Ragnar Frisch

Circulation Planning: Proposal For a National Organization of a Commodity and Service Exchange

1. Intrinsic tendencies towards contraction and expansion in an exchange system 261 2. The indebtedness factor in exchange contraction and expansion ....... 265 3. A simplified example of a planned exchange 272 4. The correction of the request-matrix by the principle of partakers percentages 273 5. Generalized principles of correcting the request-matrix ..... ...... .. 282 6. The limitational condition for the total volume of operations ......... 286 7. A general differential method of adaptation for the minimum factors.. . 293 8. An analytic method of adaptation 302 9. A numerical example showing details of the computation .... ........ 306 10. Estimate of the amount of work involved when the number of variables is very great 320

Alfred Marshall's Theory of Value

I. The various orders of change, 496. — II. Normal equilibrium with reference to short periods, 499. — III. Normal equilibrium with reference to long periods, 507. — IV. The relationship between short period normal and long period normal equilibrium, 519.

An Implementation System for Optimal National Economic Planning without Detailed Quantity Fixation from a Central Authority

Through my lifelong study of economics, including the traditional and orthodox approach, and for the last thirty years with special emphasis on new and rational forms of macroeconomic planning, I have reached certain conclusions which in a nutshell can be expressed as follows.

Rational price fixing in a socialistic society

3. The macro-optimal prices. I. The authorized list of variables II. The system of equations III. The bounds IV. The preference function V. The optimal solution VI. Definition of optimal prices VII. Computation of optimal prices VIII. Interpretation of optimal prices 0. Marginal preferency in the optimum 1. In general 2. Linear 3. Labour theory of value in Mehrwert form 4. Friedrich v. Wieser Marginal utility theory of value in Mehrwert form

Changing harmonics and other general types of components in empirical series

The method outlined in the present article is an attempt to approach the general problem of components in empirical series by a principle less rigid than the principle of analytical formulae with constant parameters, on which the usual methods of curve fitting, harmonic analysis etc. are based. The main points of the method were first set forth in April 1927 in an article: The Analysis of Statistical Time Series, mimeographed for private circulation. The method is actually worked out with considerably more details than here given. Numerical applications are also under way. I hope that a full account of the method, accompanied by extensive numerical applications, may be published some time next year.

PARAMETRIC SOLUTION AND PROGRAMMING OF THE HICKSIAN MODEL

Publisher Summary This chapter discusses an explicit general solution of the Hicksian Model, holding true for any period of time t and with any arbitrarily given right member—the term which makes the difference equation non-homogeneous. The solution has one degree of freedom—one arbitrary function of time—when the parameters of the model are given. Programming techniques are indicated either to determine desirable values of the parameters in the Hicksian Model or to choose one of the variables as a decisional function of time. In both cases, one may haze a linear or a more general preference function having the aim of minimizing fluctuations in incomes from their long run growth path and/or assuring rapid growth in the long run. The recurrence method and the method of characteristic roots for solving a linear difference equation of any order with constant co-efficients and an arbitrary right member—the non-homogeneous case—are discussed in the chapter with a special application to the Hicksian Model.

A multilateral trade clearing agency

This chapter describes a multilateral trade clearing agency. It presents nine principles on which a multilateral trade clearing agency must be built. The agency must be built on the existence of national states that retain a considerable degree of sovereignty so far as the internal organization of their economics and political systems is concerned. Each country must be given an opportunity to voice its own desires regarding its own economic targets, such as different types of investments to be made, different directions in which to push its exports, and so on. It is found that if each of these independently worked-out systems of economic targets and plans were to be carried out, they might, and in general will, turn out to be completely inconsistent. They will work counter to each other. It is precisely this inconsistency that produces the basic difficulty in patterns of international trade. The different systems of targets and plans have to be made consistent. The manner of making them consistent is precisely where the multilateral trade clearing agency has a role to play.

On the inversion of a moving average

Abstract At the request of the Faculty of Science of Stockholms Hogskola I had the pleasure to act as opponent at the doctoral discussion on Mr. HERMAN WOLDʼns dissertation: »A Study in the Analysis of Stationary Time Series». Both the reading of the book, the public discussion and a subsequent private correspondance with the author, I have found very interesting and stimulating. I have also had the pleasure to discuss to some extent this matter with Professor CRAMER. Some of the points raised during our exchanging of views have been covered by Mr. Wold in his note in this issue of the »Aktuarietidskrift», but not all. It may therefore be worth while to add a few remarks. I need not dwell upon the various merits of the book, they speak for themselves. Here, I shall confine myself to one particular point where some difference of opinion still seems to persist, namely the significance of the formula (255) in the dissertation, which is the same as (13) in Mr. WOLDʼn note in this issue. This formula is intended...

Preface to the Oslo Channel Model

The most primitive approach to medium and long term forecasting is a mechanical trend extrapolation for some specific variable which one may be interested in, or a mechanical trend extrapolation made separately for each of a number of variables.

On approximation to a certain type of integrals

Abstract Some years ago, in the course of an analysis of upper and lower limits for incomplete moments of statistical distributions I established an elementary summation formula1 which proved rather useful for the purpose I had in view. Subsequently the formula was generalized by professor Steffensen, who showed2 that the formula in question could be looked upon as giving the first term of an expansion in a certain type of series. Professor Steffensen established recurrence formulae for the coefficients of the series and computed the second, third and fourth term and the corresponding remainders1, but did not arrive at a general, explicite expression for the coefficient of the n-th term and the corresponding remainder. A year later I found these expressions accidentally while I was working on some other problem. I also discovered the real nature of the procedure in question which proved to be a certain kind of least square fitted polynomial approximation. I did not, however, at the time publish the result...