Knowledge that Transforms

IN A STUDY THAT the author has had the opportunity of making on certain aspects of the economic history of the Continent of Europe in the early nineteen-twenties, he was struck by the similarity in immediate causes and in actual development which characterize the process of exchange depreciation and currency inflation in almost all countries in this area. Of course, as is well known, the extent to which depreciation actually proceeded differed greatly from country to country. Stabilization was achieved in France, Belgium, and Italy at rates of the order of one-fourth of the prewar parity; the stabilization value for the German reichsmark was only 10-12 of that of the old gold mark. Notwithstanding this extreme difference in magnitude, the underlying mechanism which could serve to describe the course of events in all these countries appears to have been substantially the same. It is intended to give in the present paper a brief outline of the main features of this mechanism. Many competent analyses have indeed been performed of the intriguing phenomenon of exchange depreciation in a particular country. Mention should be made of BrescianiTurroni's excellent analytical description of the German experience' and de Bordes' treatment of the Austrian crown.2 A comparative study of a number of European countries has been made by Aftalion.3 From these, as well as from a number of other case studies,4 the major part if not all of the structural equations-to use Frisch's termin the model developed below have been drawn. But in none of these studies are these essential relations made sufficiently explicit to be used as such; and, moreover, as the elimination of what should be considered the very minimum set of structural equations cannot be performed without writing down the relations concerned in mathematical symbols, a full picture of the essentials of exchange depreciation has, it would seem, never been put forward. Nothing more than the very essentials can be given here. It would seem that these alone are already of considerable assistance in clarify-

WITHOUT GETTING INTO a detailed discussion of the ramifications of the concept of depreciation, it should be recalled that depreciation is based to a great extent upon the degree of loss of the service capacity of physical property. Where a plant account consists of property of the same type, such as electric meters, transformers, underground cable, etc., certain types of mortality laws are found to apply to the retirements from the account and when this is true it is possible to determine by well-known actuarial processes the expectation of life of this property at different ages. The variation of this expectation of life from age to age offers a basis for determining loss in service capacity of the property in question. Methods of estimating accrued depreciation, however, not only take into account loss in expected service capacity, but also are influenced by the accounting problem of amortizing the original plant investment over the life of the plant in a reasonably simple manner. The problem of determining depreciation of a plant is thus unavoidably composed of two elements: (1) Determination of variation of expected service capacity of plant in time, relative to expected service capacity when new; (2) the effect of such variation upon a simple and reasonable program of amortization. In this article certain aspects of the first element of the problem are considered; namely, the behavior of plant balance in relation to gross additions and retirements, under operation of a constant mortality law of retirement. The significance of these relationships lies in the effect they have upon the age distribution of the plant account at a given time, and the fact that knowledge of the age distribution and mortality law determines future expectation of life of plant at the time in question, relative to expectation of life when new, thus offering a basis, in many cases, for determination of relative loss in service capacity of plant. For example, a mortality law which can be approximated by

WITH THE STUDY OF problems of capitalization, credit, and discount, the peaceful parade of equationally determinate barter economy' comes to an abrupt halt. The systems of equations expressing the conditions of equilibrium theory differ in number from the unknowns to be determined. Equational determinacy is established only by the introduction of money into the system. This conclusion is, I believe, novel in general-equilibrium theory. It is an obvious confirmation to an essentially monetary theory of interest-as distinguished from a real capital theory admitting of short-run monetary dislocations. In its support, demonstration of the following subordinate propositions will be attempted: In a static, but not stationary,2 barter economy it is necessary, first, to posit a plurality of interest rates in order to secure the equality of demand and supply of loans for each of the various goods and services lent in natura.3 It is necessary, second, to provide for yet another plurality of discount rates, to take account of the loan aspect of payments for services made at times other than those at which their final products are sold. It is necessary, third, to establish various fixed relationships, which I call capitalization rates, between the prices of services and the prices of the goods which are their sources, so that individuals may be able to choose rationally between the purchase (sale) of the goods and the purchase (sale) of the services. Under barter, there are no clear interrelationships between these various rates. The lack of interrelationships renders indeterminate each of the three