= farms, and persuaded to continue in the service of their employers, their wages plus the interest on the capital needed to lay out a farm must be equal to what the "product of labor" of the farm would be after its completion. These conditions may be expressed mathematically. If wages=a+y, the rate of interestz, "product of labor" of one man p, the number of units of capital used by one man cultivating the new farm=q, whose value is q (a + y), since each unit of capital has the value of one year's wages, then, in order for the laborer to be deterred from laying out the farm, this equation must exist: (a+y) + q (a+y) z=p;* or (a+y)=1+q2; or Here a, p, and q are known quantities, and 2= p-(a + y) y and z are unknown. We have now obtained an equation expressing the interdependence of wages and interest. The next problem is to find an independent expression for wages. To enable him to find this expression, Thünen supposes that a number of laborers combine to lay out a farm on the margin of cultivation of the isolated state. This new farm is to be of the same character as those already existing in the state. The combination of laborers divide themselves into two groups, which we shall call group A and group B. The laborers in group A remain in the service of undertakers, and by means of the surpluses of their wages furnish the means of subsistence to the laborers of group B, who lay out the farm. In order to avoid confusion, we shall call the laborers in groups A and B capital-producers.† In the course of a year the farm is completed, and la It must be remembered that Thünen considers the isolated state under static conditions, for otherwise equilibrium would not be maintained even if the relation existed expressed by the equation (a+y)+q (a+y) z = p. In a progressive state the laborers would secure a large advantage in laying out marginal farms, owing to the growth in value of those farms, due to general progress. Cf. Professor J. B. Clark, “De l'Influence de la Terre sur le Taux des Salaires," p. 256 of Revue d'Économie Politique, 1890. †Thünen calls the laborers in groups A and B kapitalerzeugende Arbeiter (p. 151). borers are employed to cultivate it. The wages of each of these laborers must be so great that the income which each of them receives from his surplus when that surplus is placed at interest — i.e., yz — will be equal to the sum received by each of the capital-producers as his share of the rent of the farm; for, if this were not the case, the laborers would lay out farms for themselves. * These facts Thünen expresses in mathematical language, and is thereby enabled to obtain the formula: Natural wages Vap. He uses the following symbols: = = Let a+y=the year's wages of a laboring family, a and y retaining the same meanings that they have had throughout this paper. ng the number of capital-producers in group B; that is, the number of men needed to lay out the farm. Thünen admits that, to lay out the farm, is needed not only labor, but also capital; but he summarily dismisses this difficulty by saying, "According to § 13, we can reduce the co-operation of capital to terms of labor" (p. 152). Later on I shall show that in the ascertainment of the quantity ng lies the error which vitiates the formula Vap. As the farm is completed in one year, its value is equal to nq units of capital. anq=the amount consumed by the nq men in group B. ang y = = the number of capital-producers in group A, since the capital-producers in group A support those in group B by means of their surpluses. n=number of men employed to cultivate the farm after its completion. n (a + y) = total wages paid n men. p="product of labor" of one man, working with q units of capital. np total "product of labor." np -n (a + y) = y Rent is used here in the sense noted above, and means earnings of capital, not land rent. producers, or his portion of the rent of the farm. In this last expression all the quantities are known excepting y. Now, it has already been observed that, for the laborers to be induced to work on the new farm, the income which each receives from his surplus when that surplus is placed at interest must be equal to the rent received by each [p−(a+y)] y capital-producer: hence yz must be equal to q (a + y) Capital-producers and laborers, therefore, have a common interest in making the above function as large as possible; and, when the function has reached its maximum value, the interests of capital-producers and laborers will be satisfied. The question is, then, For what value of y will [p―(a+y)] have a maximum value? q (a + y) Differential calculus enables Thünen to answer this question. He solves the problem by differentiating the function with respect to y, and then placing the differential equal to zero. He finds that the function will have a maximum value when (a+y)=√ap. Having obtained the formula for natural wages,* he is able to find the expression for the natural rate of interest by substituting Vap for (a+y) in the equation z= p-(a+y) q (a + y) JOHNS HOPKINS UNIVERSITY. H. L. MOORE. Thünen placed such great value upon the formula Vap that he requested it should adorn his tombstone. According to Schumacher (J. H. v. Thünen: Ein Forscherleben, p. 322) his wish was respected: "Die Krone seiner Gesetze, das Resultat mühseliger Untersuchungen über das Verhältniss des Arbeitslohns zum Zinsfuss und zur Landrente, wie solches aus seinem Arsenale mathematischer Formeln siegreich hervorging: Der naturgemässe Arbeitslohn = √ap schmückt als Denkspruch seinen einfachen Grabstein im Hügellande von Mecklenburg, wie er in schöner Stunde selber gewünscht." BIBLIOGRAPHY. Johann Heinrich v. Thünen: Der naturgemässe Arbeitslohn und dessen Verhältniss zum Zinsfuss und zur Landrente. Part II. 1 of Thünen's Der isolirte Staat in Beziehung auf Landwirthschaft und Nationalökonomie. Dritte Auflage. Berlin. 1875. J. A. R. v. Helferich: J. H. v. Thünen und sein Gesetz über die Theilung des Produkts unter die Arbeiter und Kapitalisten. Tübinger Zeitschrift für die gesammte Staatswissenschaft. 1852. pp. 393-433. A. Leymarie: Le Salaire Naturel et son Rapport au Taux de l'Intérêt, par M. Jean Henri de Thünen. Journal des Économistes. 1857. t. 15, pp. 250-264. Mathieu Wolkoff: Nouvelles Observations au Sujet de l'Ouvrage de M. de Thünen sur le Salaire Naturel. Journal des Économistes. 1857. t. 16, pp. 239-255. Étienne Laspeyres: Wechselbeziehungen zwischen Volksvermehrung und Höhe des Arbeitslohns. Heidelberg. 1860. Georg Friedrich Knapp: Zur Prüfung der Untersuchungen Thünen's über Lohn und Zinsfuss im isolirten Staate. Braunschweig. 1865. L. J. Brentano: Ueber J. H. v. Thünen's naturgemässen Lohn- und Zinsfuss im isolirten Staate. Göttingen. 1867. H. Schumacher: Ueber J. H. v. Thünen's Gesetz vom naturgemässen Arbeitslohne und die Bedeutung dieses Gesetzes für die Wirklichkeit. Rostock, 1869. W. Roscher: Geschichte der Nationalökonomik in Deutschland. pp. 879-902. Georg v. Falck: Die Thünen'sche Lehre vom Bildungsgesetz des Zinsfusses und vom naturgemässen Arbeitslohn. Leipzig. Carl Knies: Der Credit. pp. 125–131. Th. Mithoff: Der naturgemässe Arbeitslohn. In Schönberg's Handbuch der politischen Oekonomie. Band I., pp. 636–640. Dritte Auflage. H. Schumacher: J. H. v. Thünen: Ein Forscherleben. Zweite Auflage. Rostock u. Ludwigslust. 1883. W. Launhardt: Mathematische Begründung der Volkswirthschaftslehre. Leipzig. 1885. pp. 138-140. C. Schmidt: Der natürliche Arbeitslohn. Jena. 1887. pp. 16-40. Maurice Block: Les Progrès de la Science Économique. Vol. II. 1890. p. 259 et seq. J. Lehr: Grundbegriffe und Grundlagen der Volkswirthschaft. pp. 325–328. *I have been unable to secure a copy of Brentano's dissertation. It is out of print. STATE REGULATION OF PRICES AND RATES. THE extraordinary development of corporations characteristic of the present century has given rise to many new problems, social, political, and legal. The concentration of industry resulting from the employment of great aggregations of capital united under a single control has created conditions which to many persons have seemed to require a revision of previously accepted economic doctrines and a resort to extraordinary legal remedies. Competition, where each competitor must engage in business on a scale requiring an initial capital of millions of dollars, has not produced results satisfactory either to the public or to those concerned in the prosperity of the business. The power acquired by those controlling vast combinations of capital has not always been exercised discreetly; and the belief that the consuming public should be protected from exorbitant charges made for the benefit of those interested in such combinations has become wide-spread. The cure for evils serious enough in reality, but still greater in the popular imagination, has been sought in legislation regulating the conduct of business; and, with the further extension of the conditions. referred to, it is probable that such relief will be more widely attempted. Since laws directed to this end are, for the most part, under our form of government, outside the scope of the powers conferred upon Congress, it is a matter of importance to consider how far the Federal Constitution restricts the several States in such legislation. This presents two principal questions; namely, whether the Federal Constitution imposes any restrictions upon the kind of business that may be regulated, and whether it imposes any restrictions upon the nature or degree of regulation that may be established. It is the |