Analisis dan Eksistensi Kontrol Optimal pada Model Ramsey-Cass-Koopmans

Sya'banah, Sulistia Jamil (2023) Analisis dan Eksistensi Kontrol Optimal pada Model Ramsey-Cass-Koopmans. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Pertumbuhan ekonomi mengakibatkan peningkatan produksi barang dan jasa. Salah satu faktor yang mendorong terjadinya pertumbuhan ekonomi adalah pengeluaran perusahaan atau investasi. Investasi dapat meningkatkan konsumsi, karena dengan melakukan investasi perusahaan dapat meningkatkan kapasitas produksinya. Salah satu faktor yang memengaruhi konsumsi adalah utilitas, yaitu nilai guna yang diperoleh dari kegiatan konsumsi atau penggunaan barang dan jasa. Berdasarkan faktor utilitas yang memengaruhi konsumsi, maka dapat diketahui pentingnya tingkat utilitas konsumsi dalam suatu produksi. Pada Tugas Akhir ini dibahas model Ramsey-Cass-Koopmans dengan fungsi produksi Cobb-Douglas. Selanjutnya dianalisa penyelesaian positif dan unik, eksistensi, kontrol optimal dan penyelesaian numerik. Penyelesaian kontrol optimal menggunakan Metode Tidak Langsung dan Langsung. Penyelesaian numerik menggunakan Runge Kutta orde 4. Berdasarkan hasil analisa solusi model didapat bahwa model Ramsey-Cass-Koopmans memiliki solusi positif dan unik. Kemudian dari hasil pembuktian eksistensi kontrol optimal, didapat bahwa kontrol investasi pada model terbukti eksis. Setelah dilakukan penyelesaian kontrol optimal menggunakan Metode Tidak Langsung dan Langsung, terbukti bahwa kontrol investasi dapat memaksimalkan utilitas konsumsi.
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Economic growth results in an increase in the production of goods and services. One of the factors that drive economic growth is corporate expenditure or investment. Investment can enhance consumption because by investing, companies can increase their production capacity. One factor that affects consumption is utility, which is the value obtained from consumption activities or the use of goods and services. Based on the utility factor that influences consumption, the importance of the level of consumption utility in production can be determined. This final assignment discusses the Ramsey-Cass-Koopmans model with the Cobb-Douglas production function. Furthermore, positive and unique solutions, existence, optimal control, and numerical solutions are analyzed. The optimal control solutions are obtained using Indirect and Direct Methods. The numerical solution is obtained using the 4th-order Runge-Kutta method. Based on the analysis of the model's solution, it is found that the Ramsey-Cass-Koopmans model has a positive and unique solution. Furthermore, from the proof of the existence of optimal control, it is established that investment control in the model is proven to exist. After conducting the optimal control solutions using Indirect and Direct Methods, it is proven that investment control can maximize consumption utility.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Economic Growth, Ramsey-Cass-Koopmans Model, Existence, Optimal Control, Pertumbuhan Ekonomi, Model Ramsey-Cass-Koopmans, Eksistensi, Kontrol Optimal
Subjects:	H Social Sciences > HG Finance > HG4910 Investments Q Science > Q Science (General) > Q180.55.M38 Mathematical models Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions Q Science > QA Mathematics > QA372.B9 Differential equations--Numerical solutions. Runge-Kutta formulas--Data processing. Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Sulistia Jamil Sya'banah
Date Deposited:	31 Jul 2023 01:41
Last Modified:	31 Jul 2023 01:41
URI:	http://repository.its.ac.id/id/eprint/100374

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