Bertrand-Cournot ranking reversal of the optimal privatization level

We consider a vertically related differentiated product mixed duopoly market where a public and private firm compete in the downstream market. The public firm is partially privatized and a welfare maximizing regulator chooses the privatization level. The production of the final commodity requires a key input that is supplied by a foreign monopolist who in the upstream market can practice either uniform or discriminatory pricing. We show that with uniform pricing regime the privatization is always larger under Cournot competition while in case of discriminatory pricing regime, the privatization level under Bertrand competition is always larger. We also find that under discriminatory pricing regime, the Cournot-Bertrand ranking of other relevant variables are sensitive to the degree of substitutability.