Universal laws for the control of global economic growth with nonlinear hereditary dynamics

摘要

In this paper, we show that the growth of isolated capital stock or national income can be described as a nonlinear hereditary system. When n such systems are linked up to others in the region by a solidarity function which may be taken to be the effect of government and other factors on the subsystem of n firms, we use investment, export, money holding, and consumption strategies as the firms' vector instruments to control the growth of capital stock. Government vector instruments include nominal value of money, taxation, and investment (for example, into innovation). The control problem is viewed as a game of pursuit between government and the firms. Proven theorems provide universal laws for the growth of capital stock from an initial endowment to a target. Though the control strategy constructed to reach the target may not be usable, except when linear or if nonlinear, under some exceptional circumstances because the fundamental matrix is too difficult to construct, the consequences nevertheless provide a solution to this century's burning problem of how much government intervention (compared with private firms) should be to ensure economic growth. For this alone, i.e., (6.8), (6.9), (6.10), the research here seems important. A very simple model of the Austrian economy is presented.