Economic Growth by Means of Interspecific Functional Response of Capital-Labour in Dynamical System

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Oyoon Abdul Razzaq
Najeeb Alam Khan
Noor Ul Ain
Muhammad Ayaz


Physical capital and labour force are two major factors of any economy, which play a key role in its growth. The association of these two components with each other is also a matter of study, which is carried out in this endeavour by means of an ecological system with Holling-type II function. The governing model is an avantgrade approach for economic theory as its equilibrium states and the stability analysis so obtained, referrer to different economic states with detail information about the capital-labour interaction. This novel assessment also contributes a significant way to scrutinize the capability of labours on consuming time on the capital and the efficiency of capital on processing output. Moreover, different patterns and cyclic behaviour of the Cobb-Douglas and constant-elasticity production functions, for different steady and oscillating states of the system are also provided comparatively. In addition, a numerical example is also discussed graphically with economic significance. These measurements will consequently keep the production cycle moving and so sustain the economic growth.

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  1. D. Cai, H.Ye and L. Gu, A generalized Solow-Swan model, Abstr. Appl. Anal. 2014 (2014), Art. ID 395089.
  2. M. Zhou, D. Cai and H. Chen, A Solow-Swan model with technological overflow and catch-up, Wuhan Univ. J. Nat. Sci. 12(6) (2007), 975-978.
  3. R.M. Solow, A contribution to the theory of economic growth, Quart. J. Econ. 70 (1956), 65-94.
  4. E. Pelinescu, The impact of human capital on economic growth, Proc. Econ. Finance. 22 (2015), 184- 190.
  5. L. Gallaway and V. Shukla, The neoclassical production function, Amer. Econ. Rev. 64(3) (1974), 348- 358.
  6. A. Hochstein, The Harrod-Domar model in a Keynesian framework, Int. Adv. Econ. Res. 23 (2017), 349-350.
  7. A.N. Link and M.V. Hasselt, A public sector knowledge production function, Econ. Lett. 175 (2019), 64-66.
  8. M.D.P.P. Romero, A.S. Braza and A. Exposito, Industry level production functions and energy use in 12 EU countries, J. Clean. Prod. 212(1) (2019), 880-892.
  9. M.D.P.P. Romero and A.S. Braza, Productive energy use and economic growth: energy, physical and human capital relationships, Energy Econ. 49 (2015), 420-429.
  10. A.J. Lotka, Elements of physical biology, first ed., Williams and Wilkins, Baltimore, 1925.
  11. V. Volterra, Variazioni efluttuazioni del numero di individui in specie animali conviventi, Mem. Reale Accad. Naz. Lince. 2 (1926), 31-113.
  12. L. Nie, Z. Teng, L. Hu and J. Peng, The dynamics of a Lotka-Volterra predator-prey model with state dependent impulsive harvest for predator, Biosyst. 98 (2009), 67-72.
  13. B. Chakraborty and N. Bairagi, Complexity in a prey-predator model with prey refuge and diffusion, Ecol. Complexity. 37 (2019), 11-23.
  14. B. Sahoo and S. Poria, Dynamics of predator-prey system with fading memory, Appl. Math. Comput. 347(15) (2019), 319-333.
  15. A. Bouskila, Games played by predators and prey, Encyclopaedia Ani. Behav. (2019), 382-388.
  16. S.L. Tilahun, Prey predator hyperheuristic, Appl. Soft Comput. 59 (2017), 104-114.
  17. V. Castellanos and R.E.C. Lopez, Existence of limit cycles in a three level trophic chain with LotkaVolterra and Holling type II functional responses, Chaos Solitons Fractals. 95 (2017), 157-167.
  18. M. Liu, C. Du and M. Deng, Persistence and extinction of a modified Leslie-Gower Holling-type II stochastic predator-prey model with impulsive toxicant input in polluted environments, Nonlinear Anal. Hybrid Syst. 27 (2018), 177-190.
  19. Z. Xiao, X. Xie and Y. Xue, Stability and bifurcation in a Holling-type II predator-prey model with Allee effect and time delay, Adv. Difference Equ. 2018 (2018), Art. ID 288.
  20. J. Carkovs, J. Goldsteine and K. Sadurskis, The Holling-type II population model subjected to rapid random attacks of predator, J. Appl. Math. 2018 (2018), Art. ID 6146027.
  21. G.E. Vilcu, A geometric perspective on the generalized Cobb-Douglas production functions, Appl. Math. Lett. 24 (2011), 777-783.
  22. X. Wang and Y. Fu, Some characterizations of the Cobb-Douglas and CES production functions in microeconomics, Abstr. Appl. Anal. (2013), Art. ID 761832.
  23. K.J. Arrow, H.B. Chenery, B.S. Minhas and R.M. Solow, Capital-labour substitution and economic efficiency, Rev. Econ. Statist. 43(3) (1961), 225-250.
  24. K. Sato, A two-level constant-elasticity of substitution production function, Rev. Econ. Stud. 34(2) (1967), 201-218.