Aggregated Dynamic Model of a Two-Sector Economy with Venture Investment

Venture capital now is a significant part of investments in innovative projects. In this article it is proposed dynamic model of a two-sector economy with venture investment. There are five economic agents: the population, the banks, resellers and producers, divided into two sectors the traditional and innovative. The article gives microdescription of firms in both sectors. The main sector companies at any given time are founded by moving into it one of the venture sector firms, where several firms are being created in each moment. Innovative firms parameters are set by the normal distribution. Venture investor takes loans of the banking system, and is fully in control of gains and losses of the venture sector. People invest money in the firms which join the traditional sector to gain their share in profits. The article describes the process of exiting the innovation sector by firms and their sale. Also it is described the process of liquidation of unprofitable firms in both sectors. The results of numerical experiments with a closed mathematical model are presented. The proposed model shows the exponential growth in which stands a distinctive kink in the time when the investments of the population reaching the level of bank loans.

venture investment, mathematical modelling, optimal control, numerical methods, mathematical economics