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In the period of the approval of the innovative and information model of Ukraine's economic development, the actual problem is the formation of a new institutional base, which should create favorable conditions for the preservation and accumulation of domestic human capital. After all, the state, reproduction and development of human capital are determined primarily by the nature of its institutional base. Formal legislative acts and informal norms influence the activities of educational, scientific, medical, cultural and other organizations that play a significant role in the formation and increase of human capital. At the same time, the state policy on the human capital formation should provide the social development: the reformation of pension system, education and health care, labor market; modernization of the economy and society: deregulation of the economy, social mobility growth, development of the banking system and financial institutions, such as venture, pension, accumulation and investment funds, the stock market and the insurance services market, as institutions of investment resources for the development of human capital. The analysis of the legislative base showed that not all provisions which are enshrined in the laws of Ukraine realized, that leads to a decrease in the efficiency of the institutional system and inhibits the formation of the human capital system of the information society. In order to overcome these shortcomings and ensure the formation of human capital on an investment basis, it is necessary to create an effective system of distribution of public funds in the system of development and reproduction of human capital. Formation of the human capital system of the information society on an investment basis requires the stimulation of the development of information sectors and science. Obviously, in order to ensure the transition to the information society and the development of the intellectual potential of human capital, legislators need to develop regulatory instruments for preferential taxation of innovative activity of enterprises, which should b exemption from taxation of funds aimed at advanced training or retraining and funds for financing scientific activity The process of human capital diagnostics for the main subjects of human capital investment should consist of successive stages, the realization of which provides full information on the state and the need to invest in human capital by the main subjects.

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The paper develops a mathematical model of population growth in an agricultural community, covering the 17th century ad. The model takes into account two types of resources that provided life, and the influence of management structures on population growth. The analytical results are compared with the estimated data of historians and economists on the world population. Based on the statistical approach, a model for estimating the possible dynamics of population growth is proposed.