Introduction to dynamic programming applied to economics. Daron acemoglu mit economic growth lectures 6 and 7 november 15 and 17, 2011. An example of a function satisfying these assumptions, and that will be used repeatedly in the course, is f k. Comprised of eight essays, this book begins with an introduction to hamiltonian dynamics in economics, followed by a discussion on optimal steady states of nsector growth models when utility is discounted. Study guide for use with principles of macroeconomics by robert h frank, ben bernanke, lars osberg, brian maclean, melvin cross, kam hon chu, jane waples and a great selection of related books, art and collectibles available now at. Since articles are the primary means through which economists communicate, you should read at. The hamiltonian approach to dynamic economics cass, david, shell, karl on. Can you think of a good way to solve this hamiltonian function with two control variables and one state. Well see the relationship between c and k when we talk about our constraint in just one minute. Saddle points of hamiltonian trajectories in mathematical economics. Macroeconomicsoptimal growth wikibooks, open books for. Refer to f as the instantaneous objective function or the payoff function and.
Jeffersonian thought is the main competitor of the hamiltonian school, especially since both men were actually alive during the same time. Both are good, but both have a really annoying flaw. The hamiltonian approach to dynamic economics sciencedirect. One main clash came from jeffersons admiration for the french rather that gb. Applications to economics optimal control theory has been extensively applied to the solution of economics problems since the early papers that appeared in shell 1967 and the works of arrow 1968. Inspired by, but distinct from, the hamiltonian of classical mechanics, the hamiltonian of optimal control theory was developed by lev pontryagin as.
Most physics majors will use modern dynamics in their careers. The equilibrium can be characterized in terms of an hjb equation for the value function v. The present value hamiltonian evaluates the optimal behavior in terms of period 0 value. An example of a function satisfying these assumptions, and that will be used repeat. The next example is from chapter 2 of the book caste and ecology in social. In other macroeconomic topics, such as monetary economics, labor. Schaums outline of introduction to mathematical economics. Principles of macroeconomics really worth buying both of them. Lecture notes for macroeconomics i, 2004 yale economic. The notes here heavily borrow from stokey, lucas and prescott 1989, but simplify the exposition.
Finding a wave function equation determining the energy levels. Pdf a simple proof of the constancy of the pontryagin hamiltonian. Hamiltonian synonyms, hamiltonian pronunciation, hamiltonian translation, english dictionary definition of hamiltonian. Fertile area of research, excellent dissertation topics. Notes for macroeconomics ii, ec 607 university of michigan. Newest economics questions mathematics stack exchange. Citeseerx document details isaac councill, lee giles, pradeep teregowda.
With few exceptions, the articles are also summarized in romer or blanchard and fischer. Emphasis is placed on the stability of longrun steadystate equilibrium in models of heterogeneous capital accumulation. Navigate to the global search form search landmark. Economics during the fifties and sixties was marked by a substantial resurgence of interest in the theory of capital. Using dynamic constrain t, simplify those rst order conditions. I think that hamiltonian function shouldnt redirect tho hamiltonian mechanics, so other areas would only look for the use of hamiltonian function. A practical guide to stopping the next global financial meltdown. Introduction to hamiltonian dynamics in economics sciencedirect. The subsequen t discussion follo ws the one in app endix of. First that we should try to express the state of the mechanical system using the minimum representa tion possible and which re ects the fact that the physics of the problem is coordinateinvariant. Driscoll brown university and nber1 december 21, 2003.
What is the difference between a lagrangian and a hamiltonian. Economic dynamics in discrete time by jianjun miao books. Let us associate to the optimal control problem p the hamiltonian h. Elsewhere, the seach will be visibly opened after this button is selected. Where im going stochastic models of distribution and growth or heterogeneous agent models or micro to macro want to get you started on building these kind of models why should you be interested in this. It is thus not necessary to read all or even most of the articles on the list. Like you pointed out, for example, the hamiltonian itself kinetic energy plus potential energy will be conserved, which means you can understand where a system is stable or where its unstable by looking at level curves in position and momentum, the sets. Macroeconomicsoptimal growth wikibooks, open books for an. Hamiltonian definition of hamiltonian by the free dictionary. Most modern dynamic models of macroeconomics build on the framework described in solows 1956 paper. Lecture notes in macroeconomics university of houston. Overview hamiltonians and phase diagrams princeton. The ramseycasskoopmans model, or ramsey growth model, is a neoclassical model of economic growth based primarily on the work of frank p. Intuitively, the rm always has the option not to reoptimize as the price changes and secure a linear pro t function.
Or perhaps youd like to investigate why working women earn a fraction of what men earn, the effectiveness of policies aimed at improving the environment or even the impact of our economys growing globalization. The maxim um principle hamiltonian the hamiltonian is a useful recip e to solv e dynamic, deterministic optimization problems. Can rewrite the necessary condition in terms of hamiltonians as follows. Iournal of economic theory 12, 110 1976 introduction to hamiltonian dynamics in economics david cass and karl shell department of economics, university of pennsylvania, 3718 locust walk cr, philadelphia, pennsylvania 19174 received december 20, 1975. Economics majors are required to complete five mandatory courses and four electives within the department. Majors need to take calculus before they take certain intermediatelevel courses but do not need to have taken any economics in high school. Partial differential equation models in macroeconomics. Economic dynamics in discrete time ebook written by jianjun miao. This can be stated and proved see book if interested. The hamiltonian method ilarities between the hamiltonian and the energy, and then in section 15.
Chaos, networks, space and time publishes this week novermber 18, 2019, available from oxford university press and amazon. A viscosity solution of 5 is a continuous function vsuch that the following hold. For a problem to be a concave problem, fmust be concave and the constraint set must be convex. Extra resources for construction of mappings for hamiltonian systems and their applications pd sample text this property will allow us to turn the difference equation of a digital filter into an algebraic equation and then determine the mathematical description of a digital filter, called its transfer function. Onegood models were studied in detail, as were manygood models of production. Lectures 6 and 7, neoclassical growth daron acemoglu mit november 15 and 17, 2011. Often, there is some assumption that has to be explained in order to identify where the model has been simplified.
From wikibooks, open books for an open world function. The ramseycasskoopmans model differs from the solowswan model in that the choice of consumption is explicitly microfounded at a point in time and so endogenizes the. It can be understood as an instantaneous increment of the lagrangian expression of the problem that is to be optimized over a certain time horizon. Newest selfstudy questions economics stack exchange. H a mathematical function that can be used to generate the equations of motion of a dynamic system, equal for many such systems to the sum of the. The hamiltonian is a function used to solve a problem of optimal control for a dynamical system.
Of all the schools, american foreign policy stays the most consistent w hamiltonian thought. This includes questions about the formulation or solution of models from microeconomics or macroeconomics. Ramsey, with significant extensions by david cass and tjalling koopmans. Find the top 100 most popular items in amazon books best sellers. The hamiltonian approach to dynamic economics focuses on the application of the hamiltonian approach to dynamic economics and attempts to provide some unification of the theory of heterogeneous capital. Oct 06, 2014 hamiltonian mechanics also offer some nice advantages, mathematically and physically, in representing physical solutions geometrically. An introduction to lagrangian and hamiltonian mechanics. Rcc institute of information technology, kolkata, india. The production function in the economy is nondecreasing. This is a summary of some basic mathematics for handling constrained optimiza. While the advances during this period were very impressive, there was also an uneveness in the development of the subject. Powered by create your own unique website with customizable templates. The second edition of introduction to modern dynamics. Do you want to engage in discussions about health care, financial markets or social security reform.
As in the 1d case, time dependence in the relation between the cartesian coordinates and the new coordinates will cause e to not be the total energy, as we saw in eq. Hamiltonian mechanics has a very intuitive picture as the flow of a vector field on a manifold, and the simpler structure of first order equations allows one to derive many theorems, as well as a much wider range of changes of variables. Dynamic optimisation hamiltonian function approach file 1. The hamiltonian approach to dynamic economics 1st edition. The hamiltonian economic program was the set of measures that were proposed by american founding father and first secretary of the treasury alexander hamilton in four notable reports and implemented by congress during george washingtons first administration.
Local theory 02102011 6 hamiltonian and langrangian ormfulations 6. General formulation consider the general optimal control problem two slides back. Hamiltonian mechanics also offer some nice advantages, mathematically and physically, in representing physical solutions geometrically. References in the notes refer to articles given on the reading list. There is an alternative representation of static technological opportunities that is more congenial to dynamic analysis, that is, the representation of the technology by its hamiltonian function. Macroeconomics 1880 1900 1920 1940 1960 1980 2000 matthiasdoepke universityofchicago andreaslehnert boardofgovernorsofthe federalreservesystem andreww. The scheme is lagrangian and hamiltonian mechanics. This chapter presents an introduction to hamiltonian dynamics in economics. Principles of macroeconomics, first edition abebooks. A function is concave if the convex combination of the images of flies below the function at the convex combination. Download for offline reading, highlight, bookmark or take notes while you read economic dynamics in discrete time. For some reason we use k \displaystyle k as the argument in this function.
Such functions are, of course, nondecreasing and strictly concave. Newtonian, lagrangian and hamiltonian mechanics reading feynman. Is there any educational resource on hamiltonian function optimal. It starts with wellknown applications to consumer and producer theory, and to the theory of option pricing and then introduces new applications that emerge from current research some of which is the authors own in bounded rationality. Its original prescription rested on two principles. How twelve brilliant minds would solve todays biggest problems. Economic dynamics in discrete time by jianjun miao books on. Economic growth current and present value hamiltonian september 27, 2005 to derive the formulae for the current hamiltonian knowing the present value hamiltonian goes as follows. Construction of mappings for hamiltonian systems and their.
Hamiltonian function with two control variables and one. The initial and terminal conditions on k t pin then do wn the optimal paths. Hamiltonian mechanics is rarely used for practical engineering problems, but used constantly by mathematicians. Newtonian, lagrangian and hamiltonian mechanics reading. Newest mathematicaleconomics questions economics stack. Over 2 million books and magazines booksee download books for free. Professor acemoglu s book or books on optimal controldynamic programming, e. We want to get all of the binding constraints attached to multipliers.