Comparing Bertrand and Cournot Outcomes in the Presence of Public Firms

We revisit the classic comparison between Bertrand and Cournot outcomes in a mixed market with private and public firms. A departure from the standard setting, i.e., one where all firms maximize profits, provides new insights. A welfare-maximizing public firm's price is strictly lower while its output is strictly higher in Cournot competition. And whereas the private firm's quantity is strictly lower in Cournot (as in the standard setting), its price can be higher or lower. Despite this ambiguity, both firms, public and private, earn strictly lower profits in Cournot. The consumer surplus is strictly higher in Cournot under a linear demand structure. All these results also hold with more than two firms under a wide range of parameterizations. The ranking reversals also hold in a richer setting with a partially privatized public firm, where the extent of privatization is endogenously determined by a welfare-maximizing government. As a by-product of our analysis, we find that in a differentiated duopoly setting, partial privatization always improves welfare in Cournot but not necessarily in Bertrand competition.