Optimal Control of the Growth of Wealth of Nations PDF Download
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Author: E.N. Chukwu
Publisher: CRC Press
ISBN: 1482264846
Category : Mathematics
Languages : en
Pages : 409
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Book Description
Students and researchers in applied mathematics and applied economics can use this introductory-level graduate text. It looks at the current problems of the development of the global economy by studying the dynamics of key economic variables, such as gross national product, interest rates, employment, value of capital stock, prices (inflation) and
Author: E.N. Chukwu
Publisher: CRC Press
ISBN: 9780415269667
Category : Mathematics
Languages : en
Pages : 412
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Book Description
Students and researchers in applied mathematics and applied economics can use this introductory-level graduate text. It looks at the current problems of the development of the global economy by studying the dynamics of key economic variables, such as gross national product, interest rates, employment, value of capital stock, prices (inflation) and balance of payments. Validation of the model is attempted using the economic time series of several countries. The constructed models explain the macroeconomic data of nations as dynamic games of pursuit, which are equivalent to "control" problems and are used to study mathematical optimal control of the growth of the wealth of nations. This invaluable reference for graduates and researchers compares the extent of government intervention in the economy with private firms to ensure the controllability of the economy.
Author: Ethelbert N. Chukwu
Publisher: World Scientific
ISBN: 9789810243814
Category : Business & Economics
Languages : en
Pages : 544
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Book Description
This monograph derives from familiar economic principles the dynamics of national income, the interest rate, employment, the value of capital stock, prices, and the cumulative balance of payments. This is a Volterra neutral integrodifferential game of pursuit. The quarry control is government intervention in the form of taxation, control of money supply, tariffs, foreign credit, interest equalization tax, preferential trade agreements (which reduce trade barriers and enhance trade flows between nations), transportation and distance between trading partners. The pursuer controls include wages and productivity. The book provides conditions for controllability and then deduces how big government intervention (compared with private firms' contributions) should be to ensure the possibility of growth.The reader is assumed to be familiar with advanced calculus and to have a working knowledge of ordinary differential equations. The required theory of hereditary systems can be obtained from the book itself.
Author: Ethelbert N. Chukwu
Publisher: Elsevier
ISBN: 0080459528
Category : Mathematics
Languages : en
Pages : 793
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Book Description
The book presents a careful mathematical study of Economic Cooperation and Competition among Nations. It appropriates the principles of Supply and Demand and of Rational Expectations to build the dynamic model of the Gross Domestic Products of two groups of nations which are linked up together. The first group consists of Nigeria, the US, the UK and China. The second group is made up of Egypt, the US, Jordan and Israel. The link connecting the four nations of each group is mirrored in the net export function which is broadened to include trade, debts and the inflow or the outflow of wealth from the competing and cooperating nations. This realistic models of the four interacting GDP's, a hereditary differential game of pursuit are validated with historical data from International Financial Statistic Year Book. The Mathematical model is then studied for controllability: from a current initial GDPs a better state can be attained using government and private strategies which are carefully identified. We use regression and differential equation methods to test whether the four countries are competing or cooperating. The consequences of competition or cooperation are explored. Cooperation can be realized and the growth of wealth assured because the system is controllable and we can increase the growth of GDP and then increase the coefficient of cooperation. The outcome may be unbounded growth of wealth for all concerned – the triumph of cooperation. With analogous simple examples the book shows that sufficiently cooperating systems grow unbounded and competing ones are either bounded at best, or become extinct in finite time. If competition is small, i.e., limited, or regulated the GDP's need not be extinct even after a long time. This results are in contrast with popular opinion which advocate competition over cooperation. The detailed policy implication of the cooperation analysis at one time or the other were advocated by Pope John Paul II, President Clinton and President Bush. The mathematical message is clear: the strategy of cooperation is the best way in an Interconnected World: Cooperation triumphs over competition. The same type of analysis allows the book to argue through modeling that prosperity, internal peace and harmony can flourish in Nigeria among the old three regions and the newer six geopolitical regions. The same is true for the four powerful states in the Middle East.Thus the author's refreshing approach is the "scientific" treatment of cooperation and competition models of the gross-domestic product of two groups of nations – Nigeria, the USA, the UK, and China, and the USA, Egypt, Jordan and Israel. Attempts are made to provide "scientific" answers to broad national policies. It allows predictions of growth to be made with some degree of accuracy for up to 4 years. MATLAB and Maple programs in accompanied CD are provided. The author's individual nations economic models are cited. The dynamics are ordinary and hereditary games of pursuit also cited from the original earlier writings of the author are models of the economic state of each nation – a vector of six things – the gross domestic product (GDP) (y), interest rate R; employment (or unemployment) (L), value of capital stock (k), prices p(t), and therefore inflation and cumulative balance of payment (E). Each economic state is isolated except the impact of export function on aggregate demand.The main difference between this earlier contributions and this book is the link and its apparent policy implications and consequences.Key features:
Author: Eugeniu Grebenikov
Publisher: CRC Press
ISBN: 9780203409831
Category : Mathematics
Languages : en
Pages : 282
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Book Description
Asymptotic Methods in Resonance Analytical Dynamics presents new asymptotic methods for the analysis and construction of solutions (mainly periodic and quasiperiodic) of differential equations with small parameters. Along with some background material and theory behind these methods, the authors also consider a variety of problems and applications in nonlinear mechanics and oscillation theory. The methods examined are based on two types: the generalized averaging technique of Krylov-Bogolubov and the numeric-analytical iterations of Lyapunov-Poincaré. This text provides a useful source of reference for postgraduates and researchers working in this area of applied mathematics.
Author: I. Ya Kats
Publisher: CRC Press
ISBN: 0203218892
Category : Mathematics
Languages : en
Pages : 256
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Book Description
Nonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of stability theory and the theory of stabilization of nonlinear systems with random structure in terms of new developments in the direct Lyapunov's method. The analysis focuses on dynamic systems with random Markov parameters. This high-level research text is recommended for all those researching or studying in the fields of applied mathematics, applied engineering, and physics-particularly in the areas of stochastic differential equations, dynamical systems, stability, and control theory.
Author: Vladislav I Zhukovskiy
Publisher: CRC Press
ISBN: 1482264994
Category : Mathematics
Languages : en
Pages : 299
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Book Description
A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theor
Author: N.V. Azbelev
Publisher: CRC Press
ISBN: 9780415269575
Category : Mathematics
Languages : en
Pages : 246
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Book Description
Stability of Differential Equations with Aftereffect presents stability theory for differential equations concentrating on functional differential equations with delay, integro-differential equations, and related topics. The authors provide background material on the modern theory of functional differential equations and introduce some new flexible methods for investigating the asymptotic behaviour of solutions to a range of equations. The treatment also includes some results from the authors' research group based at Perm and provides a useful reference text for graduates and researchers working in mathematical and engineering science.
Author: Tomasz Rynarzewski
Publisher: Poznań University of Economics and Business
ISBN: 837417918X
Category :
Languages : en
Pages : 374
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Book Description
The book was prepared by the academics and doctoral students of the Faculty of International Business and Economics of the Poznań University of Economics and Business to celebrate the 90th anniversary of the University and the 10th anniversary of the Faculty itself. The subject of this Volume reflects the variety of issues that are researched by academics from all departments of the Faculty. The rationale for publishing this Volume was to signal current work and research progress in the area of international economics, business and management. As the title of the Volume suggests, we need to anticipate changes and implement a new approach to face the challenges in the world economy for it is transforming in an unprecedented way now, at a fast pace, and the global economic map is constantly redrawing. Papers published in this Volume are written by individual authors and workgroups. They are results of research conducted in departments and have been assigned to eight chapters discussing crucial aspects of the world economy. The deliberations are held on a micro- and macroeconomic level in both theoretical and empirical terms. We hope that the contents of individual papers will inspire both readers and authors themselves to make further studies, to carry out follow-up research, to network with one another in order to find answers to the most important problems of the world economy and international business.
Author: Yu. A. Mitropolsky
Publisher: CRC Press
ISBN: 1482264897
Category : Mathematics
Languages : en
Pages : 390
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Book Description
Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov func
Author: Ethelbert Nwakuche Chukwu
Publisher: Springer Science & Business Media
ISBN: 9491216260
Category : Mathematics
Languages : en
Pages : 214
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Book Description
This monograph, a sequel to the author's highly successfull A Mathematical Treatment of Economic Cooperation and Competition Among Nations: With Nigeria, USA, UK, China and Middle East Examples (Academic Press, 2005), extends the study to all member states of the United Nations. It derives the equations of the key economic variables of gross domestic product, interest rate, employment value of capital stock prices (inflation) and cumulative balance of payment. The derivation is based on the differential market principle of supply and demand and on the rational expectation principle. The models are validated using economic time series of each country and MATLAB programs. The emerging dynamics is a differential game of pursuit which is converted to a hereditary control system for a single nation. Following the same method we derive the full hereditary economic model of all members of the United Nations joined together by external trade, investment capital flow consumption employment and governments' economic intervention all mirrored by interacting gross domestic products. The system is validated with IMF and World Bank data.Studies are made on how to arrest economic recession and depression and promote economic growth and prosperity. Diffusion of wealth is also touched upon. Policies regarding economic stimulus, how to dam the decay of capital flow, as well as conditions to promote full employment are discussed. Examination is made to test for the global systems controllability the possibility of steering any current bad economic state to a state of growth of its GDP, low interest rate, full employment, good value of capital stock, low inflation and a positive value of the cumulative balance of payments. The book prescribes verifiable broad policies for all nations together to promote prosperity, diffusion of wealth and longevity. The book comes with full programs, output and identified equations which can be downloaded from the publishers' website. Detailed information is available inside the book.The book is a most valuable source of reference for world leaders, central bank directors, graduates and academic researchers in applied mathematics and applied economics concerned with the current problems and growth of the global economy.
