A novel method for calculating the contribution rates of economic growth factors

Maolin Cheng; Bin Liu; Maolin Cheng; Bin Liu

doi:10.3934/math.2023932

AIMS Mathematics

2023, Volume 8, Issue 8: 18339-18353. doi: 10.3934/math.2023932

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A novel method for calculating the contribution rates of economic growth factors

Maolin Cheng ^{1
,
,},
Bin Liu ²

1.
School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, China
2.
School of Business, Suzhou University of Science and Technology, Suzhou 215009, China

Received: 07 February 2023 Revised: 29 April 2023 Accepted: 23 May 2023 Published: 29 May 2023
MSC : 65K10, 91B02, 93B40

The common production functions include the Leontief production function, the Cobb-Douglas (C-D) production function, the constant elasticity of substitution (CES) production function, the variable elasticity of substitution (VES) production function and so on. With different elasticity of substitution of factor, the production functions have different ranges of applications. In the production functions, the C-D production function is used the most widely because of its simple form, while the CES production function and the VES production function have limitations in applications due to their complicated forms. However, the C-D production function has the elasticity of substitution of factors of 1, and the CES production function has the elasticity of substitution of factors which is not 1 but a constant, so the two production functions both have limitations in applications. The VES production function with the variable elasticity of substitution is more practical in some application cases. This paper studies the applications of the VES production function model and gives a method of calculating the contribution rates of economic growth factors scientifically. As for the parameter estimation of the model, this paper gives an improved Sine Cosine Algorithm (SCA) to enhance the convergence rate and precision. Finally, the paper makes an empirical analysis on the contribution rates of economic growth factors of Shanghai City, China, using the method proposed.
- production function,
- economic growth,
- contribution rates of factors,
- SCA
Citation: Maolin Cheng, Bin Liu. A novel method for calculating the contribution rates of economic growth factors[J]. AIMS Mathematics, 2023, 8(8): 18339-18353. doi: 10.3934/math.2023932

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Abstract

The common production functions include the Leontief production function, the Cobb-Douglas (C-D) production function, the constant elasticity of substitution (CES) production function, the variable elasticity of substitution (VES) production function and so on. With different elasticity of substitution of factor, the production functions have different ranges of applications. In the production functions, the C-D production function is used the most widely because of its simple form, while the CES production function and the VES production function have limitations in applications due to their complicated forms. However, the C-D production function has the elasticity of substitution of factors of 1, and the CES production function has the elasticity of substitution of factors which is not 1 but a constant, so the two production functions both have limitations in applications. The VES production function with the variable elasticity of substitution is more practical in some application cases. This paper studies the applications of the VES production function model and gives a method of calculating the contribution rates of economic growth factors scientifically. As for the parameter estimation of the model, this paper gives an improved Sine Cosine Algorithm (SCA) to enhance the convergence rate and precision. Finally, the paper makes an empirical analysis on the contribution rates of economic growth factors of Shanghai City, China, using the method proposed.

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