Abstract: Since the beginning of the reform and opening in 1978, China has implemented company type joint-stock reform of state-owned firms, private firm. Joint venture enterprises continuously increase, and promote the rapid economic development in our country. In September, 2015, the Central Committee of the Communist Party of China and the State Council issued "Guidelines on Deepening the Reform of State Enterprises", pointing out that there still exist some problems for state-owned enterprises to be solved, to deepen the reform of state-owned enterprises. At the same time, attracting foreign investment actively has become one of the important development strategies in developing countries. Advanced production technology can be introduced through the penetration of foreign investment, which is conducive to the development of firms and the improvement of the production rate of domestic firms indirectly. Therefore, studying the degree of privatization of public firms, the foreign penetration of joint venture is of great significance to the firms and social development. Considering the factors such as the product differentiation of firms, the degree of privatization and foreign penetration,the relationship among the degree of privatization, foreign penetration and social welfare is researched, and the impact of the degree of privatization and foreign penetration on the mixed duopoly market under Bertrand competition is analyzed. A mixed duopoly model of Bertrand competition is first established, and the Bertrand equilibrium solution is obtained, then the optimal degrees of privatization respectively for substitutes and complementary goods under government's social welfare maximization are derived. Furthermore, the impact of foreign penetration or domestic stockholding of joint venture on the degree of privatization and the mixed duopoly market is analyzed. The results show that, while the firms producing substitution goods compete in prices, the degree of privatization is reduced to zero, which means that the firm becomes a pure public firm, to achieve the maximum of social welfare, increase in proportion of domestic stockholding of joint venture will improve the optimal social welfare. The decrease of product differentiation will reduce the maximum social welfare, the profits of firms become larger with the increase of domestic stockholding of joint venture in proportion. When the firms producing complementary goods compete in prices, the government can adopt the policy of partial privatization policy in order to maximize social welfare, and should reduce proportion of privatization with the increase of domestic stockholding of joint venture in proportion. The government should encourage product diversification and reduce penetration of foreign capital to obtain the maximum social welfare. From the whole society and the enterprise^'s point of view, joint-stock reform of state-owned firms or part privatization of public firms is the best strategy. Finally, the conclusions are verified through a numerical example of simulation, which is consistent with the results. In this paper, the relevant conclusions can provide some implications for related firms' managers in decision-making to promote social and economic development.

Key words: partial privatization, bertrand competition, foreign penetration, social welfare, product differentiation