Introduction

It is usually taken as a postulate in Marxian discussions that the rate of profit is equal, at equilibrium, for all capitalists. Such a phenomenon should not, however, be a postulate, but rather a theorem, for what capitalists try to do is maximize profits, and any macroeconomic phenomenon (such as an economy-wide unique rate) should be derived as a consequence of individual capitalist accumulation behavior. In Chapter 1 we showed that for a special linear model where all capitalists face the same Leontief technology, profit rates are equalized at reproducible solutions. It was also shown, in the monopolistic competition model of that chapter, how imperfect entry could prevent the equalization of profit rates.

In the general model of Chapter 2, profit rates are not equalized at reproducible solutions. (Clearly the model of monopolistic competition is a special case of the general model.) This is due to the non-existence of a market for finance capital: Capitalists are not able to borrow or lend. In this chapter, a finance capital market is appended to the model of Chapter 2, and it is shown that Marxian equilibria continue to exist and, furthermore, profit rates are always equalized at equilibrium.

This sounds like a familiar story – the existence of a capital market will allow investment funds to be efficiently allocated, so that the rate of return on the marginal dollar is everywhere the same.

Introduction

In the preceding two chapters, we have shown that the rate of profit will not fall as a consequence of rational, competitive technical change if the real wage is held constant. It is clear that if the real wage rises, however, the equilibrium rate of profit may fall. To develop a full theory of a dynamic rate of profit, one would require a theory of how the real wage changes as a consequence of technical change. From the Marxian point of view, such a theory cannot be entirely “economic,” in the usual sense, as what wage the workers succeed in receiving depends on subjective elements that become realized in class struggle. In this chapter we investigate one simple model which posits a relationship between technical change and the real wage. Briefly, we shall assume that real wages adjust after the innovation so that the relative shares of labor and capital remain unchanged.

In recent discussions of the labor process by the Marxian economists, there has been some controversy as to whether technical change is introduced by capitalists because it is efficient, or because it allows capitalists better to control workers and hence extract surplus value. [See, for instance, the writings of Marglin (1974), Stone (1974), Braverman (1974), Gordon (1976), Edwards (1979), and Gintis (1976).] In the final section of this chapter, we shall indicate how the model presented can be used to discuss this dichotomous aspect of technical change.

Because issues discussed in the introductory chapter were primarily methodological, it is appropriate for these final words to summarize some main points of content of the book. In addition, because the line that defines where a book of this type stops must be drawn somewhat arbitrarily, the reader's indulgence is asked if some mention is made of current work not reported upon in previous chapters, but that bears upon the issues.

The task of Chapters 1 through 3 is to place the Marxian notions of economic reproduction and exploitation into a general equilibrium context. In most mathematical treatments of Marxian economics, only the production side of the economy is studied, and it is simply asserted that a certain price vector (the vector that equalizes profit rates across sectors) is the “equilibrium” vector. This formulation is inadequate, because no specific behavior of capitalists and workers is stipulated, with respect to which equilibrium has been defined. An equilibrium of an economy is a situation where the optimizing behavior of all individuals aggregates to social behavior that is consistent; clearly, then, the definition of equilibrium requires a prior specification of what the behavior of individuals is. This may seem a small point; it is not, as can be seen from common disagreements or confusions that have emerged between Marxists and neoclassicists concerning Marxian equilibrium. For instance, a neoclassicist asks how there can be an “equilibrium” with a positive rate of profit in an economy with constant returns to scale.

In the growth models of the preceding chapter, we assumed that factor markets function perfectly. Although such an assumption may be reasonable in developed economies, it is rather questionable in developing countries. Dualistic models have been a prominent feature of the development literature for some time (Lewis 1954; Fei and Ranis 1964). Although the concept of unlimited supplies of labor is no longer as popular as it was fifteen to twenty-five years ago (e.g., Kelley et al. 1972), the notion of an industrial wage set by institutional forces at a level above the agricultural wage is still widely accepted (e.g., Little et al. 1970, pp. 80–99, 335–6; Healey 1972; International Labour Office 1973; Morawetz 1974). The present chapter will use this assumption to construct a model of economic growth and capital utilization.

The model to be presented in this chapter is a model of the industrial sector. Formally, it differs from that of Chapter 10 only in that the wage rate is fixed, but the present model should be viewed as a component of a larger model containing at least two sectors, rather than as a model of the entire economy. The implications of the fact that there are other sectors in the economy will be mentioned at various points in the discussion.

Just as in Chapter 10, we shall distinguish between the static effects and the growth effects of an increase in utilization.

A typical factory can be operated for eight, sixteen, or twenty-four hours per day by making use of one, two, or three shifts of workers. The decisions with respect to the number of shifts are not made, we believe, entirely by accident but depend in large part on economic considerations. Only fairly recently have economists given serious attention to explanations of what these considerations are and how they affect shift-work behavior.

The topic is of considerable intellectual interest in its own right. Moreover, the theory of production is seriously incomplete without a thorough treatment of capital utilization. But the subject should also be of interest to a rather wide audience of economists and other social scientists for at least three reasons. First, the lives of workers engaged in permanent night-work or rotating shift-work are typically adversely affected either by the disruption of biological rhythms or by the reduction in contact with family and community. Second, and on the positive side, more intensive utilization of the capital stock normally increases the output available to the society, both in the present and in the future; the additional output makes possible increased consumption by capitalists or workers or both. Third, a preliminary view of the matter suggests that the distribution of the increased output would be especially favorable to the workers, in the form of higher wages or more jobs.

One section of the preceding chapter described the effect of shift-work on factor prices in a general-equilibrium static model. The stock of capital and the total labor force were assumed to be given. The present chapter will analyze the effect of shift-work in a growth model, in which the stock of capital is the result of the accumulation of past savings.

To see more clearly the differences between the general-equilibrium model and the growth model, let us imagine a one-sector static macroeconomic model in which capital utilization is a variable. The stock of capital and the labor force are given. It is obvious that an increase in capital utilization will increase total output and the wage rate. These gains may be called the static effects of the utilization change. Now let us convert our static macroeconomic model into a growth model in which the labor force grows exogenously and the capital stock at any given time is the accumulation of past savings. In the growth model an increase in utilization at any given time will still have the static effects on output and the wage rate, but it may also change the rate of capital accumulation and hence the ratio of capital stock to labor. If an increase in utilization leads to a higher capital-stock-to-labor ratio than would have existed otherwise, then we may say that utilization is more powerful in a growth context than in a static context.

At this point it is useful to review the current state of empirical knowledge about the long-run determinants of capital utilization in light of both the theory developed in Part I and the analysis in the preceding chapter. Given the long-run emphasis of our analysis, cross-sectional studies rather than time-series studies constitute the appropriate focus of our review. Because a major aim of this survey is to provide a perspective from which to view the empirical measurements and the results presented in the next two chapters, we shall discuss these cross-sectional studies from the point of view of testing propositions about the long-run determinants of capital utilization. Therefore, comments on descriptive material in these studies and comments on solely descriptive studies will be postponed until Chapter 8.

All but two of the studies under consideration are based on data for individual plants. The two exceptions are the early empirical studies on the subject (Marris 1964, Chapter 7; Winston 1971). Because these two studies illustrate the general nature of the problems faced by subsequent investigators, they will be discussed first. The remaining studies can be placed into the following two categories: those based on the use of continuous measures of utilization and those based on discrete measures of utilization. Because the choice of different utilization measures leads to some important differences between the two sets of studies, the two categories will be considered separately.

Our first task in this final chapter is to summarize the main conclusions of Chapters 1 through 11. This task will occupy us in Section 12.1. Then in Sections 12.2 and 12.3 we shall discuss, in a tone more subjective and speculative than in the rest of the book, the human costs of shift-work and the public-policy issues raised by our general subject.

Summary of findings and conclusions

The conclusions will be listed under the headings of methodological issues, substantive findings on the determinants of shift-work, and the productive and distributive effects of shift-work. With the exception of statements 3, 4, 10, and 17, which apply to shift-work exclusively, all of the following conclusions are applicable to both shift-work and capital utilization.

Methodological issues

1. According to economic theory, shift-work is both cause and consequence of capital intensity. On the consequence side, this statement has been part of conventional wisdom for a long time; the causal aspect was pointed out first by Marris (1964). The following implication of the statement, however, has not been widely appreciated: Observed correlations between capital intensity and shift-work do not provide empirical confirmation that capital intensity is a cause of shift-work.

2. Shift-work may be both cause and consequence of scale. Shift-work is always a cause of large scale in the sense that the undertaking of shift-work causes total factory output to be larger than it would otherwise be.

Our interest in capital utilization began to develop about ten years ago,at a time when the literature was extremely sparse and the topic seemed to be unduly neglected in light of its intellectual and practical significance. After collaborating on a number of articles on the subject, we reached the conclusion during 1975 that the time was ripe to attempt a more comprehensive treatment of the subject. Our aim was to write a book that would systematize the existing body of literature, which by then had grown much larger, while advancing the frontiers of knowledge in several important directions. The reader will be the judge of the success of our efforts.

A project as ambitious as this requires support from a number of sources. On the institutional side, sabbatical leaves to both authors during the initial phase of research for the book were extremely beneficial in two ways. They gave us time to work on the project and opportunities to interact with other researchers working on capitalutilization at Boston University (C.K.C.) and at the International Labor Office (R.R.B.). In addition, the General Research Board at the University of Maryland provided summer support for one of the authors (R.R.B.) during 1977. Finally, computer time was provided by the University of Maryland Computer Science Center.

On an individual level, our thanks go to Y. Kim and G. Winston for their very useful comments.

In this chapter we take the final step in bridging the gap between the theory and the data. Thus the first subject for discussion will be the nature of the primary data base used in the study and the datacleaning process (Section 6.1). The subsequent four sections are devoted to discussion of the measurement of each of the four variables identified in earlier chapters as being major determinants of the shift-work decision: capital intensity (Section 6.2), the elasticity of substitution (Section 6.3), the degree of economies of scale (Section 6.4), and the shift differential (Section 6.5). The empirical specifications of the working-capital hypotheses introduced in Chapter 2, Section 2.4, constitute the subject of Section 6.6. In the last section we put together the discussion of the previous ones, and we conclude by setting out in tabular form the models to be implemented empirically with our data.

Before addressing the topics just outlined, we should indicate some general characteristics of the subsequent sections. One way of viewing the discussion to be undertaken here is simply as the specification of the independent variables in terms of the actual data available in our samples. Thus, the distinction between the restricted-form specification and the free-form specification of the independent variables, introduced in Chapter 4, plays an important role in the subsequent arguments.

In most countries the vast majority of workers go to their jobs during the normal working hours. The majority of business establishments operate only one shift. A great many people, when first confronting these facts, are struck by the apparently low levels of capital utilization that are typically observed. For this reason a good way of approaching our subject is to classify the reasons for capital idleness.

We must first distinguish between intended and unintended idleness. One of the reasons that physical capital lies idle is that events do not always occur in the way that business managers expect. Demand may be less than expected, input supplies may be disrupted, or machinery may break down. These are examples of unintended capital idleness.

The reasons for intended idleness of capital depend on the type of activity involved. For example, some products and most services cannot be stored, and the timing of their production must be arranged to coincide with fluctuation in demand. In addition, many outdoor activities in agriculture, fishing, and construction are strongly affected by the weather and by the amount of daylight; obviously much idleness of capital in these sectors is explained by such factors.

The factors just mentioned do not apply to the great bulk of manufacturing activity, and yet much of the fixed capital in that sector is idle for much of the time.

In the previous chapters the analysis has relied on the assumption that the level of output that the firm plans to produce during the day will be the same for all systems of operation. With this assumption, profitmaximizing behavior leads to the same results as cost-minimizing behavior. In this chapter we shall investigate the consequences of relaxing this assumption for the previously established results, and we shall establish several additional results.

In the next section we discuss the issues that arise for the analysis of the shift-work decision when each system operates at its optimal level of output under the criterion of profit maximization. The discussion of these issues suggests the need to analyze the decision to work shifts under two different types of technologies. This analysis is undertaken in Section 3.2 under the assumption of a constant-β technology, which is a technology such that the degree of economies of scale is independent of the level of output. The results presented in this section are by and large available in the literature, primarily in the work of Clague (1975, Section II) and Millan (1975, Chapter 3). As a matter of fact, one of the main conclusions of this section is that the cost ratio discussed in earlier chapters always provides an accurate guide to the choice of system under profit maximization (Proposition 6A), and this conclusion is available in our earlier work (Betancourt and Clague 1975, footnote 13).