Application of a modified VES production function model

Maolin Cheng; Bin Liu

doi:10.3934/jimo.2020099

Article Contents

2021, Volume 17, Issue 5: 2889-2902. Doi: 10.3934/jimo.2020099

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Application of a modified VES production function model

Maolin Cheng^1, , and
Bin Liu^2,

1.
School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, 215009, China
2.
School of Business, Suzhou University of Science and Technology, Suzhou, 215009, China

^* Corresponding author: Maolin Cheng
^* Corresponding author: Maolin Cheng

Received: November 2019

Revised: February 2020

Early access: May 2020

Published: September 2021

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

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Abstract

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.

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

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Figure 1. Two algorithms' objective function value variation curves with the changes of the number of iteration

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

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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

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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

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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

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