Mathematical Economics I

ECON30320 Mathematical Economics I 20 Full year Undergraduate Level 3 Klaus Schenkhoppe Unit coordinator Economics 1 FHEQ level (Framework for Higher Education Qualifications) ' Middle part of Bachelors ' European Credit Transfer & Accumulation System Rating : 10.0 Economics has made a huge jump forward when it became a more formal science. In  particular when economics started to formulate its models using mathematics and to use mathematical tools to solve these models. This is what the course is about: Mathematical Modelling and Analysis. Both of which constitute core skills of economists. The course unit develops students' knowledge of mathematical and quantitative methods in the context of consumer theory, the theory of the firm, game theory and other subjects. You will learn how to express an economic idea in mathematical terms. In addition you will learn mathematical methods how to find equilibria, and how to analyse the behaviour of equilibria when exogenous circumstances change. The techniques you will learn on this course are used in almost all branches of economics. The course content is really a  universal (mathematical) toolbox for economic modelling. Although we will look into economic applications, this course is not about learning new economics. You will further your knowledge of economics in the micro, macro,  development, etc. economics courses. The objectives of this course are that students will be able to: <ul> <li>solve economic optimization problems; </li> <li>apply duality theory to construct expenditure and demand functions </li> <li>understand and apply methods of comparative statics </li> <li>solve simple games, including duopoly games </li> <li>solve economic models involving first order one-dimensional and two-dimensional difference equations </li> <li>solve economic models involving first order one and two-dimensional differential equations. </li></ul> Economics has made a huge jump forward when it became a more formal science. In  particular when economics started to formulate its models using mathematics and to use mathematical tools to solve these models. This is what the course is about: Mathematical Modelling and Analysis. Both of which constitute core skills of economists. The course unit develops students' knowledge of mathematical and quantitative methods in the context of consumer theory, the theory of the firm, game theory and other subjects. You will learn how to express an economic idea in mathematical terms. In addition you will learn mathematical methods how to find equilibria, and how to analyse the behaviour of equilibria when exogenous circumstances change. The techniques you will learn on this course are used in almost all branches of economics. The course content is really a  universal (mathematical) toolbox for economic modelling. Although we will look into economic applications, this course is not about learning new economics. You will further your knowledge of economics in the micro, macro,  development, etc. economics courses. The objectives of this course are that students will be able to: <ul> <li>solve economic optimization problems; </li> <li>apply duality theory to construct expenditure and demand functions </li> <li>understand and apply methods of comparative statics </li> <li>solve simple games, including duopoly games </li> <li>solve economic models involving first order one-dimensional and two-dimensional difference equations </li> <li>solve economic models involving first order one and two-dimensional differential equations. </li></ul> The aim of this course is to develop students' knowledge of the analytical and mathematical techniques used in static and dynamic economic theory.  At the end of this course students should be able to: <ul> <li style="margin-left: 5.7pt;">solve economic optimization problems; </li> <li style="margin-left: 5.7pt;">apply duality theory to construct expenditure and demand functions </li> <li style="margin-left: 5.7pt;">understand and apply methods of comparative statics </li> <li style="margin-left: 5.7pt;">solve simple games, including duopoly games </li> <li style="margin-left: 5.7pt;">solve economic models involving first order one-dimensional and two-dimensional difference equations </li> <li style="margin-left: 5.7pt;">solve economic models involving first order one and two-dimensional differential equations. </li></ul> Critical thinking, Problem solving, Problem posing, conducting and reporting on research, Critical reflection and evaluation, decision-Making.  Ability to conduct rigorous analysis of problems, Planning independent research, Mapping and modelling, Peer review.  <ul> <li>Applying Subject Knowledge </li> <li>Developing Research Proposals </li> <li>Developing sophisticated reports with structured arguments</li></ul> Analytical skills Critical reflection and evaluation. Decision-making. Problem solving Ability to conduct rigorous analysis of problems. Research Planning, conducting and reporting on independent research. Other Mapping and modelling. Peer review. Applying subject knowledge. ProvisionalSemester 1:<ul><li>What is Mathematical Economics about? Learning goals </li><li>Preferences and utility </li><li>Uncertainty and lotteries </li><li>Review of (constrained) optimisation </li><li>Incentives and their applications </li><li>Mathematical financial economics </li><li>Implicit Function Theorem and its applications in micro and macroeconomics </li><li>Demand theory </li><li>Summary and review</li></ul>Semester 2:This part of the course covers Game Theory and Dynamic Systems.I Game Theory  IA Static Games:<ul><li>Definition of games, games in normal and strategic forms </li><li>Solution concepts, best responses, Nash equilibrium with pure strategies </li><li>Mixed strategies, Nash equilibrium with mixed strategies, existence of Nash equilibrium </li><li>Applications in economics, Cournot and Bertrand duopoly/oligopoly as a game</li></ul>IB Dynamic Games:<ul><li>Game trees, games in extensive form, sequential move, multistage and repeated games </li><li>Solution concepts for dynamic games, subgames, subgame perfection, refinements of Nash equilibrium, subgame perfect Nash equilibrium </li><li>Applications in economics, duopoly/oligopoly with sequential moves,Stackelberg duopoly, investment/capacity decisions and other examples from industrial organization II Dynamic systems</li></ul>IIA Discrete time:<ul><li>First order linear difference equations, steady state, stability and solutions </li><li>Applications in economics, market stability </li><li>First order linear systems of difference equations, steady state, stability and solutions </li><li>Cyclicality of solutions </li><li>Applications in economics, the linear first order macroeconomic model, Samuelson's accelerator model, dynamic Cournot duopoly.</li></ul>IIB Continuous time:<ul><li>First order linear differential equations, steady state, stability and solutions </li><li>Applications in economics, the Philips curve </li><li>First order linear systems of differential equations, steady state, stability and solutions </li><li>Cyclicality of solutions </li></ul> Synchronous activities (such as Lectures or Review and Q&A sessions, and tutorials), and guided self-study 0 Other 100% Smester One 35% Exam 15% Online test (five, worth 3% each)Semester Two 40% Exam 10% Mid-term test <ul> <li> Tutorial exercises.</li> <li> Online tests.</li> </ul> ECON20071 Advanced Mathematics Pre-Requisite Compulsory ECON20192 Introduction to Mathematical Economics Pre-Requisite Compulsory Pre-requisites: (ECON20071 and ECON20192)ECON20071 Adv Maths and ECON20192 Intro Math Econ  Y Semester 1: Reading: Detailed lecture notes are available on Blackboard (one chapter for each hour of lecture). Please read the relevant chapter BEFORE each lecture. Reading list: The following textbooks are useful references for the material covered during the semester: <ul> <li>Hammond, P., and K. Sydsæter, Mathematics for Economic Analysis, Prentice Hall, 1995 </li> <li>Sydsæter, K., Hammond, P., Seierstad, A. and Strom, A., Further Mathematics for Economic Analysis, Prentice Hall (now in its second edition). </li> <li>Sydsæter, K., Hammond, P., and Strom, A., Essential Mathematics for Economic Analysis, Prentice Hall (now in its fourth edition) </li> <li>Simon, C.P. and Blume, L.E., Mathematics for Economists, W.W. Norton (paperback and hard cover) </li> <li>Jehle, J., and P. Reny, Advanced Microeconomic Theory, Addison Wesley, 2 ed., 2000. </li> <li>Nicholson, W., Microeconomic Theory, 9 ed., 2005. </li> <li>Rubinstein, A, Lecture Notes in Microeconomic Theory, Princeton University Press, 2 ed., 2002 </li></ul>Prerequisite: The students are expected to have a good knowledge of calculus. Among  required topics:  partial derivatives, the chain rule in several variables, static optimization, etc. Those who feel insecure with the above material (although this is taught in the  prerequisite maths modules) should revise it before taking the module. The book of Hammond and Sydsæter "essential mathematics for economic analysis" as well as the advance mathematics unit textbook may serve as good references.Students are expected to revise the mentioned material before semester 1 starts.  Weekly preparation: (1) Read the handout, (2) solve the exercise questions, (3) read the textbook as instructed in the handouts. Semester 2: Sets of notes along with exercise sets will be made available on the course website.  Further suggested readings are mentioned within those notes. Answers to exercises will be covered during example classes (but WILL NOT be made available by the lecturer). A useful reference for some of the material that will be covered is: <ul> <li>Hammond, P., and K. Sydsæter, Mathematics for Economic Analysis, Prentice Hall, 1995. </li> <li>Hal R. Varian, Intermediate Microeconomics a Modern Approach, 8 edition, Norton 2010.</li></ul> 0 0 0