Production and Distribution of Income in a Market Economy

The aim of this book is to study the implications of economic interactions between heterogeneous individuals, both for macroeconomic outcomes and for the evolution of the income and wealth distribution. As these interactions are extremely complex, we organize our analysis around several key simplifications.

First, we will assume throughout that there are two factors of production: an "accumulated" factor and a "non-accumulated" factor. We will frequently refer to the former as "capital" and to the latter as "labor." As we discuss below, however, the important point is that the economy's (as well as the households') endowment with the former is endogenously determined by savings choices, whereas the economy's endowment with the latter is exogenously given.

Second, we will assume throughout that all individuals have the same attitude toward savings, i.e., that any two individuals would behave identically if their economic circumstances were identical. This is not to say that heterogeneity in preferences between present and future consumption is unimportant in reality. Allowing for systematic differences across individuals along this dimension, however, would tend to yield tautological results: one might, for example, find that the poor are and remain poor due to their low propensities to save. It is much more insightful to highlight other sources and effects of large differences in incomes across individuals: we will highlight the role of macroeconomic phenomena (such as capital accumulation and associated changes in factor prices, market imperfections, and economic policies) for the dynamics of the distribution of income and wealth and their feedback to the long-run process of economic development. Heterogeneous propensities to save are clearly of some importance in reality, but will not induce a systematic bias in our results if they are random and unrelated to economic circumstances.

Third, in many of our derivations we will assume that only one good is produced in the economy and can be used for either consumption or investment. Investment then coincides with forgone consumption, to be understood broadly as leisure choices are subsumed in consumption choices. The single-good assumption is adopted throughout part 1 (with the exception of the appendix to chapter 4) and part 2. In part 3, we relax it and consider the interrelation between distribution and growth when there are many goods and when the structure or consumption differs between rich and poor consumers.

As a further general principle, we will apply standard tools of modern macroeconomic analysis, formulating all models in formally precise and consistent terms. Even as we strive to take individual heterogeneity into account when studying macroeconomic phenomena, we will often find it useful to refer to situations where some or all of the implications of heterogeneity are eliminated by appropriate, carefully discussed assumptions, so that a representative agent perspective is appropriate for some or all aspects of the analysis. Specifying and carefully discussing deviations from these assumptions will make it possible to highlight clearly problems of heterogeneity and distribution, as well as their interaction with macroeconomic phenomena.

This first chapter sets the stage for our analysis. We introduce notation and set out basic relationships both at the level of the family and at the aggregate, making the important distinction between accumulated and non-accumulated income sources. Then, we analyze the relationship between distribution and the efficiency of production in a "neoclassical" setting of perfect and complete markets. Firms maximize profits and take prices as given, all factors of production are mobile, there is complete information, and all economic interactions are appropriately accounted for by prices (there are no externalities). In that setting we discuss in some detail the conditions under which macroeconomic aggregates do not depend on income distribution and on technological heterogeneity, so that production and accumulation can be studied as if they were generated by decisions of "representative" consumers and producers. As is often the case in economics, the model's assumptions are quite stringent, so we discuss briefly conceptual problems arising when certain tractability conditions are not met. In particular, if factors of production cannot be reallocated, aggregation becomes very problematic unless stringent conditions are met regarding the character of technological heterogeneity. This qualifies, but certainly does not eliminate, the usefulness of stylized models as a benchmark when assessing the practical relevance of deviations from the neoclassical assumptions.

1.1 Accounting

Consider an economy with many households endowed with two types of production factors: accumulated and non-accumulated. By definition, accumulated factors are inputs whose dynamics are determined by microeconomic savings decisions. At the aggregate level, these decisions affect both the distribution of accumulated factors across individuals and the dynamics of macroeconomic accumulation. In contrast, non-accumulated factors are, by definition, production factors that evolve exogenously (or, for simplicity, remain constant) in the aggregate. We will frequently refer to the accumulated factor as "capital" and to the non-accumulated factor as "labor." However, the simple capital/labor distinction may be misleading. For instance, an individual's human capital is essential for the efficiency of its "labor" but clearly affected by an individual's savings choices. In contrast, incomes from real estate ("land") as well as non-contestable monopolies are often counted as part of capital income but are, according to our definition, part of non-accumulated factors' rewards.

While here we take the evolution of non-accumulated factors as given, it is important to note that, in reality, the economy's supply with these factors is subject to households' supply choices. Here we abstract from the endogeneity of the supply of their non-accumulated factors and from endogenous fertility behavior. We subsume labor/leisure choices under the consumption choice.

A family or household i is endowed with...