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: