The general nature of the enquiry that lies before us is now becoming apparent. The one-week relations, which we were discussing in the last chapter, determine the course of the model in week T, when everything that has happened before week T is taken as given. Having determined the course in week T, we can then proceed to week T + 1, applying similar relations, but with the performance of week T now forming part of the past. And so on, and so on. The path of the economy, over any number of successive weeks, can thus be determined.
Any of the determining elements—technology, consumption propensities and so on—may of course be changing from week to week; but we shall make most progress in understanding the working of the system if we keep these determining elements constant, in some sense or other. For it will be a path that is constructed on this plan which will best exhibit the short-run and long-run effects of a particular cause. Such a path will begin from an initial position that is taken as a datum; its course, near the beginning, and perhaps long after, will be deeply affected by the nature of the initial position from which it has started. It is however possible (though, as we shall see, far from certain) that a point will finally be reached when the particular characteristics of the initial position cease to have much effect upon the path—when it comes to be determined (at least in some respects) by the current determining elements only. If this happens we may say that the model has reached a steady state.
A simple (but important) example of this proceeding is to be found in the application to the Fixwage economy, previously discussed. Suppose that a new technique, more profitable than any previously available, is introduced at time 0, when the sequence starts; but, during the period to be considered, there is no further 'invention'. All processes started after time 0 will use this 'modern' technique; but in the initial position there will still be old processes, using techniques that have become obsolescent, that are uncompleted. Gradually, as time goes on, these