Introduction, 295. — I. Increasing eosts and the distribution of earnings, 296. — II. Increasing costs and the rate of return, 299. — III. Implications and conclusions, 301.

I. Introduction: widespread use of community indifference curves, 1. — II. Attempts to justify the use of community indifference curves, 3. — III. Proof of the nonexistence of community indifference contours, 4. — IV. Nature of Scitovsky's community indifference contours, 6. — V. Problem of family preference: a parable, 8. — VI. Optimal ways of achieving income redistribution, 12. — VII. Regular properties of social indifference contours, 14. — VIII. Perfect competition and bliss, 19. — IX. Final summary, 21.

IN an earlier article it was shown that there was a fall in private fixed investment in 1948-50 which played a considerable part, and possibly the most important part, in inducing the fall in production and reduced inventory investment in the United States from late in 1948 until early I950.1 It is proposed to examine here aspects of private fixed investment during the period I946-50 which have some theoretical significance. When the official investment statistics are broken down by sector and industry, a considerable variety of cyclical patterns emerges. Rates of postwar expansion and dates of turning points differ considerably. The dates of turning points of total investment have little significance unless they are viewed as averages; this in itself is not a particularly novel conclusion. This pattern in turning points becomes significant when considered in relation to the more general causes of the postwar expansion in investment, and in relation to both the immediate and deeper influences that may have checked the expansion. When the statistics of investment in producers' durable equipment are examined from the point of view of type of equipment, a similar variety of cyclical patterns emerges, which because of the clearness of the pattern and the greater reliability of the statistics can be related in quite a precise way to the causes of the expansion or, more generally, to the determinants of the rate of investment. In summary form, the conclusions drawn from the statistical studies are as follows. On most types of durable goods, the peak and ensuing decline in expenditures occurred earlier (i.e., more quickly after the end of the war) the greater the expansion in expenditures during the war. The rates of expansion just before the war, the rates of expansion in the postwar period, and relative price changes do not alter this conclusion, although they are needed as elements to supplement the exDlanation. The sector analysis, which includes private new construction, supports these conclusions, although it is obvious and well known that special factors influenced investment on farms, railroads, public utilities, and residential construction. Neither the annual change in output, the annual level of output, nor the level of corporate profits can be satisfactorily related to the changes in the rate of fixed investment over the period in ways which would provide explanations of the rate of investment. The set of circumstances governing the changes in the rate of investment after the war would appear to be (a) the different wartime rates of investment of different corporations, industries, and sectors; and (b) the different wartime rates of investment in different types of plant and equipment. Generally, the less a firm had invested during the war, or the lower the production of a particular type of equipment (presumably because of the wartime allocation of resources), the longer was the period after the war during which the firm's investment, or investment in the particular type of equipment, increased. The deferred investment demand of the war years or the deferred replacement investment was a large enough proportion of total investment for the gradual falling off of the former in I948-49 to cause a change in the total. The absence of any noticeable accelerator or profit relations except possibly a short-period accelerator effect in the middle of I 949suggests that that investment which was not specifically deferred replacement investment continued to increase after 1948. It is this which explains the recovery in total investment expenditures in early I950, and which partly explains the short lived character of the I949 slump.2 These conclusions have been based upon a study of the available official statistics. Annual figures have been used throughout, both

In his article, Exchange Rate Adjustment and Relative Size of the Depreciating Bloc, Professor Orcutt set out to attack the notion that by a large bloc versus the rest of the world generally would be substantially less effective than depreciation by a small country versus the rest of the world. Indeed, he goes so far as to conclude that for the case of actual large blocs, such as the dollar bloc or the sterling bloc, application of the model developed in this paper would seem to indicate that effectiveness of depreciation would be substantially greater than in the case of the small country versus the rest of the world. This conclusion merits evaluation.

STATE income payments are the sums of the streams of wages and salaries, of proprietors' income, of property incomes, and of transfer payments flowing to the states' residents. In highly industrialized states the flow of wages and salaries will be relatively larger than in states more sparsely populated and heavily dependent upon farming. In the latter group of states, the flow of proprietors' income will be relatively larger. To some extent, at least, the recipients of property incomes may choose their place of residence without regard to the location of the property or activity giving rise to the income. rules under which persons receive some of the transfer payments, such as unemployment insurance or workmen's compensation, gear these payments closely to industrial activity. Other transfer payments, such as old-age pensions or veterans' benefits, may be distributed under rules which are largely independent of the type or magnitude of the industrial activity near the recipients' residences; these rules, however, may make qualifying for the transfer payments more attractive in some localities than in others. These component payments vary widely by state. It is the purpose of this paper to examine the interstate variability of the income components and their effects on state differences in per capita incomes. basic data are those provided by the National Division relating to I929, I933, and I939-5i, and by King and Leven for I919-2I.1These data are in terms of the aggregate amounts received by the residents of each state. Two series of adjustments are made to compensate for the large differences in state population. first is to reduce the data to a per capita basis.2 second is to express each component as a percentage of the state's total income payments. latter adjustment, while not explicitly taking state population differences into account, renders the data independent of these differences. Unlike national income, state income payments do not measure the returns to the factors of current productive activity during a specified year. Only those payments actually received by persons are included, and these are included whether they arise from current or from past economic activity. Consequently, these data cannot be used to judge whether there have been shifts in factor returns over the period.3 They do show, however, the changes in the forms in which income is made available to the residents of the various states. Some of these changes may have stemmed from changes in the relative importance of factors, such as the relative productivity of labor and capital; others, however, may simply reflect transitory phenomena, such as a short-lived increase in corporate savings. In the next section the relative interstate dispersion of per capita income is studied as a function of the manner in which the four components combine to form state per capita incomes. This is followed by an examination of the composition of state incomes in terms of their components. Finally, the wages and sal*This report was developed as a part of the Study of Differences in State Per Capita Incomes, which is being financed jointly by Duke University and Rockefeller Foundation. Mrs. Rena B. Webster supervised the basic computations for this report. 'Survey of Current Business, August I953, for I950-5I data; August I952, for I948-49 data; August I950, for I942-47 data; and August I945, for I929, I933, and I9394I data. W. I. King and M. Leven, in the Various States, Its Sources and (National Bureau of Economic Research, New York, I925), provide estimates for I9I9-2I. King-Leven estimates include transfer payments in wages and salaries. State income for I9I9-2I iS taken as the sum of the components and omits certain imputed and in-kind incomes separately estimated by King and Leven. District of Columbia is excluded from this analysis. 2 National Division estimates divided by the most recent Census Bureau estimate of state population as of July i of the relevant year. 'For recent discussion of changes in factor returns, see Jesse Burkhead, Changes in the Functional of Income, Journal of the American Statistical Association, 48 (June I953), I92; Edward F. Dennison, Distribution of National Income, Survey of Current Business (June 1952), i6, and Income Types and the Size Distribution, American Economic Review, Papers and Proceedings, xLiv (May I954), 254; and George J. Schuller, The Secular Trend in by Type, I869-I948: A Preliminary Estimate, this REViEW, xxxv (November I953),

IT is widely believed that productivity normally increases substantially faster in the United States than it does elsewhere, but a survey of the relevant statistics relating to the present century suggests that this is far from certain, at least in peacetime. It may be that we sometimes suffer from an optical illusion in this matter. We can, for example, easily be misled by comparing a recent prewar year (such as I937 or the average of I934-38), when the United States was depressed, with a postwar year like I949 or I950, when the rest of the world had not fully recovered from the war. In making comparisons of Britain and America we can also be misled if we ignore the rapid growth in the American population, which is increasing by nearly one million every four months. In I955 it was 28 per cent greater than in I937, a year often used for comparisons with the present. During the same period the United Kingdom population rose by only 8 per cent. Britain, moreover, has probably been less successful in raising productivity than many other countries. And, perhaps most important of all, we may not always take sufficient account of the two world wars which have played such havoc with the economies of many nations outside the United States. We are of course discussing proportionate rates of growth in productivity. It is undeniable that the absolute level of productivity and the absolute annual increase in output per head are much higher in the United States than in most other countries; and the absolute gap in living standards is steadily widening. This raises important economic and political problems, but it is not the question at issue here. It should be noted that the diagrams throughout this article are drawn on semi-logarithmic, or ratio, scales so as to show proportionate, rather than absolute, changes in the magnitudes portrayed. We shall have to examine the behavior of a good many index numbers, and a once-for-all warning and apology at this stage will avoid tedious repetition. Index numbers are, for good theoretical reasons, notoriously and inevitably dangerous to interpret, especially when longterm trends are in question; and some of the figures we shall have to use are in addition based on shaky estimates and of doubtful comparability. To some extent this is inevitable. Better basic figures, at least about the past, may never be available. But there is also scope for more careful exploration of the data that exist (including statistics bearing indirectly on the subject and nonstatistical information as well) than was possible for our present purpose. It is to be hoped that others will attempt this task, but, in the meantime, we must seek provisional conclusions from the figures presented in the following pages. It is certainly impossible to form a judgment without any figures at all; for, as we shall see later, there is no clear a priori reason why productivity should increase much faster in the United States than it does elsewhere. The statistics that follow exclude Russia and China throughout, and usually the countries of Eastern Europe after I939 1 (the index numbers have then, of course, been linked at a prewar year, and so require no upward adjustment in postwar years to give a true picture of rates of growth). We start with a summary of production (not productivity) of raw materials, foodstuffs, and manufactures in the United States and in the * This paper will appear, in a somewhat different form, as a chapter in a forthcoming book on the dollar problem to be published by Macmillan. It will be supported by an Appendix but, since this is as long as the text itself, it has not been possible to reproduce it here. The references to it have, however, been retained so that the reader may have some idea of the statements and figures that are more fully explained in it. The conclusions reached here should not be taken to imply that there is, or is not, a long-run dollar problem; the relation between rates of growth of productivity in different areas and the balance of payments between them is a complex one. No account is taken in this paper of possible differences in rates of innovation. I am greatly indebted to Miss Monica Verry and Mr. Maurice Scott for invaluable assistance and to many others who have commented on the draft. The exception is the index of raw material production, where it was statistically more convenient to include Eastern Europe throughout.

I. Introduction and review, 537. — II. Many-goods model, 539. — III. Euler necessary conditions, 541. — IV. Case of satiated production, 544. — V. Physical analogy of small vibrations, 547. — VI. Case of utility satiation, 549. — VII. Practical computation, 553. — VIII. Hamiltonian formulation, 554. — IX. Pay-off in terms of initial state, 559. — X. Conclusion, 561.