Dynamic Optimization of Capital Stock: An Application of Maximum Principle

Determining the optimized level of economic variables is very influential in compiling economic plans and policies. This study deals with the determination of the country's optimized capital stock by the use of Pontryagin's Maximum Principle in the time period 1972-2017. The product function is assumed as Cobb-Douglas, and the coefficients of product function are measured by Eviews software. After that, the achieved differential equation applying from Maximum Principle is solved by the use of numerical methods via MATLAB software. Then, under certain hypotheses about the rate of depreciation and the ratio of savings, the optimized capital stock is calculated and is compared to the real ones. Findings of the study approve that there are big gaps between the existing situation and the optimized capital stock in Iran. In order to decrease the gap, it is urgent to increase investment and take policies for provoking the private sectors.