A Neokaleckian Analysis of the Stability of the Sraffian Supermultiplier

We received a very interesting reference from Prof. Franklin Serrano, about a Prof. Allain ´s paper, (2013) Tackling the Instability of Growth: A Kaleckian Model with Autonomous Demand Expenditures, where it shows the dynamic stability of the sraffian supermultiplier Franklin Serrano (1995).

Dear friends:

Here is Prof. Allain´s most welcome contribution on the dynamic stability of the sraffian supermultiplier.

Note that  his stability condition ,  given in equation c5 (p.13) of this version, is:

                                                  

Prof. Allain unfortunately follows the bad  Lance Taylor habit of implicitly assuming the normal capital output v  to be equal to one (his equation (1) p.4). Once we realize this and changing to our more familiar symbols we get:
 

                            vx < s − vz

                            z+x < s/v

and it means in plain english that the marginal propensity to spend in the vicinity of the fully adjusted position  must be below one during the adjustment.

This  is exactly the same condition Prof Fabio  Freitas found in the early 2000s and is reported (with no formal proof)  in our joint 2007 Revista Circus paper (here);  and found  also (with the formal proofs) on Margarita Olivera´s  book (here)