Partial privatization in mixed duopoly

We investigate a quantity-setting duopoly involving a private firm and a privatized firm jointly owned by the public and private sectors. The private firm maximizes profits, while the privatized firm takes both profits and social welfare into consideration. We consider how many shares the government should hold in the privatized firm. We find that neither full privatization (the government does not hold any shares) nor full nationalization (the government holds all of the shares) is optimal under moderate conditions.