Abstract: The economic function of a city is to undertake the tasks in the economies of certain geographical areas and to serve as an economic center. Urban economic functions can be divided into internal and external economic functions. External economic functions are based on leading industries or leading economic sectors, mainly support goods and services for outside areas, and output capital or technologies, whereas internal economic functions provide basic guarantee for production and living activities of the city. Urban internal economic and external economic functions interact with each other and help each other move forward. With the society entering the information age, the producer services, such as finance, science and technology, computer software and information services, have strongly influenced urban industrial and spatial structures, and greatly promoted urban economic functions. Most of the current researches use theoretical analysis to first study the economic functions and then the development of producer services. In this paper, by using social economy, input-output, city population data in 2005 and 2010, based on Input-output model and urban flow model, from two levels of internal and external functions, we analyzed industrial relationships, spatial agglomeration and service products output of producer services, which have greatly improved economic functions of Beijing City. The conclusions are as follows: (1) Economic contribution rate of Beijing's producer service industry is always rising, driving the development of other industries, but at the same time its development is limited by those industries. It also promotes comprehensive benefits of manufacturing industry. Intermediate demand of manufacturing industries and producer services for information, finance, and commercial services increases, which in turn necessitate the upgrade of industrial structure. (2) Financial services, scientific research, information services and business services present an agglomeration in city center, showing a trend to diffuse to suburb areas, with the characteristics of industrial clusters, they have strengthened the function of agglomeration economies of Beijing, leading Beijing to transform from service economy to producer services-oriented economy. (3) Professional level and city flow intensity of producer services are the strongest, and producer services also dominant industries in terms of economic relations with foreign countries. Investment in research, science and technology output, R & D resources has increased significantly, and as a result, the investment has put out a lot of talent and technology as well as labor and capital, with a variety of financial institutions and formation of strong financing scales. (4) Net mix amount and exports of producer services both increased, promoting the output of domestic and international service products in Beijing. The producer services have more advantages in the domestic market, mainly export-oriented. Producer services have higher regional impact on product flow than other industries, and scientific and technical services and financial services industry are the most influential ones. Research on the development of producer services and the economic functions of Beijing City will help understand the productive service industries and their effects on the urban economic growth, agglomeration and diffusion. However, the compositions of urban economic functions include gathering, production, services, innovation and management. Although this paper has touched upon those aspects, detailed studies are required in the future.

Key words: Beijing, economic function, industry association, producer services, spatial agglomeration