This paper explores the implications of regional income convergence for measures of inequality at the national level. In general, such convergence occurs as poorer regions overtake more developed ones. It is difficult to imagine any realistic scenario in which rising incomes in poorer regions would not have the effect of reducing absolute poverty. At the same time, it seems reasonable to assume that national inequality would fall as the mean incomes in the various regions converge. Given these general presumptions, the recent economic history of regional convergence between the southern United States and the rest of the nation is quite puzzling. Over the last twenty-five years mean family income in the southern United States has gone from about 80% of the national mean to about 93%. At the same time inequality in the South and that in the non-South have been changing only slightly when measured by Gini coefficients. Under these circumstances with no serious deterioration in intraregional measures of inequality, we would expect to observe a substantial reduction in national inequality as these two broad regions converge in mean incomes. Nevertheless, there has been no significant decline in the national Gini coefficient.' This apparent paradox is in contrast to an earlier period in U.S. history in which regional convergence occurred while national inequality was falling (Smolensky, 1961, 1963). The purpose of this paper is to demonstrate that the relationship between regional convergence and overall inequality is far from obvious. In particular, we shot that the convergence of mean incomes among regions, ceteris paribus, is not a sufficient condition for a reduction in common measures of ov erall inequality such as the Gini coefficient. The ceteris paribas conditions here are that the distribution of population across regions and the relative distribution of income within each region are held constant. The proof of this assertion is made in section II. In section III, we demonstrate the relevance of this analysis to the U.S. case. We show that the simple mean convergence of family incomes between the southern United States and the rest of the nation over the last twenty-five years should not have been expected to have a direct effect on national inequality. The naive link between regional income convergence and national income distribution does not hold up in this important case. Hence the arguments of section II are more than analytical curiosa. In a situation where the direct effects of income convergence are insufficient to reduce overall inequality there is the possibility that the broader process of regional convergence achieves this result more indirectly. Regional convergence may involve economic changes that work on intra-regional income distributions or the distribution of population across regions in ways favorable to greater national equality. In section IV we speculate on such indirect effects. From a theoretical point of view we conclude that the direction and extent of such interactions are not obvious.

T HE concept of exploitation, while primarily associated with Marxian economics, has a long if somewhat neglected history within the neoclassical tradition. Pigou and other neoclassicists concerned with the welfare implications of their theory found it natural to define exploitation of labor as the difference between labor's marginal product and its real wage.' Whether or not the normative connotation of the term, exploitation, is deserved, the Pigouvian definition opens important questions for positive economics. In particular, the level of exploitation can be interpreted as a measure of the relative bargaining power of labor and employers in an imperfect market economy. In this context, Pigouvian exploitation provides a useful way of introducing and testing many of the interesting insights of bargaining theory in a more rigorous framework.2 Despite its theoretical importance, Pigouvian exploitation has received little empirical attention.3 However, the development of reliable data and econometric tools for estimating production functions has made the quantification of the concept quite feasible. While most studies of production have been oriented toward questions of growth, technological change and input substitution, there is no reason why these same techniques cannot be used for exploring theories of the income distribution and exploitation. Indeed, two recent research efforts, those of Thurow, and Hildebrand and Liu, have derived marginal products from the partial derivatives of empirically estimated production functions.4 While the first of these studies is based on time series data for the entire United States economy and the second on cross-sectional data for manufacturing industries, both suggest that labor is paid substantially less than its marginal product.5 Given the existence of Pigouvian exploitation, the natural question is what factors determine its extent. The purpose of this paper is to explore this question at both the macro and micro levels. Specifically, we concentrate on testing several well-known (if somewhat intuitive) arguments drawn from labor economics. The emphasis on the level of exploitation, rather than on the real wage rate, allows for the supposition that in a market economy, wages are limited by marginal productivity. Hopefully this effort will demonstrate the importance and feasibility of research concerning Pigouvian exploitation. Received for publication December 18, 1972. Revision accepted for publication May 28, 1973. * We would like to thank the referee and our colleagues of the Department of Economics, University of Alabama in Birmingham for many helpful comments. 1A. C. Pigou, (1952) pp. 555-560 and pp. 883-884. To be sure, this definition has been subject to a good deal of criticism on the grounds that such a divergence may not be a deliberate result of employer actions. For a discussion of this minor controversy see A. M. Cartter (1959), pp. 6570. Moreover Pigou, himself, was careful to distinguish the level of exploitation from the level of unfairness, i.e., the divergence between factor payments and marginal productivities which would hold in a perfectly competitive economy in equilibrium. 2 The authors feel that the normative interpretation of exploitation is important. The common content of principles courses and the long standing interest in refuting the distributional implications of the labor theory of value, belie the pure positivist position. For perhaps the strongest normative statement concerning marginalist analysis see John Bates Clark (1899). For a statement of the more widespread positive approach see Schumpeter (1954), pp. 868870 and pp. 883-884. 3 This lack of attention is probably due to the fact that marginal productivity, unlike the average labor productivity of Marxian economics, eludes easy quantification. Indeed, some neoclassicists may have regarded the Pigouvian definition as desirable precisely because of these difficulties. 4 Lester Thurow, (1968), G. H. Hildebrand and T. C. Liu (1965). Both Thurow and Hildebrand and Liu used variants of the Cobb-Douglas production function estimated directly from data concerning labor and capital. Thus, they avoid the generally indefensible approach which uses wage data to estimate production functions on the assumption that marginal products are equated to wage rates by an invisible hand. 5 Thurow finds that the rate of Pigouvian exploitation, defined as the ratio of marginal product to wage rate, has fallen from about 177% in 1930 to about 159% in 1965, although the rate of decline has been sporadic. Hildebrand and Liu compute rates of exploitation of production workers to vary between 171% in the stone, clay and glass industries and 87% in the transportation equipment industry. The la ter is the only industry with a rate of exploitation below 100%. It should be noted that Hildebrand and Liu also found substantially higher rates of exploitation among nonproduction workers.