Inferior factor in Cournot oligopoly revisited

We reconsider the recent work by Okuguchi (J Econ 101:125–131, 2010) on (possibly asymmetric) Cournotian firms with two production factors, one being inferior for each firm. It is shown there that an increase in the price of the inferior factor does raise the equilibrium industry output. In addition of providing a simpler and more rigorous proof of that result, we generalize it to the case of technologies with $sge 2$ factors and also allow some firms not to use the inferior one.