An Optimal Policy for Economic Growth

Abstract

Leontief's closed economic model is optimized using Pontryagin's maximum principle. The objective functional is maximization of time integrated utility. Pontryagin's/1/ "Maximum Principle" has been successfully applied to problems of optimal policy for economic growth by several authors. Shumpei Kumon/2/ presented a one-sector model using linear flow and stock functions at the 1966 Far Eastern Metting of Econometric Society. Kurz/3/ and Stolery/4/ analysed two-sector growth models where relevant equations were not necessarily linear. Chakravarty/5/ formulated an n-sector model using Leontief matrices of stock and flow coefficients. Superiority of the Maximum Principle over the classical calculrs of cariations lies in the fact that policy variables are treated endogeneously and regions of policy variables may be closed set, giving rise to endogeneous policy variables (the control functions) which may be discontinuous. Switching control functions were observed in the growth models of Kurz, Stoleru, and Kumon. The Chakravarty model did not produce switching control function and the functions found were insensitive to utility function.