conversations.from: human
conversations.value: Provide a description for a book titled Foundations of Mathematical and Computational Economics about Matlab, Excel, Sections with the genre: Science & Math, Mathematics.
conversations.from: assistant
conversations.value: This is a book on the basics of mathematics and computation and their uses in economics for modern day students and practitioners. The reader is introduced to the basics of numerical analysis as well as the use of computer programs such as Matlab and Excel in carrying out involved computations. Sections are devoted to the use of Maple in mathematical analysis. Examples drawn from recent contributions to economic theory and econometrics as well as a variety of end of chapter exercises help to illustrate and apply the presented concepts.
conversations.from: human
conversations.value: Swap the first and the last sentence.
conversations.from: assistant
conversations.value: Examples drawn from recent contributions to economic theory and econometrics as well as a variety of end of chapter exercises help to illustrate and apply the presented concepts. The reader is introduced to the basics of numerical analysis as well as the use of computer programs such as Matlab and Excel in carrying out involved computations. Sections are devoted to the use of Maple in mathematical analysis.This is a book on the basics of mathematics and computation and their uses in economics for modern day students and practitioners.
conversations.from: human
conversations.value: Provide the first three paragraphs for the book.
conversations.from: assistant
conversations.value: Foundations of Mathematical and Computational Economics
  A theory or model is the tool by which we organize our thought about a phenomenon and has to have the ability to explain or forecast. Economic processes are the outcome of the interaction of decisions made by many economic agents. It follows that any economic theory has to be based on some model of decision making by economic agents, be it individual, household, firm, or government. Preferably the behavioral assumptions underlying such a model are applicable to a variety of agents and do not vary in an ad hoc manner, because a science worthy of the name cannot consist of a bunch of unrelated models, each of which is applicable to only a special case. Indeed, it is quite easy to find a rationalization for any event or phenomenon after the fact.
  A theory or model is the tool by which we organize our thought about a phenomenon and has to have the ability to explain or forecast. Economic processes are the outcome of the interaction of decisions made by many economic agents. It follows that any economic theory has to be based on some model of decision making by economic agents, be it individual, household, firm, or government. Preferably the behavioral assumptions underlying such a model are applicable to a variety of agents and do not vary in an ad hoc manner, because a science worthy of the name cannot consist of a bunch of unrelated models, each of which is applicable to only a special case. Indeed, it is quite easy to find a rationalization for any event or phenomenon after the fact.
  The work of marginalists in the nineteenth and early twentieth centuries laid the foundation of a unified economic theory. Antoine Augustin Cournot studied the profit maximizing firm, Johann Heinrich von Thunen applied it to cost minimization by firms, and Hermann Heinrich Gossen studied utility maximizing consumers. In the latter part of the nineteenth century the first generation of professional economists, Leon Walras, William Stanley Jevons, and Carl Menger, developed these ideas into a comprehensive theory of the economy. Many others including Alfred Marshall contributed to this endeavor.
conversations.from: human
conversations.value: Provide four more paragraphs.. End with the sentence ' To model the movement from one equilibrium to another and to study the path of different variables when the system is out of equilibrium, we need dynamic models.'.
conversations.from: assistant
conversations.value: The mathematical device that epitomizes the birth of modern sciences is the differential equation.1 Newton's second law states that the acceleration of a particle is inversely proportional to its mass and is directly related to the force applied to it. Thus,
  Economic life is a dynamic process and it seems natural to model economic phenomena using differential equations. An objection may be raised here that in economics all variables are measured at discrete time intervals. Therefore, models that treat time as a continuous variable may not be suitable for economic analysis. We can offer two counterarguments.
  First, in economic life, time is a continuous variable; it is the measurement convention that is artificial. At every moment numerous decisions are made, many transactions are concluded, and many production processes never stop. It is always possible to model an economic process using continuous time and differential equations and then approximate it with the discrete time model for estimation and simulation. Second, mathematical theory of differential equations is too rich and powerful to forego it in economic analysis.
  Equilibrium analysis in economics produces a benchmark against which to gauge actual events and the workings of an economy. Comparative static analysis compares two equilibrium points in order to determine the effects of a change in exogenous variables or parameters of a model on endogenous variables. Yet we know that in the real world the economy is always in the process of adjustment and, therefore, out of equilibrium. It is as if the economy is chasing an equilibrium and before reaching it, the position of the equilibrium has changed. To model the movement from one equilibrium to another and to study the path of different variables when the system is out of equilibrium, we need dynamic models.
conversations.from: human
conversations.value: Provide the last four paragraphs.. End with the sentence ' Note that the eig function in Matlab returns normalized eigenvectors.'.
conversations.from: assistant
conversations.value: It follows that whenever y 1 is positive, it is decreasing and whenever y 2 is less than y 1, then y 2 is increasing. The movement of the system in different regions is shown in Fig. 17.7. As can be seen, the system is stable, because in every region it is directed toward the equilibrium. This is not true for an unstable system. For example, if we replace the first equation with  the system will not be stable in all regions. The reader may want to follow the procedure of Fig. 17.7 and ascertain that indeed the altered system is not stable everywhere.
  The phase portrait of the Ramsey model is shown in Fig. 17.8. As can be seen, the model is not stable everywhere. There are three equilibrium points,  (point E), , and the point to the right of  where the curve  intersects the horizontal axis. Among the three points only E is stable. There are only two regions in which the movements of both k and c are toward the equilibrium point E. In these regions we can find a path (shown with the arrows passing through E) that converges to the equilibrium. All other paths will either diverge or end up in an unstable equilibrium.
  Whereas the theory developed in this chapter is quite general and pertains to a system of two and more differential equations, for the ease and clarity of exposition, with a few exceptions, we will confine ourselves to systems of two equations.
  To obtain the Jordan canonical form one can use either normalized eigenvectors--that is, vectors of unit length--or eigenvectors of any length. In the text both normalized and nonnormalized eigenvectors are used. Normalized eigenvectors, however, are required for the radial decomposition of a positive definite matrix, discussed in Chap. 7. Note that the eig function in Matlab returns normalized eigenvectors.