




TL;DR: The experimental results suggested that GA is very fast and is able to produce economically significant result with an average mean error 0.142% and standard deviation 0.021%.
Abstract: The current study deals with maximizing consumption per worker in connection with the economic growth of society The traditional Solow model based approach is well-studied and computationally complex The present work proposes a Genetic Algorithm (GA) based consumption maximization in attaining the Golden rule An objective function derived from traditional Solow model based on depreciation rate and amount of accumulated capital is utilized The current study considered a constant output per worker to incorporate a constant efficiency level of labor Different ranges of Depreciation rate and accumulated capital are tested to check the stability of the proposed GA based optimization process The mean error and standard deviation in optimization process is utilized as a performance metric The experimental results suggested that GA is very fast and is able to produce economically significant result with an average mean error 0142% and standard deviation 0021%
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In the current study a wellknown Darwinian principle inspired metaheuristic Genetic Algorithm is employed in maximizing the consumption (The Golden rule of capital accumulation) in terms of depreciation and capital accumulation.
Initial condition to achieve the Golden rule level of capital is; marginal product of capital should be equals to depreciation rate.
Maximization of consumption is traditionally done by employing a long time consuming and computationally complex Solow modelbased mathematical approach.
The Golden rule of capital indicates a state (a unique value of depreciation rate and amount of capital accumulated) that ensures maximum consumption level, thereby assures a strong economic growth [18].
Hommeset al. [16] reveled that GA can converge to a series of near Nash equilibrium solutions, where the heterogeneous agent behavior has been modeled using GA.
𝑀’.After achieving the steady state level of capital, there is a state where the authors maximize the consumption per worker that is generally known as the Golden rule level of capital [11, 18].
The optimum results indicated that in maximizing the consumption per worker the value of depreciation rate (𝛿) tends to the lower bound of the given range which indicates a lower depreciation rate.
At point ‘𝐴’it can be observed that the investment curve is steeper than the depreciation, so here investment is greater than the depreciation thus, if investment takes place it would enrich the capital stock which would lead to higher output.
The capital increases from the point ‘𝐴’and moves toward point ‘𝑀’ while in case of the point ‘𝐵’ the depreciation is steeper than the depreciation.
The plots reveal that GA is extremely fast in maximizing the objective function and is better than traditional methods [18] because these involve calculation of mathematical differentiation of complex functions and is proved to be NP - Hard (exponential complexity)[17].
The solution generated by the proposed system is a pair of values consisting 𝛿 (depreciation rate) and 𝑘∗ (amount of capital accumulated) with in the given range of search.