An Algorithm for the Dynamic Programming of Economic Growth

An Algorithm for the Dynamic Programming of Economic Growth

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The paper studies the computational properties of an algorithm for optimal resource allocation over time, and applies the algorithm to a model of the U.S. economy. The algorithm is applicable to multisector models with differentiable production and objective functions, and uses a method of successive approximation by linear-logarithmic functions, in which the recursive features of dynamic programming are combined with exact formulas for optimal solutions in the linear-logarithmic case. Memory and computing requirements go up approximately linearly with the number of state variables, and experience indicates that the algorithm can handle a model with 10 sectors and 50 time periods in a few minutes on a machine like the IBM 7094. The algorithm is applied to a four-sector empirical model of the U.S. economy, and various optimal paths are compared with the observed path of the economy from 1910 to the present. The sensitivity of the optimal solution to the parameters of the system is studied in some detail. A horizon of 50 gives a good approximation to the solution for an infinite horizon; this can be improved by suitable approximations for the value of final stocks. (Author).3-l., Walue of Selected Statistics of Descriptors for Wariant s Of the Obtained Changing the Walue of One Parameter 4Os Standard Case ... 2+1Tl |2 OuOp1T OuU„89, OuU„ 1 2981 2325 Oy79 2l47 7823 3 OuOs6o 1-1 O 1.34% T202 T5+Os 43Os 2783 Os a, OuOp17 OuU„71OuOs Os28 +U„Os358 |23 68 OuU„UŠOs OpOmOu1Tl OoUŠ1321 2917 2626 ol+Os 82 7823aquot; n 2.68 % 1.34% 8133 T926 61+Os .90= l where TUŠU„U‡Os The horizon T=l100, except for Case OyOuOs.

Title:An Algorithm for the Dynamic Programming of Economic Growth
Publisher: - 1968


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