Knowledge that Transforms

So long as the marginal propensity to consume out of is greater than that out of profits, any rise in wage rates at the expense of profits will the aggregate marginal propensity to consume-since the marginal propensity to consume out of will receive an increased weight relative to that out of profits-thus raising the level of income that can be supported by a given level of investment and federal expenditure. And the marginal propensity to consume out of will be higher than the marginal propensity to consume out of profits so long as the average wage income is lower than the average profit income, which may be expected. This for two reasons: (1) the marginal tax rate on high incomes is higher than that on low incomes; (2) the evidence shows that the marginal propensity to consume out of disposable income is lower at higher disposable incomes. It is occasionally asserted that wise business policy would favor increasing wage rates at the expense of profits, since the consumption effect would the general level of activity and reverberate to the benefit of profits. The argument runs as in the previous paragraph until an increased level of income is proved a consequence; then the conclusion is drawn that higher aggregate profits will accompany the higher income level. Whether or not the last step of this argument is taken with tongue in cheek, it is interesting to see whether total profits can be raised through decreasing the relative profit share of income and, if they can, what the conditions are under which they may be so increased and whether these conditions may likely prevail. Mathematically it can be shown that there are conditions, extreme but not unreasonable conditions, under which the raise profits through higher wages argument is valid; the conclusions mathematically arrived at can be demonstrated verbally. The analysis here is entirely static: the values of all economic variables are assumed to be mutually determined by simultaneous solution of demand functions and economic identities. For simplicity, all functions are taken as linear. The conclusions can be stated as follows: 1. So long as government expenditure and investment are constant a rise in wage rates at the expense of profits will increase aggregate income but decrease profits, if the marginal propensity to consume out of is less than unity. 2. When we complicate our system by admitting relationships between, e.g., investment and income, or government expenditures and

In a recent paper' we presented the first stage of a statistical inquiry into the nature of the abstraction involved in the use of national series for the description and analysis of business cycles. The results were given of an analysis of one aspect of the cyclical behavior of national income-its percentage rate of change. This rate of change of the national total was interpreted as a parameter of the frequency distribution of the respective rates of change of the component parts of the larger area, and statistics describing a certain pattern of behavior of these distributions were shown. The distributions appear to have a characteristic shape approximating logarithmic normality, and there is a suggestion of a systematic development as the different phases of the business cycle unfold. The skews of the distributions appear to be positive during the period of the expansion when the rate of growth is increasing. When the rate of growth begins to decline, it was tentatively suggested that the skew shifts to a negative and remains a negative through the absolute turning point of national income and during the period when the rate of contraction is increasing. When this rate of contraction begins to decline, the skew of the distribution again shifts to the positive. An attempt was made to rationalize this cyclical evolution of shape of these distributions. It was further noted that the extreme movements from year to year are found generally among the same set of states, there being a tendency evident for the more sparsely settled states that are highly specialized in raw-material production to cluster in the ends of the distribution and, in years of marked change, in the same end of the distribution. It is proposed in the present paper to discuss in more detail the geographical make-up of these annual frequency distributions of regional rates of business change. We think that certain generalizations may be made regarding a regional pattern of short-run business change, and we should like to analyze possible factors that might account for the observable similarities and differences. Our previous discussion of the factors determining the cyclical responsiveness of a given region laid emphasis upon industrial location or specialization and the institutional and physical factors influencing the region's commercial ties. The question we raise now has to do with certain attributes of industrial location that we regard as particularly relevant for regional businesscycle analysis.

IN an article published in the April, 1946, issue of this JOURNAL, Dr. Klein presents a new approach to the problem of the construction of macroeconomic values,1 a problem which has not yet been given the wide attention it deserves. Two criteria for aggregates are proposed in Dr. Klein's article: (1) if there exist functional relations that connect output and input for the individual firm, there should also exist functional relations that connect aggregate output and aggregate input for the economy as a whole or an appropriate subsection, and (2) if profits are maximized by the individual firms so that the marginal-productivity equations hold under perfect competition, then the aggregative marginal-productivity equations must also hold.2 In this note, we shall first show that these criteria are too restrictive and unnecessarily so. On the basis of our criticisms, we shall then attempt to establish different criteria for the construction of macroeconomic values in the general case. I. Let us first consider, in nonmathematical terms, what the first criterion really means. It means, as one can easily see after following carefully Dr. Klein's arguments, that the aggregate output must be independent of the distribution of the various inputs. If X represents the aggregate output and N and Z represent two aggregate inputs, labor and capital, the first criterion requires that X depends only on the magnitudes of N and Z, and not on the way in which N and Z are distributed among different individual firms, nor on the way in which N and Z are distributed among the different types of labor and capital within any individual firm. In other words, as long as N and Z are kept constant, the way in which they are distributed must be of no significance. It is obvious that this criterion is most unlikely to be satisfied in any practical case. If this criterion is strictly adhered to, one will find in most cases that either no aggregates can be found to fulfil this criterion, or, in the case where this criterion is satisfied by the manipulation of the construction of aggregates, the aggregates will become such monsters that they are completely void of any economic significance.3 The field in which macroeconomics may apply would then indeed be extremely limited.

Mr. J. E. Meade' published recently a very interesting essay dealing critically with some welfare propositions in Lerner's Economics of Control.2 He summarizes very ably some of the most important objections to the present theory of welfare economics. We propose to show in this note that these objections can be dealt with rather easily on the basis of a slight amplification of the existing theory, as presented for instance in Mr. Lange's important essay.3 We are going to use three devices to meet Mr. Meade's criticism: (1) appropriate definitions of commodities, (2) dynamization of the theory, (3) introduction of higher-order utility functions, analogous to Lange's social-value function. Following Lange, we will first restate some of his important propositions: Assume that there are 0 people in a community. There are n commodities and services. Denote by x(t) the amount of good or service r possessed by individual i. Let u(i) be his utility index depending on all commodities and services that he possesses, x() . . , x('). Let X.= E'lx(') be the total amount of commodity or service s in the community. Assume also the existence of a transformation function F(X1,. . . , Xn)=O. Now let us maximize u(i), keeping u(k) (kXi) constant. This means we want to make everybody as well off as possible without making anybody worse off. This is the first stage of welfare economics. We have of course also to take into account the transformation function (F = 0). The first-order conditions can be expressed in matrix form4 which seems more appropriate than the use of Lagrange multipliers: Denote derivatives by subscripts so that us i(i) means cu(i)/cx1(i). If we take derivatives with respect to the x(i) it follows that the following matrix must be zero: