Comments and Questions

Prof. Popov's report is very instructive. We are most grateful for the time he took reading our manuscript and also for writing a kind crash course of Economics' view on the mechanisms underlying various types of recessions. He raises two issues. The first one is that our claim about the universality of the shape of recessions may not hold for some types and sub-types of recessions whose mechanism he explains in details. He then suggests that the shape of the GDP may be something else, such as a parabola. Taking the example of an economy whose all sectors shrink at the same rate and then recover for some reason, he argues that the first phase of such kind of recessions corresponds to setting both rates \lambda_+ and \lambda_- to the same value, hence that the fitting equation is not adequate for this case. It may be, and we would be grateful if such an real-life example can be pointed out tu us in order to study this case in details. But the wording 'sectors' should not be taken literaly: one can always try to fit this peculiar kind of recession with the proposed function. But once again, one would first to find a few examples of such events and fit them. It is possible in passing that the examples included in our submission do contain at least in part such mechanisms. Similarly, if the transfer rate is indeed the essential limiting factor of the speed to recover, the fitting equation does not assume the existence of such mechanisms. We wish to point out once more that the fitting equation that we propose works because it respects the auto-catalytic hence exponential nature of (both positive and negative) economic growth. We also wish to say that the ongoing worldwide recession shows that our model does not take well into account the very first stages of recessions, as it implicitely assumes that the GDP is a convex function, whereas the GDP of the UK ( http://www.statistics.gov.uk/cci/nugget.asp?id=192 ) is clearly a concave function during the first few quarters. This may be due to the fact that the numbers of sectors affected by the slowdown increases as a function of time, that is, that f is not a constant at the beginnning of the crisis. We are of course willing to amend our article to emphasize this point. The second issue concerns the theoretical model that we analyze in the second part of our submission. He rightly points out that we need to be more specific at places and to expand the discussion so as to take into account his suggestions, in particular with respect to the optimal transfer rate. In short, we understand better the need to adjust the way we present our main ideas and our results so as to be more precise and to communicate better to the audience of the journal.