I recognized the function because of my background.  The question I left un-asked is how a theory could be constructed that could relate the function to the economic phenomena it is proposed to describe.  What seemed to me to be the most important part of the comment was that the oscillations damped out afterthe step transition, instead of building up before the transition, as proposed in the theory, and to suggest a model that would conform to the proposed theory by reversing the arrow of time from that shown in the graph.  A really satisfying theory would account for that reversal as well.   The classical economists did too much damage with inappropriate borrowing of math functions from physics for me to want to repeat that!

As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."