I. Introduction, 127. — II. One commodity, 128. — III. Aggregation, 130. — IV. Many commodities, 131. — V. Relation to the capital controversy, 131.

The problem, 274. — Subjective risk, 275. — Subjective uncertainty, 280. — Graphical illustrations, 281. — Methodological considerations, 301. — Empirical verification, 302. — Relation to welfare economics and economic policy, 305.

Journal Article A Note on Economic Aspects of the Theory of Errors in Time Series Get access Gerhard Tintner Gerhard Tintner Iowa State College Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 53, Issue 1, November 1938, Pages 141–149, https://doi.org/10.2307/1884111 Published: 01 November 1938

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:

THE following production functions have been derived from business records of 609 Iowa farms for 1942, kept at Iowa State College.2 These records give a complete picture of all the business transactions and holdings of each farm and are carefully checked. They are, however, far from typical for the average Iowa farm. Their relationship to actual production conditions at the farm is perhaps comparable to the relationship between yields from careful experiments at an agricultural experiment station to the actual yields of an average field. We have included altogether 609 farm records in our analysis. They have been divided into four main types of farming (dairy, hogs, beef feeders, crops). We use as a regression equation a function which is linear in the logarithms. This is none other than the production function which Paul H. Douglas used in his many empirical studies.3 We do not, however, make the assumption of homogeneity, i.e., the sum of the regression coefficients is not necessarily equal to one. In fact, we shall later present a test of significance designed especially to test, in a fashion, the assumption of a linear homogeneous production function. The reasons which prompt us to use this particular form of the production function are the following: (1) It gives immediately elasticities of the product with respect to the factors of production (Paul H. Douglas called them flexibilities). That is, we get answers to the question: By how many per cent will the product increase on the average if the given factor increases by 1 per cent. Elasticities are dimensionless numbers and independent of the units of measurement. (2) Our form of the production function permits the phenomenon of decreasing marginal returns to come into evidence without using too many degrees of freedom. This would not be possible if we should fit a linear function

IT IS THE PURPOSE of this paper to generalize the demand theory of Hicks and Allen2 for the dynamic case. It also could give a somewhat firmer theoretical foundation to the dynamic demand theory of the Econometrists, especially G. C. Evans3 and C. F. Roos.4 We propose to derive income, price, and interest elasticities of demand under the assumption that the individual has definite plans for the future and definite expectations of future incomes, prices, and interest rates. Hence uncertainty in the sense of F. H. Knight5 is ruled out, whereas risk may be taken into account. We make the same assumptions as in the previous paper on Maximization of Utility over Time.6 The individual plans for n discontinuous points in time in the discontinuous case, where utility is a mere function. Utility becomes a functional rather than a function in the continuous case.

SUPPOSE provisionally the existence of a utility function F. Let us assume further that the individual in question consumes only three goods x, y, and z. The argument can easily be extended later to any number of commodities. The individual is at the point in time 0 and plans for the period of time 1, 2, , n. Consumption takes place at these n discontinuous points in time. We denote by xi the quantity of the commodity x which the individual plans to consume at the point in time j; similarly, y2 and zj. He does not accumulate any commodity stocks. The utility function F will depend on those quantities which the individual expects to consume: