Knowledge that Transforms

IT IS IMPORTANT for problems of storage and of price discrimination to know whether the total-revenue curve is convex or concave. I shall try to state the conditions for the demand curves under which the totalrevenue curve is convex or concave. Let D be the quantity. is the demand curve and the total-revenue curve. The total-revenue curve is convex if d2[DF(D)] /dD2 0. In the first case, d2[DF(D) ]/dD2 O, or DF(D) -2F'(D). If the total-revenue curve is a straight line, DF(D) =2F'(D), and by solving this differential equation we get = a/D + b, where a and b are constants (a>O). These are Marshall's constant-outlay curves, a/D, shifted up or down by any constant quantity b (Figure 2). If the case of a straight-line total-revenue curve, = a+bD, we have F'(D) = -a/D2 (Figures 1, 2), F(D) =2a/D3 (Figure 1), and DF(D) = 2a/D2 (Figure 1). In Figure 2 some demand curves and their marginal curves for straight-line total-revenue curves are represented. If the marginal curve, F'(D) =I'(D), of a given demand curve, = I(D), cuts one of the curves F'(D) =-a/D2 from above at a point P', then its slope at this point is smaller than the slope of the curve F'(D) =-a/D2. Since the slope of the curve F'(D) =I'(D) is F(D) =I(D) and the slope of the curve F'(D) = a/D2 is F(D) = 2a/D3, the relation

The ever-increasing demand for more and better statistics relating to agriculture in its many phases can be met by the two governmental agencies responsible for these statistics, (The Agricultural Marketing Service of the U. S. Department of Agriculture and the Bureau of the Census of the Department of Commerce) by the development and practical use of objective methods of sampling and, estimation. Three specific suggestions for using objective sampling methods in strengthening agricultural statistics were made by the writer in a previous paper, as follows: (1) Use a split schedule in Census enumerations to broaden the scope of basic agricultural statistics by from 50 to 200 percent, (2) Take a rotating partial census in intercensal years in commercial fruit and truck areas to obtain more reliable and more useful basic statistics regarding these specialty crops than is possible in connection with a general enumeration, (3) Take a nation-wide annual enumerative sample of individual farms covering crop acreages and production, livestock numbers and production, etc. The need for these improved methods has been developed more fully in the present paper, in which a critical description has been given of some of the more important methods of sampling and estimating now used by the U. S. Department of Agriculture and of some of the results obtained in developing more objective sampling methods.

THE OBJECTIONS which have been raised against the fundamentals of the value theory of the classical school of economics hardly ever went so far as to affect the principle upon which the Ricardian explanation of land values was based, viz., the idea that the value of land is not to be explained in terms of cost, but in terms of a residual rent. This idea when developed into its consequences has even facilitated the insight into many value phenomena other than land values. However neither Ricardo nor his postclassical followers ever attempted thoroughly to examine the question whether and with what modifications the residual rent concept can be used in interpreting the economic phenomena presented by the existence of urban land values. To my knowledge the first author who undertook the task of establishing a consistent theory of the urban ground rent was the Austrian economist F. von Wieser.' Wieser emphasized an important distinction obtaining between the agricultural ground rent and its urban counterpart with respect to the relations between the factors which are instrumental in producing the differential returns: the former is due to the fact that, owing to increased demand for farm products, agricultural production may be profitable also at increased costs, with the result that a surplus profit accrues to those farmers whose production is privileged by lower costs. On the other hand, according to the Wieserian theory, the residual rent of urban sites is largely independent of differences in costs of construction; it is due to differences in the demand for the services rendered by different real-estate properties and, consequently, to differences in the prices paid for such services. Von Wieser has specified his theory by distinguishing within each locality a range of housing markets which differ according to the situation of the sites. The tendency to exploit the privileged sites to the fullest possible degree is reflected in the process of intensifying the utilization of land of this type both horizontally and vertically. The larger the portion of the lot which is utilized for dwelling and renting purposes and. in addition. the larger the number of dwellinL;s and premises * Paper presented at Colorado Springs, July 26 and 27, 1939, before Cowles Commission Fifth Annual Research Conference on Economics and Statistics, under title of Some Dynamic Aspects of the Urban Ground Rent. 1 v. Wieser, Theorie der gesellschaftlichen Wirtschaft in Grundriss der Sozialdkonomie, 1, p. 362.

IN RECENT YEARS a number of theoretical and statistical investigations' in the field of business-cycle analysis have made use of differeince equations, or mixed difference and differential equations. These equations serve to study the possible endogenous movements of a schematized economic system governed by a set of as many structural relations as there are variables, the movements of which are considered. In the investigations referred to, the treatment of such a set of equations has been to eliminate successively all variables but one, which leaves one from which the possible movements of the system under consideration are studied. If the final equation in the variable Zt is a linear homogeneous difference equation or mixed difference and differential equation, possible movements of Zt are found by substituting for it in the final equation an expression of the form2

IN MODERN business-cycle research the following proceeding is being commonly used: First, a mathematical model (a determinate dynamic system) is set up, as an attempt to describe approximately the interconnections between a set of economic variables, their time derivatives, lagged values, and so on, in terms of strict functional relations. By some statistical procedure the constants in the system are estimated from the corresponding observed time series. Then the system is solved, i.e., the variables are expressed as explicit functions of time, involving the estimated parameters. The degree of conformity between these theoretical solutions and the corresponding observed time series is used as a test of the validity of the model. In particular, since most economic time series show cyclical movements, one is led to consider only mathematical models the solutions of which are cycles corresponding approximately to those appearing in the data.' This means that one restricts the class of admissible hypotheses by inspecting the apparent form of the observed time series. This condition for a good theory is of course not a sufficient one, since there are in general many different a priori setups of theory which are capable of reproducing approximately the observed cycles. But, what is more important, it may not even be a necessary condition, and its application may result in a dangerous and misleading discrimination between theories. The whole question is connected with the type of errors we have to introduce as a bridge between pure theory and actual observations. Compared with actual observations, each equation in a dynamic model splits the observed variations into two parts, one part which is explained by the equation, and another part which is not accounted for, and which is ascribed to external factors. This kind of splitting is common to all theory. We usually consider such equations as good and useful theories if, in order to get full agreement between theory and observations, it is and continues to be sufficient to allow for only relatively small and random external factors. There are two main ways in which such external factors may be