Model of Optimisation of Investment Expenditures

The market economy provides such conditions when all enterprises are connected, to a certain degree, with the investment activity and with making investment decisions. Each enterprise has limited financial resources, available for investing. This results in appearance of the task of optimisation of investment decisions. The modern micro- and macro-economic theories use such a powerful method as mathematic modelling. Using mathematics allows allocation and formal description of the most significant properties of economic processes and studying these properties and making conclusions that would be adequate to the studied process. That is why, it becomes topical to search for methods of study and calculation of mathematical models of complex processes, dynamics of which is described by non-linear systems. The article considers the model of management of investment decisions with the Cobb-Douglas production function. It provides a mathematical task setting for maximisation of the sum of profit. Using the principle of maximum, the article obtains the system of non-linear differential equations. It conducts a quality analysis of the system with the help of its phase portrait near points of equilibrium.