I. Introduction, 131. — II. Scope of the model, 132. — III. Mathematical statement of the model, 134. — IV. Profit maximization, 140. — V. Cost-quantity silhouettes, 145.

I. Introduction, 437. — II. Possible leverage role of the steel industry, 439. — III. Bottleneck phenomena, 448. — IV. Bottlenecks and formulation of counter-cyclical policy, 456.

N this REVIEW' and in volume ten of Studies In Income And Wealth Professor Kuznets and the economists of the Department of Commerce have argued about the statistical determination of factor in national income accounting. The writings of the Commerce Department are filled with apologies and some apparent embarrassment for having to deal with the term out in the open, but Kuznets is more bold and unabashed. The dispute between Kuznets and the Department of Commerce economists is over what omissions and additions should be made to the statistical data so that factor returns or payments will represent factor as defined in economic theory. They find themselves involved in messy questions about the role of government services in production and use of resources, direct and indirect taxes, subsidies, and the cost of profits. Factor costs, Kuznets says, can be defined in terms of a partial (business firm) analysis or in terms of an aggregative (social) analysis. Factor in the partial sense are costs to enterprises that engage the factors.2 These factor are computed by adding the payments made by firms to the agents who own the labor, capital, or land employed but by excluding enterprise profits on the grounds that they are not a cost to the firm. Kuznets states that profits bridge the difference between the cost and market value of a firm's activity. To derive the factor of partial analysis, Kuznets subtracts undistributed profits of corporations and that portion of entrepreneurial net income that represents net profits from the net output valued at market prices. Although Kuznets in his social or aggregative viewpoint does not clearly distinguish between factor returns and factor costs, he believes that the sum of factor must always equal the market value of the total final product of the economy. The difficulty in perceiving the identity of factor and factor returns to the whole community is that the government, as a producer, complicates the relationships since there is no necessarily close connection between indirect taxes and intermediate government output. Social factor costs, which are identical with social factor returns, exclude all taxes but include the final product of government activity. The economists of the Commerce Department present a definition of statistical factor costs, which, as Professor Kuznets says, falls between his two definitions. Evidently the Commerce factor may be used in either the partial or aggregative analysis, for the Commerce economists write that factor are costs incurred by final buyers of output for the services of the productive resources embodied in their purchases. Or, for that matter, they are to the nation as a whole, which has only a limited quantity of economic resources to allocate among alternative uses. 3 From the payments made for the services of productive resources they would exclude excise taxes that enter market prices, but not undistributed profit items. Government services are considered as final products and do not enter into the private production as an intermediate factor. Mr. Denison admits that insofar as the free government services are used by business the market prices of privately produced commodities are less than their cost of production including profitbut he prefers not to estimate the size of the free government service in the absence of a definitive criterion.4 In concentrating on details and fine points, Professor Kuznets and the Commerce economists have raised a controversy about factor cost statistics which tends to obscure and certainly is irrelevant to the larger question which suggests itself to the student of national income. I Discussion Of The New Department Of Commerce Income Series, Simon I Income: A New Version; Milton Gilbert, George Jaszi, Edward F. Denison, Charles F. Schwartz, II Objectives of National Income Measurements: A Reply To Professor Kuznets, this REVIEW, xxx (August 1948). 2 op cit., p. I57. Gilbert et al., op. cit., p. 190. 4 Edward F. Denison, Report On Tripartite Discussions Of National Income Measurement, Studies In Income And Wealth, vol. I0, p. 73.

Abstract The article represents a yield formula for calculating irregular installment payments. A fundamental problem in the mathematics of finance is the present valuation of future payments. When they take the form of an annuity of C every period for "n" periods, we have the concise formula P= C(1 -&mul;)/I, which may be expanded in an elementary series. If there is only one future payment, the formula is even simpler, P = Cμ n , and the series is quite as elementary. There are cases in which payments are not all for the same amount. If the variations follow some law, there is still a formula to be had but it becomes more complex. In this fall increasing, decreasing, and deferred annuities, bonds and serial bonds and "balloon note" and "drop payment" installment finance deals. The author proposes to derive an approximation formula for the rate of interest in the general case of future repayments of a present indebtedness, whether they be many or one, equal or unequal and when such a formula, has been obtained, one shall find that it includes both the annuity and single payment formulas as special cases.