Analisis pada Modifikasi Model Siklus Bisnis Kaldor
Main Article Content
Abstract
Model siklus bisnis adalah salah satu sistem dinamika dalam bidang ekonomi. Ada beberapa model siklus bisnis, di antaranya adalah model Kaldor. Model siklus bisnis Kaldor direpresentasikan dalam sistem persamaan diferensial. Model ini melibatkan variabel produksi dan stok modal yang dipengaruhi oleh investasi dan simpanan. Dalam tulisan ini, investasi dan simpanan diasumsikan sebagai fungsi logistik dan logaritma dari produksi. Selanjutnya ditentukan titik kesetimbangan model dan dianalisis kestabilannya pada daerah di sekitar titik kesetimbangan tersebut. Diperoleh dua titik kesetimbangan, satu besifat tak stabil sementara satunya stabil dengan lintasan (trajectory) spiral. Solusi numerik juga ditampilakn dengan menggunakan metode Runge-Kutta orde empat.
Article Details
Section
Applied Mathematics
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References
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[18] Rochmad, Persamaan Diferensial, Bahan Ajar Jurusan Matematika FMIPA UNNES, Semarang, 2008.
[19] Soekartawi, Teori Ekonomi Produksi: Dengan Pokok Bahasan Analisis Cobb Douglas, Jakarta: Rajawali Pers, 1990.
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[21] >. Syarif, E. Cahyono, dan P. Adam, Study on business cycle in Indonesian economy: A signal processing approach. Global and Stochastic Analysis. Vol. 5 [6], pp.35-43, Special Issue 2018.
[22] P.N.V. Tu, Dynamical Systems: An Introduction with Applications in Economics and Biology, New York: Springer-Verlag, 1994.
[2] D.K. Arrowsmith, dan C.M. Place, Dynamical System: Differential Equations, Maps and Chaotic Behaviour, London: Chapman & Hall/HRC, 1992.
[3] I. Bashkirtseva, L. Ryashko, dan A. Sysolyatina, Analysis of stochastic effects in Kaldor type business cycle discrete model. Communication in Nonlinear Science and Numerical Simulation, Vol.36, pp.446 - 456, 2016.
[4] I. Bashkirtseva, L. Ryashko, dan T. Ryazanova, Stochastic sensitivity analysis of the variability of dynamics and transition to chaos in the business cycles model, Communication in Nonlinear Science and Numerical Simulation, Vol.54, pp.174 - 184, 2018.
[5] R. Bellman, dan K. L. Cooke, Differential-Difference Equations. New York-London. Academic Press, 1963.
[6] E. Cahyono, Pemodelan Matematika, Bahan Kuliah pada Jurusan Matematika FMIPA UHO, Kendari, 2009.
[7] E. Cahyono, Pemodelan Matematika, Bahan Kuliah pada Jurusan Matematika FMIPA UHO, Kendari, 2013.
[8] E. Cahyono, L. O. Saidi, Makkulau, M. Syarif, dan R. Raya. Quantitative aspects of business/economic cycle. Proceeding of the 3rd SHIELD International Conference, pp.56-64, 2018.
[9] W. W. Chang and D. J. Smyth, The Existence and Persistence of Cycles in a Non-linear Model: Kaldors 1940 Model Re-examined. Review of Economic Studies 38, pp.3744, 1971.
[10] R. Dwiningtias and Abadi, Model Siklus Bisnis IS-LM dengan Tundaan. MATHunesa, Vol.2(3), pp.24-30, 2014.
[11] I. Fudziah and A. A. Raed, Solving Delay Differential Equations Using embedded singly diagonally Implicit runge-kutta methods. Acta Mathematica Vietnamica, Vol. 3, pp. 95-105, 2008.
[12] A. Howard and R. Chris, Elementary Linear Algebra with Applications, nine Edition, New York: J. Willey, 2005.
[13] J. Kodera, J. Radova, and T. V. Quang, A Modification of Kaldor-Kalecki Model and its Analysis, 30th International Conference Mathematical Methods in Economics, pp.420-425, 2012.
[14] A. Krawiec and M. Szydlowski, The Kaldor-Kalecki model of business cycle as a two dimentional dynamical system. Nonlinear Mathematical Physics 8, pp. 288-271, 2001.
[15] N. G. Mankiw, Principles of Economics, South Western: Cengage Learning, 2017.
[16] W. H. Morris, S. Stephen, and L. D. Robert, Differential Equations, Dynamical Systems, and An Introduction To Chaos Second Edition, California: Academic Press, 2004.
[17] A. Panfilov, Qualitative Analysis of differensial Equations, Utrecht: Utrecht University, 2010.
[18] Rochmad, Persamaan Diferensial, Bahan Ajar Jurusan Matematika FMIPA UNNES, Semarang, 2008.
[19] Soekartawi, Teori Ekonomi Produksi: Dengan Pokok Bahasan Analisis Cobb Douglas, Jakarta: Rajawali Pers, 1990.
[20] S. H. Strogatz, Nonlinear Dynamics and Chaos, With Applications to Physics, Biology, Chemistry, and Engineering, Massachusete: Addison-Wesley Publishing Company, Reading, 1994.
[21] >. Syarif, E. Cahyono, dan P. Adam, Study on business cycle in Indonesian economy: A signal processing approach. Global and Stochastic Analysis. Vol. 5 [6], pp.35-43, Special Issue 2018.
[22] P.N.V. Tu, Dynamical Systems: An Introduction with Applications in Economics and Biology, New York: Springer-Verlag, 1994.