Monday, March 30, 2015

More oligopolistic behavior

Even very simple models require attention to detail. In [link] we described simple model from the literature. A related model with a coupling constraint that limits pollution emissions is described in:

  1. Jacek Krawczyk and James Zuccollo, NIRA-3: An improved MATLAB package for finding Nash equilibria in infinite games, Victoria University of Wellington, December 2006
  2. Lars Mathiesen, Regulation of pollution in a Cournot equilibrium, The Norwegian School of Economics and Business Administration, Bergen, June 2008.

The Nash-Cournot model without pollution controls is simply:

image

Adding the pollution controls using taxes (or tradable quotas) is not that difficult:

image

Still for this simple model I get different results for the base case (no pollution controls). My results are:

----    135 PARAMETER results 

                     output      profit    emission       price

no control  .j1      55.351      61.274
no control  .j2      14.914      13.345
no control  .j3      53.684      57.639
no control  .k1                             419.978
no control  .k2                             301.125
no control  .-                                            1.761
with control.j1      21.145       8.942
with control.j2      16.028      15.414
with control.j3       2.726       0.149
with control.k1                             100.000
with control.k2                              81.164
with control.-                                            2.601

The paper [1] has the following results:

image

The second part corresponds to my solutions, but the first part shows differences. As the problem with controls is an extension of the problem without controls, there is actually a reasonable chance my solution is correct.