\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Application of a modified VES production function model

  • * Corresponding author: Maolin Cheng

    * Corresponding author: Maolin Cheng 

This work is supported in part by the National Natural Science Foundation of China(11401418)

Abstract Full Text(HTML) Figure(2) / Table(3) Related Papers Cited by
  • In the analyses on economic growth factors, researchers generally use the production function model to calculate the contribution rates of influencing factors to economic growth. The paper proposes a new modified VES production function model. As for the model's parameter estimation, the conventional optimization methods are complicated, generally require information like the gradient of objective function, and have the poor convergence rate and precision. The paper gives a modern intelligent algorithm, i.e., the cuckoo search algorithm, which has the strong robustness, can be realized easily, has the fast convergence rate and can be used flexibly. To enhance the convergence rate and precision, the paper improves the conventional cuckoo search algorithm. Using the new model, the paper gives a method calculating the contribution rates of economic growth influencing factors scientifically. Finally, the paper calculates the contribution rates of influencing factors to economic growth in Shanghai City, China.

    Mathematics Subject Classification: Primary: 65K10, 91B02; Secondary: 93B40.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  Two algorithms' objective function value variation curves with the changes of the number of iteration

    Figure 2.  The distribution diagram of contribution rates of influencing factors to economic growth in Shanghai City, China

    Table 1.  Related data about the economic growth of Shanghai city, China

    Year $ Y $ $ K $ $ L $
    1999 4222.30 1856.72 733.76
    2000 4812.15 1869.67 745.24
    2001 5257.66 1994.73 752.26
    2002 5795.02 2187.06 792.04
    2003 6762.38 2452.11 813.05
    2004 8165.38 3084.66 836.87
    2005 9365.54 3542.55 863.32
    2006 10718.04 3925.09 885.51
    2007 12668.12 4458.61 909.08
    2008 14275.80 4829.45 1053.24
    2009 15285.58 5273.33 1064.42
    2010 17433.21 5317.67 1090.76
    2011 19533.84 5067.09 1104.33
    2012 20553.52 5254.38 1115.50
    2013 22257.66 5647.79 1137.35
    2014 24060.87 6016.43 1197.31
    2015 25643.47 6352.70 1361.51
    2016 28178.65 6755.88 1365.24
    2017 30632.09 7246.60 1372.65
    2018 32679.87 7623.42 1430.82
     | Show Table
    DownLoad: CSV

    Table 2.  The comparison of results of two CS algorithms

    Method Conventional CS Improved CS
    $ A_{0} $ 4.9963 3.9414
    $ \sigma $ 0.0450 0.0433
    $ \delta_{1} $ 1.1503 1.4430
    $ \delta_{2} $ 4.9788 6.6868
    $ a $ 4.9940 5.0012
    $ b $ 3.2084 3.1064
    $ c $ 0.1988 0.1497
    $ \mu $ 0.8231 0.8293
    Number of Iteration 252 54
    $ G, $ Optimal Value of Objective Function 1.0319e$ + $07 9.9439e$ + $06
    $ R^{2}, $ Coefficient of Determination of Model 0.9935 0.9937
     | Show Table
    DownLoad: CSV

    Table 3.  Verification results of conditions of production function

    Year $ f_{1} $ $ f_{2} $ $ f_{11} $ $ f_{22} $ $ f_{12} $ $ ff $
    1999 1.2536 6.5002 -9.275e-5 -13.7e-4 -5.69e-5 1.2364e-7
    2000 1.2387 6.2050 -7.511e-5 -11.8e-4 -9.53e-5 7.9713e-8
    2001 1.2487 6.1583 -6.335e-5 -10.9e-4 -1.15e-4 5.5835e-8
    2002 1.2665 6.1774 -5.439e-5 -9.92e-4 -1.23e-4 3.8894e-8
    2003 1.2922 6.2664 -4.787e-5 -9.33e-4 -1.27e-4 2.8559e-8
    2004 1.3090 6.3446 -3.959e-5 -8.48e-4 -1.21e-4 1.8918e-8
    2005 1.3397 6.4705 -3.565e-5 -7.93e-4 -1.19e-4 1.4196e-8
    2006 1.3780 6.6312 -3.337e-5 -7.56e-4 -1.18e-4 1.1381e-8
    2007 1.4150 6.7923 -3.086e-5 -7.15e-4 -1.14e-4 8.9777e-9
    2008 1.4472 6.9094 -2.805e-5 -6.34e-4 -1.06e-4 6.5751e-9
    2009 1.4950 7.1239 -2.709e-5 -6.20e-4 -1.06e-4 5.6539e-9
    2010 1.5549 7.3862 -2.754e-5 -6.24e-4 -1.09e-4 5.2946e-9
    2011 1.6274 7.7058 -2.929e-5 -6.53e-4 -1.17e-4 5.4122e-9
    2012 1.6907 7.9924 -2.949e-5 -6.59e-4 -1.20e-4 5.0563e-9
    2013 1.7496 8.2616 -2.888e-5 -6.48e-4 -1.19e-4 4.5043e-9
    2014 1.8078 8.5239 -2.803e-5 -6.28e-4 -1.17e-4 3.9252e-9
    2015 1.8582 8.7431 -2.631e-5 -5.82e-4 -1.10e-4 3.1723e-9
    2016 1.9281 9.0661 -2.625e-5 -5.83e-4 -1.11e-4 2.9566e-9
    2017 1.9985 9.3922 -2.600e-5 -5.81e-4 -1.11e-4 2.7283e-9
    2018 2.0695 9.7171 -2.563e-5 -5.71e-4 -1.10e-4 2.4778e-9
     | Show Table
    DownLoad: CSV
  • [1] A. Assad and K. Deep, A Hybrid Harmony search and Simulated Annealing algorithm for continuous optimization, Information Sci., 450 (2018), 246-266.  doi: 10.1016/j.ins.2018.03.042.
    [2] V. O. Bohaienko and V. M. Popov, Optimization of operation regimes of irrigation canals using genetic algorithms, in International Conference on Computer Science, Engineering and Education Applications, Advances in Intelligent Systems and Computing, 754, Springer, Cham, 2019,224–233. doi: 10.1007/978-3-319-91008-6_23.
    [3] M. A. CardeneteM. C. Lima and F. Sancho, An assessment of the impact of EU funds through productivity boosts using CES functions, Appl. Econ. Lett., 26 (2019), 872-876.  doi: 10.1080/13504851.2018.1508867.
    [4] J. ChengL. WangQ. Jiang and Y. Xiong, A novel cuckoo search algorithm with multiple update rules, Appl. Intell., 48 (2018), 4192-4211.  doi: 10.1007/s10489-018-1198-y.
    [5] M. L. Cheng, A generalized constant elasticity of substitution production function model and its application, J. Systems Sci. Info., 4 (2016), 269-279.  doi: 10.21078/JSSI-2016-269-11.
    [6] M. L. Cheng, A Grey CES production function model and its application in calculating the contribution rate of economic growth factors, Complexity, 2019 (2019), 8pp. doi: 10.1155/2019/5617061.
    [7] J. ChongelaV. Nandala and S. Korabandi, Estimation of constant elasticity of substitution (CES) production function with capital and labour inputs of agri-food firms in Tanzania, African J. Agricultural Res., 8 (2013), 5082-5089. 
    [8] F. Erdal, A firefly algorithm for optimum design of new-generation beams, Engineering Optim., 49 (2017), 915-931.  doi: 10.1080/0305215X.2016.1218003.
    [9] H. GuoJ. HuS. YuH. Sun and Y. Chen, Computing of the contribution rate of scientific and technological progress to economic growth in Chinese regions, Expert Systems Appl., 39 (2012), 8514-8521.  doi: 10.1016/j.eswa.2011.12.032.
    [10] Y. HeS. W. Gao and N. Liao, An intelligent computing approach to evaluating the contribution rate of talent on economic growth, Comput. Econ., 48 (2016), 399-423.  doi: 10.1007/s10614-015-9536-1.
    [11] G. V. S. K. Karthik and S. Deb, A methodology for assembly sequence optimization by hybrid cuckoo-search genetic algorithm, J. Adv. Manufacturing Systems, 17 (2018), 47-59.  doi: 10.1142/S021968671850004X.
    [12] Y. N. KiselevS. N. Avvakumov and M. V. Orlov, Optimal control in the resource allocation problem for a two-sector economy with a CES production function, Comput. Math. Model., 28 (2017), 449-477.  doi: 10.1007/s10598-017-9375-0.
    [13] X. J. MengJ. X. ChangX. B. Wang and Y. M. Wang, Multi-objective hydropower station operation using an improved cuckoo search algorithm, Energy, 168 (2019), 425-439.  doi: 10.1016/j.energy.2018.11.096.
    [14] S. K. Mishra, A brief history of production functions, IUP J. Managerial Econ., 8 (2010), 6-34.  doi: 10.2139/ssrn.1020577.
    [15] Y. Nakamura, Productivity versus elasticity: A normalized constant elasticity of substitution production function applied to historical Soviet data, Appl. Econ., 47 (2015), 5805-5823.  doi: 10.1080/00036846.2015.1058909.
    [16] S. Opuni-BasoaF. T. Oduro and G. A. Okyere, Population dynamics in optimally controlled economic growth models: Case of Cobb-Douglas production function, J. Adv. Math. Comput. Sci., 25 (2017), 1-24.  doi: 10.9734/JAMCS/2017/36753.
    [17] A. S. PillaiK. SinghV. SaravananA. AnpalaganI. Woungang and L. Barolli, A genetic algorithm-based method for optimizing the energy consumption and performance of multiprocessor systems, Soft Comput., 22 (2018), 3271-3285.  doi: 10.1007/s00500-017-2789-y.
    [18] F. E. Sarac, A general evaluation on estimates of Cobb-Douglas, CES, VES and Translog production functions, Bull. Econ. Theory Anal., 2 (2017), 235-278. 
    [19] C. Takeang and A. Aurasopon, Multiple of hybrid lambda iteration and simulated annealing algorithm to solve economic dispatch problem with ramp rate limit and prohibited operating zones, J. Electrical Engineering Tech., 14 (2019), 111-120.  doi: 10.1007/s42835-018-00001-z.
    [20] K. ThirugnanasambandamS. PrakashV. SubramanianS. Pothula and V. Thirumal, Reinforced cuckoo search algorithm-based multimodal optimization, Applid Intell., 49 (2019), 2059-2083.  doi: 10.1007/s10489-018-1355-3.
    [21] H. WangX. ZhouH. SunX. YuJ. ZhaoH. Zhang and L. Cui, Firefly algorithm with adaptive control parameters, Soft Comput., 21 (2017), 5091-5102.  doi: 10.1007/s00500-016-2104-3.
    [22] D. ZhaA. S. Kavuri and S. Si, Energy-biased technical change in the Chinese industrial sector with CES production functions, Energy, 148 (2018), 896-903.  doi: 10.1016/j.energy.2017.11.087.
    [23] C. Zhao, Y. Xu and Y. Feng, A study on contribution rate of management elements in economic growth, in International Conference on Information and Management Engineering, Communications in Computer and Information Science, 234, Springer, Berlin, Heidelberg, 2011,151–158. doi: 10.1007/978-3-642-24091-1_21.
  • 加载中

Figures(2)

Tables(3)

SHARE

Article Metrics

HTML views(849) PDF downloads(297) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return