Optimal control of the growth of income of nations

摘要

In this paper, we carefully derive the dynamics of the growth of national income as a functional differential equation. We consider autonomous consumption, export, investment and real money demand as “private control variable” or pursuer strategy. We define as “solidarity function” the quarry strategy or government control instrument, government expenditure, taxation, and nominal value of money supply, and consider our dynamics as a differential game of pursuit. Conditions for oscillation (boom and depression) will be given. Optimal strategy to attain a desired growth of income or employment rate will be deduced from the theory of optimal control of a hereditary system.