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

THE FOLLOWING THEORY of business fluctuations is claimed to be simple in the mathematical sense as stated by Jeffreys2 and also to represent the simplest possible dynamic extension of the Walrasian system. It explains the business cycle as a purely speculative short-run equilibrium phenomenon. Assume an economic system consisting of n commodities. The buyers and sellers take into account not the actual but the anticipated price. Assume further with Evans that they form their anticipations upon the prevailing price and the price tendency, i.e., the rate of change of the price in time.' If all relationships are linear (as first approximations), we get, for the demand for the ith commodity,