Price control and privatization in a mixed duopoly with a public social enterprise

We explore the issue of the optimal degree of privatization for a public firm that does not need to care about its rival's profit completely. We find that the optimal privatization of a public social enterprise under exogenous price control depends on the level of the regulated price. Namely, when the regulated price is low (medium, high), the optimal privatization is partial privatization (complete privatization, completely public owned). If the price control is optimized by maximizing social welfare, then the optimal privatization is complete privatization. For the case of the traditionally defined public firm, its optimal privatization is completely public owned when the price control is exogenously given. If the price control is endogenously determined, then privatization policy is redundant.