(401) An extension of Blach's optimum savings model. امتداد لنموذج بلاخ الأمثل للادخار
This paper, entitled “An Extension of Black's Optimum Savings Model,” attempts to expand John Black’s model of optimal savings, which itself was based on Ramsey’s theory of savings. The author argues that Black’s framework is limited because it assumes that capital alone is responsible for gene...
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The institute of national planning.
2018
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| description | This paper, entitled “An Extension of Black's Optimum Savings Model,” attempts to expand John Black’s model of optimal savings, which itself was based on Ramsey’s theory of savings. The author argues that Black’s framework is limited because it assumes that capital alone is responsible for generating income. Such an assumption is unrealistic, as actual economic systems rely on the joint contribution of both labor and capital. Therefore, the study seeks to develop a broader analytical framework that incorporates these two productive factors simultaneously. The analysis assumes an economy with fixed production techniques, implying a constant output-capital ratio, and also assumes the existence of a constant optimal savings rate. Starting from the principle of utility maximization, the paper argues that the utility derived from present consumption should be equal to the discounted stream of future utilities generated by savings over time. The study employs a marginal utility function and a constant time-discounting rate to derive mathematical expressions for determining the optimal savings rate. The findings indicate that the optimal savings rate depends not only on the time-discounting rate but also on the output-capital ratio and the utility parameter. This conclusion differs from Black’s earlier argument, which suggested that under conditions of zero time discounting, the optimal savings rate becomes independent of capital productivity. The paper further extends the analysis to include both gross and net savings and derives equations for determining their optimal levels. The study is significant because it bridges the conceptual gap between the rate of return on capital and the output-capital ratio, thereby providing a more realistic analytical framework for understanding savings and investment behavior in economic systems. |
| format | Other |
| id | ir-123456789-3794 |
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| publishDate | 2018 |
| publisher | The institute of national planning. |
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| spelling | ir-123456789-37942026-06-25T07:37:43Z (401) An extension of Blach's optimum savings model. امتداد لنموذج بلاخ الأمثل للادخار A. qayum economical development Economic planning economy This paper, entitled “An Extension of Black's Optimum Savings Model,” attempts to expand John Black’s model of optimal savings, which itself was based on Ramsey’s theory of savings. The author argues that Black’s framework is limited because it assumes that capital alone is responsible for generating income. Such an assumption is unrealistic, as actual economic systems rely on the joint contribution of both labor and capital. Therefore, the study seeks to develop a broader analytical framework that incorporates these two productive factors simultaneously. The analysis assumes an economy with fixed production techniques, implying a constant output-capital ratio, and also assumes the existence of a constant optimal savings rate. Starting from the principle of utility maximization, the paper argues that the utility derived from present consumption should be equal to the discounted stream of future utilities generated by savings over time. The study employs a marginal utility function and a constant time-discounting rate to derive mathematical expressions for determining the optimal savings rate. The findings indicate that the optimal savings rate depends not only on the time-discounting rate but also on the output-capital ratio and the utility parameter. This conclusion differs from Black’s earlier argument, which suggested that under conditions of zero time discounting, the optimal savings rate becomes independent of capital productivity. The paper further extends the analysis to include both gross and net savings and derives equations for determining their optimal levels. The study is significant because it bridges the conceptual gap between the rate of return on capital and the output-capital ratio, thereby providing a more realistic analytical framework for understanding savings and investment behavior in economic systems. يتناول البحث المعنون «توسيع نموذج بلاك للادخار الأمثل» محاولة تطوير نموذج جون بلاك الخاص بالادخار الأمثل، والذي استند بدوره إلى نظرية رامزي للادخار. ينطلق الباحث من ملاحظة أن معالجة بلاك اقتصرت على اعتبار رأس المال العامل الوحيد المسؤول عن توليد الدخل، وهو افتراض لا يعكس الواقع الاقتصادي الفعلي حيث يتم الإنتاج من خلال التفاعل بين رأس المال والعمل معًا. ويهدف البحث إلى معالجة هذا القصور من خلال بناء إطار تحليلي أكثر شمولاً يضم العاملين معًا. يفترض الباحث اقتصادًا ذا تقنيات إنتاج ثابتة بما يؤدي إلى ثبات نسبة الناتج إلى رأس المال، مع افتراض وجود معدل أمثل ثابت للادخار. وانطلاقًا من مبدأ تعظيم المنفعة، يوضح أن المنفعة الناتجة عن استهلاك الموارد الحالية يجب أن تعادل مجموع المنافع المستقبلية المخصومة المتولدة عن الادخار. كما يعتمد التحليل على دالة للمنفعة الحدية ومعدل خصم زمني ثابت لاشتقاق معادلات تحدد المعدل الأمثل للادخار. توصلت الدراسة إلى أن معدل الادخار الأمثل لا يعتمد فقط على معدل الخصم الزمني، بل يتأثر أيضًا بنسبة الناتج إلى رأس المال ومؤشر المنفعة. وتخالف هذه النتيجة ما انتهى إليه بلاك سابقًا، حيث كان يرى أن الادخار الأمثل في حالة غياب الخصم الزمني يصبح مستقلاً عن إنتاجية رأس المال. كما توسع الدراسة التحليل ليشمل الادخار الصافي بالإضافة إلى الادخار الإجمالي، وتستنتج معادلات رياضية تحدد المعدلات المثلى لكل منهما. وتتمثل أهمية الدراسة في أنها تسهم في تضييق الفجوة المفاهيمية بين معدل العائد على رأس المال ونسبة الناتج إلى رأس المال، وتوفر إطارًا تحليليًا أكثر واقعية لفهم سلوك الادخار والاستثمار في النظم الاقتصادية. 2018-08-01T08:46:58Z 2018-08-01T08:46:58Z 1964-02-23 Other http://repository.inp.edu.eg/handle/123456789/3794 other External notes;401 application/pdf The institute of national planning. |
| spellingShingle | economical development Economic planning economy A. qayum (401) An extension of Blach's optimum savings model. امتداد لنموذج بلاخ الأمثل للادخار |
| title | (401) An extension of Blach's optimum savings model.
امتداد لنموذج بلاخ الأمثل للادخار |
| title_full | (401) An extension of Blach's optimum savings model.
امتداد لنموذج بلاخ الأمثل للادخار |
| title_fullStr | (401) An extension of Blach's optimum savings model.
امتداد لنموذج بلاخ الأمثل للادخار |
| title_full_unstemmed | (401) An extension of Blach's optimum savings model.
امتداد لنموذج بلاخ الأمثل للادخار |
| title_short | (401) An extension of Blach's optimum savings model.
امتداد لنموذج بلاخ الأمثل للادخار |
| title_sort | 401 an extension of blach s optimum savings model امتداد لنموذج بلاخ الأمثل للادخار |
| topic | economical development Economic planning economy |
| url | http://repository.inp.edu.eg/handle/123456789/3794 |
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