This argument would only be confused by expanding the notation into one involving separate terms and fractions involving determinants. Diagrams cannot help here and a prose translation would presumably have to cover an explanation about the inversion of matrices and the meaning of determinants. This argument, that AY = S-1(AJ) or something even more elaborate, is in principle involved whenever one wishes to find the effect of a given disturbance on a position of equilibrium involving many simultaneous conditions. Marshall himself insisted on the fact that economic variables are interconnected and determined in just this way.7a The difficulty in making AY = S-1(AI) intelligible to persons who have not found time to learn about matrices is therefore a main obstacle in getting them to understand the ramifications of any change involving three or more interdependent variables. A set of numerical examples is probably the best available substitute for matrix algebra in cases of this kind, but it is a very poor substitute indeed. Whilst the axioms and the results should be fully translated into prose, only minor concessions should be made to the semi-mathematician in the exposition of the proof itself. But there remains one further subject that is very much the concern of the non-mathematical reader. This is the possible effects of relaxing the simplifying assumptions. Usually the writer can only guess at such effects by using his mathematical judgment. Only the mathematical readers will be able to pronounce an informed verdict on the worth of such guesses. But the non-mathematical reader will be very interested in precisely these effects and it is therefore essential that any such guesses should be accurately translated into language which both he and the mathematicians can understand. Editors may ask their contributors to bear such precepts as these in mind when compiling articles on economic theory. But they are no more than a guide, and the editor who insisted on literal obedience to them would be unlikely to publish much in this field.

substantial effect on the economy. It must be granted that the point is correct and important. Nevertheless, having so often seen this position taken as a routine matter even in course lectures, I can only wonder if the contrary view is as widespread as Professor Copeland seems to believe. Still more is blamed on the hydraulic view. The Robertsonian lag in expenditure behind receipts is questioned regarding its verifiability (how can we tell the date of receipt of the dollar we are spending now?) and its realism (some of receipts may even be spent at once). But surely this is taking the period analysis too literally. None of us, least of all, I dire say, Professor Robertson, really believes that our system is characterized by neat distinguishable lags. Their use is a device employed with explicit or implicit apology to represent the plausible hypothesis that current consumer expenditures are to a considerable extent dependent on past receipts. The lag is the formalization and hence the exaggeration of a vague psychological connection. Moreover, it is in no way connected with any statement of the genus: today's expenditure employs the very coins, bills, and so forth, which were received yesterday as appears to be implied. It is not quite clear just how some of these points are related to the hydraulic analogy.2 More important, the author seems to take theoretical abstractions at face value and to attribute obliquity to positions of his which are in fact quite generally accepted. I suspect that this polemic material may therefore result primarily in drawing the reader's attention from the volume's main contribution. In sum, this book represents the inauguration of an important task. As such, we must welcome it and apologize for the review's undue emphasis on less important sections of the work which even on the dimmest interpretation distract rather than deduct from its value.

В статье производится анализ агрегированной производственной функции, вводится аппарат, позволяющий различать движение вдоль такой функции от ее сдвигов. На основании сделанных в статье предположений делаются выводы о характере технического прогресса и технологических изменений. Существенное внимание уделяется вариантам применения концепции агрегированной производственной функции.

In the February 1967 issue of the Review we presented estimates of a relationship between changes in help-wanted advertising normalized for growth in the labor force, and changes in the unemployment rate, and new hires, and a dummy variable reflecting the phase of the business cycle [11]. Two notes by Burch and Fabricant [2] and Gujarati [3] have expanded upon our findings. Each paper presents an alternative model and finds that in its own model the relationship between the unemployment rate and the amount of help-wanted advertising is not stable over the period 1951 through 1966 or 1968. The Burch-Fabricant paper tests for the shift in the coefficient of the reciprocal of the unemployment rate before and after 1957. The Gujarati paper tests for the difference in the slope of the unemployment coefficient in ten different business cycle phases from 1951 to 1968. Both papers seem to explain a greater fraction of the variance of the dependent variable than does our model. However, our dependent variable is the change in the normalized help-wanted advertising index; in the other two papers it is the level. By the usual standards, our ]R2 of 0.82 is at least as good as the somewhat higher correlations produced in the level equations. When the two tests suggested respectively by Burch and Fabricant, and Gujarati were applied to our model, the coefficient of the unemployment rate change variable proved to be stable. We first added a variable which is zero up to 1957 and equal to the change in the unemployment rate after 1957; in effect, the regression coefficient of AU is allowed to change its value in 1957. If this variable is estimated along with the other variables in our model, a simple t test will indicate whether the coefficient did in fact change after 1957. Our original equation for the period 1951-1966, second quarter, is reproduced as (1) below. The estimated equation with the dummy variable added is shown as (2):