welfare of individual households. We now turn to questions of the welfare of society as a whole. The two topics which make up the title of this chapter are both major fields of economic investigation in their own right, and we cannot hope to give more than an outline of them here. Indeed, we are more concerned with illustrating one of the major themes of the book, that consumer theory as we have presented it is of great analytical value in other branches of economics. Social welfare functions have obvious conceptual links with individual utility functions and we shall explore these ideas in §9.1. We shall use our previous analysis to discuss possible structures for social welfare functions, and we shall argue that the index number concepts discussed in Chapters 7 and 8 can be used to provide natural units for making interpersonal comparisons of welfare. Section 9.2 is concerned with the measurement of inequality. The approach described is based on an explicit link with social welfare, pioneered by Kolm (1969, 1976) and Atkinson (1970), and we show how the analysis of §9.1 can be used to adapt the conventional measurement of income inequality to the more fundamental purpose of measuring welfare inequality.

Social welfare functions and their arguments

The social welfare function is an essential tool of welfare analysis and this section is concerned with its development and its properties. It will be used in §9.2 in specific practical contexts.

Consumer behavior is frequently presented in terms of preferences, on the one hand, and possibilities on the other. The emphasis in the discussion is commonly placed on preferences, on the axioms of choice, on utility functions and their properties. The specification of which choices are actually available is given a secondary place and, frequently, only very simple possibilities are considered. In this book, we shall have a great deal to say about preferences, and discussion of them begins in Chapter 2. We begin, however, with the limits to choice rather than with the choices themselves. Unlike preferences, the opportunities for choice are often directly observable so that, to the extent that variations in behavior can be traced to variations in opportunities, we have a straightforward and objective explanation of observed phenomena. It is our view that much can be so explained and that the part played by preferences in determining behavior tends to be overestimated. Hence, this first chapter considers what can be said about behavior without detailed consideration, of how choices are made. A large part of this book, from Chapters 2 to 9, works with one very special assumption about the opportunity set, namely that choices are constrained by fixed, known prices in such a way that the total value of the objects chosen should not exceed some predetermined total. In this case, we say that the consumer faces a linear budget constraint.

No part of economics is more contentious and more interconnected with the rest of the subject than is labor economics. We shall here attempt to separate the analysis of labor supply from labor economics as a whole, but it is inevitable that, to some extent, we shall be drawn into wider issues. One aspect of the contentiousness of the subject is the range of different approaches to it, from the institutionalists, on the one hand, to those who apply a narrow version of the neoclassical paradigm, on the other. Our approach is analytical, but we think not narrow and, as throughout the book, our aim is to formulate models relevant for good empirical work.

The chapter is divided into three sections. The first extends Chapter 4's discussion of the basic neoclassical model of labor supply to deal with the case where the individual chooses not to work at all. The choice between working and not working is referred to as the participation decision, and in §11.1, we show how it can be analyzed in terms of the divergence between the actual and an appropriately defined “shadow” wage rate. We also discuss the implications of this theoretical analysis for econometric studies of participation rates and of the labor supply of those who do work. Section 11.2 considers the effects of abandoning the linear budget constraint of the neoclassical model and takes a more realistic view of the constraints faced by households.

The problems associated with the taxation of capital gains in an inflationary situation are somewhat simpler to understand than those connected with the taxation of interest income. Perhaps for this reason they have received far more attention. As recently as 1974, Roger Brinner and Alicia Munnell could write that “it is not just as necessary to adjust wages, interest, and dividends for inflation” as it is to adjust for the effect of inflation on capital gains. As is shown in the following section, contrary to their view, when the price level is changing, the taxation of interest income does create special and serious adjustment problems.

The problems

To set the problem in the proper context, let us first consider a situation in which prices are expected to remain stable and where these expectations are fully realized. Let us assume also that an individual can lend his savings at a rate of interest of 5 percent, which will be called the real rate. To simplify the presentation, we shall avoid the complications that would be introduced by considerations of term structures of the interest rate; we shall, thus, refer to one particular rate of interest. We shall also assume that the marginal income tax rate for this particular individual is 50 percent.

Given these assumptions, if an individual lends $1,000 and after one year receives $50 of interest income – in addition to the return of his principal – this income will be taxed at the marginal tax rate of 50 percent.

One of the most important developments in recent applied economics has been the increased availability of data on large samples of individual households, particularly in the United States. Although the analysis of such data poses formidable problems of its own, it is possible, at least in principle, to apply the microeconomic theory of the preceding chapters. If, however, as is frequently the case, the data are available only for aggregates of households, there are no obvious grounds why the theory, formulated for individual households, should be directly applicable. The transition from the microeconomics of consumer behavior to the analysis of market demand is frequently referred to as the “aggregation problem.” Aggregation is seen as a nuisance, a temporary obstacle lying in the way of a straightforward application of the theory to the data. In this view, the role of aggregation theory is to provide the necessary conditions under which it is possible to treat aggregate consumer behavior as if it were the outcome of the decisions of a single maximizing consumer; this case we shall refer to as that of exact aggregation. These aggregation conditions often turn out to be stringent, which has tempted many economists to sweep the whole problem under the carpet or to dismiss it as of no importance. Some economists, indeed, see for example Hicks (1956), have held the view that microeconomic theory has greater relevance for aggregate data, arguing on largely intuitive grounds that the variations in circumstances of individual households average out to negligible proportions in aggregate, leaving only the systematic effects of variations in prices and budgets.

The major concern in this chapter is to sample and review literature of the past four decades relating to the significance of changes in age structure owing to population aging (Cowgill), especially with reference to their impact on dependency and the economic state of older dependents. However, the impact of these changes in age structure associated with decline in the rate of population growth must be distinguished analytically from the impact of decline in the rate of population growth as such (e.g., see Sauvy, 1948). The nature of the relationship between decline in the rate of population growth and increase in the relative number of older persons was illustrated broadly in Tables 2.1 and 2.2, and in greater detail in Table 2.6.

Population aging alters the age structure of the dependent population and therewith the means through which support is transferred to dependents from the individuals and institutions with whom this support originates. For example, given expectation of life at birth of 70.2 years and a Gross Reproduction Rate of 2, persons under 15 and over 59 in a stable population will constitute 45.3 percent of the population, with only 17.6 percent being 60 or more years of age. If, however, the Gross Reproduction Rate should settle in the neighborhood of the replacement level, about 40 percent of the population will be under 15 and over 59, and about one-half of these will be 60 or more years old (United Nations, 1956, p. 27; also United Nations, 1973). Should nondependent age in our example be defined as 18–64 instead of 15–59, a parallel change in the age structure of dependents would occur (e.g., see tables in Coale and Demeny).

This study summarizes and assimilates research by international scholars in economics, demography, and the other social sciences in order to provide a conceptual framework for the economics of aging. The objective of this analysis is to identify and describe the principal economic issues associated with individual and population aging and to assess the existing knowledge respecting the economic and social problems emerging with aging. The integration of interdisciplinary research is of special importance in any examination of gerontological issues, and we have been sensitive to this mandate. However, our primary focus has been on economic complexities of individual life-cycle allocation decisions and the macroeconomic problems that arise from age-structure changes.

The review is international in scope, as we trace the development of concern for population aging in Europe, the United States, and other industrialized countries. Theoretical concepts and changing demographic conditions are illustrated with data from various countries. Cross-national econometric studies are reported along with time-series and cross-sectional research on individual countries. National differences in the response to aging, the institutions that provide income maintenance to the elderly, and the economic conditions of the elderly are noted. In some cases, a single country is examined in detail to indicate a particular aspect of the economics of aging. Most frequently, the United States is chosen because of the availability of data, the greater number of empirical studies employing U.S. data, the familiarity of the authors with U.S. institutions, and the essential universality of aging phenomena.

Population aging is represented by an increase in the relative number of older persons (e.g., those over 60 or 65 years of age) in a population; it is reflected also in the associated increase in the median age of the population. Population aging thus is a counterpart to population “youthening” and the associated decline in the median age of the population (United Nations, 1951, 1956, 1973; U.S. Bureau of the Census, May 1975). Population aging tends to emerge in a mature low fertility population, whereas “youthening” may characterize a high-fertility population experiencing declining mortality among the young (Spengler, 1968).

In as much as awareness of the demographic sources of population aging is conditioned by the sensitivity of available demographic measures, we shall point first to the development of these measures. Later we shall review population changes that led to the emergence of population aging and conditions associated with it. Socioeconomic characteristics of older populations (U.S. Bureau of the Census, Nov. 1975), and implications of population aging are examined in later chapters.

Indicators of population aging

Although the age composition of a population may be affected by changes in mortality, fertility, and net external migration, careful measures of the extent of these effects were slow to be developed. Indeed, their perfection awaited the development of the concept of a stable population, a concept suggested by Leonard Euler in 1760 and later anticipated by Laplace and Quetelet (Coale and Demeny, Chapter 1; Keyfitz, 1976; Lotka, 1907, 1925; also, Unsigned, 1976). However, it was not fully articulated until 1907 by A. J. Lotka, who along with F. R. Sharpe demonstrated it in 1911 (Dublin et al., pp. 241–56; Lotka, 1925, pp. 109–20).