Can allowing to trade permits enhance welfare in mixed oligopoly?

We compare the effects of tradable emission permits (TEP) and non-tradable emission permits (NTEP) in a mixed oligopoly, where public firms and private firms compete in a product market. If all technologies and initial endowments of emission permits are symmetric among public and private firms and if the emission constraint is exogenous and binding, social welfare is greater (resp. smaller) under TEP than under NTEP when the weight of social welfare in each public firm's objective function and the degree of convexity of the production cost function and that of the abatement cost function are small (resp. large).