Mathematical Economics I

ECON20120 Mathematical Economics I 20 Full year Undergraduate Level 2 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 significant progress when it became a more formal science. In particular, the intellectual and policy debates evolved substantially when economics started to formulate principles using mathematics and rigorous arguments.This unit 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 dynamics. Though we cover basic mathematical techniques motivated by economic applications, this course is not about learning new economics but rather strengthening your methodological toolbox to tackle economic issues. The course content is a universal gallery of technical tools for economic modeling.You will acquire skills to develop rigorous economic arguments and sophisticated reasoning to represent and analyse complex economic situations, where intuition alone fails to serve a conclusion. You will also grasp the generality of economic principles and most importantly their limitations, which are often misunderstood. The techniques you will learn ιn this course are used in almost all branches of economics and are indispensable for building sophisticated models to inform empirical analysis. Such skills are essential for a well rounded modern economist and in high demand by institutions that deal with complex economic issues.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:• solve economic optimization problems;• apply duality theory to construct expenditure and demand functions• understand and apply methods of comparative statics• conceptualize and analyze strategic situations via game theoretic reasoning• solve economic models involving first order one-dimensional and two-dimensional difference equations• solve economic models involving first order one and two-dimensional differential equations. Economics has made significant progress when it became a more formal science. In particular, the intellectual and policy debates evolved substantially when economics started to formulate principles using mathematics and rigorous arguments.This unit is about mathematical modeling 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 dynamics. Though we cover basic mathematical techniques motivated by economic applications, this course is not about learning new economics but rather strengthening your methodological toolbox to tackle economic issues. The course content is a universal gallery of technical tools for economic modeling.You will acquire skills to develop rigorous economic arguments and sophisticated reasoning to represent and analyse complex economic situations, where intuition alone fails to serve a conclusion. You will also grasp the generality of economic principles and most importantly their limitations, which are often misunderstood. The techniques you will learn ιn this course are used in almost all branches of economics and are indispensable for building sophisticated models to inform empirical analysis. Such skills are essential for a well rounded modern economist and in high demand by institutions that deal with complex economic issues.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:• solve economic optimization problems;• apply duality theory to construct expenditure and demand functions• understand and apply methods of comparative statics• conceptualize and analyze strategic situations via game theoretic reasoning• solve economic models involving first order one-dimensional and two-dimensional difference equations• solve economic models involving first order one and two-dimensional differential equations. 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:• solve economic optimization problems;• apply duality theory to construct expenditure and demand functions• understand and apply methods of comparative statics• conceptualize and analyze strategic situations via game theoretic reasoning• solve economic models involving first order one-dimensional and two-dimensional difference equations• solve economic models involving first order one and two-dimensional differential equations. • Critical thinking, conceptualization of principles underpinning economic issues• Informing and advising decision-Making• Ability to develop sophisticated arguments in complex situations• Problem solving, Problem posing, conducting and reporting on research• Critical reflection and evaluation.  • Ability to conduct meaningful and well founded analysis of complex problems• Ability to model complex economic situations to inform empirical/applied research• Planning independent research• Mapping and modeling• Peer review.  • Applying Subject Knowledge,• Developing Research Proposals• Developing sophisticated reports with structured arguments Analytical skills Critical reflection and evaluation. Decision-making. Problem solving Ability to conceptualise, analyse and solve complex problems Research Planning, conducting and reporting on independent research. Other Mapping and modelling. Developing framework for empirical research. Peer review. Applying subject knowledge. ProvisionalSemester 1:• What is Mathematical Economics about? Learning goals• Preferences and utility• Uncertainty and lotteries• Review of (constrained) optimisation• Incentives and their applications• Mathematical financial economics• Implicit Function Theorem and its applications in micro- and macroeconomics• Demand theory• Summary and reviewSemester 2:This part of the course covers Game Theory and Dynamic Systems.I Game TheoryIA Static Games:• Definition of games, games in normal and strategic forms• Solution concepts, best responses, Nash equilibrium with pure strategies• Mixed strategies, Nash equilibrium with mixed strategies, existence of Nash equilibrium• Applications in economics, Cournot and Bertrand duopoly/oligopoly as a game IB Dynamic Games:• Game trees, games in extensive form, sequential move, multistage and repeated games• Solution concepts for dynamic games, subgames, subgame perfection, refinements of Nash equilibrium, subgame perfect Nash equilibrium• Applications in economics, duopoly/oligopoly with sequential moves, Stackelberg duopoly, investment/capacity decisions and other examples from industrial organizationII Dynamic systemsIIA Discrete time:• First order linear difference equations, steady state, stability and solutions• Applications in economics, market stability• First order linear systems of difference equations, steady state, stability and solutions• Cyclicality of solutions• Applications in economics, the linear first order macroeconomic model, Samuelson's accelerator model, dynamic Cournot duopoly.IIB Continuous time:• First order linear differential equations, steady state, stability and solutions• Applications in economics, the Philips curve• First order linear systems of differential equations, steady state, stability and solutions• Cyclicality of solutions• Applications in economics,dynamic Cournot duopoly in continuous time, continuous time macroeconomic model Synchronous activities (such as Lectures or Review and Q&A sessions, and tutorials), and guided self-study 0 Other 100% Semester One<ul> <li>Exam (35%)</li> <li>Online Assignments x 5 (worth 3% each, overall 15%)</li></ul>Semester Two<ul> <li>Exam (40%) </li> <li>Mid-term (10%)</li></ul> <ul> <li>Tutorial exercises.</li> <li>Online tests.</li></ul> ECON10071A Advanced Mathematics Pre-Requisite Compulsory ECON10192 Introduction to Mathematical Economics Pre-Requisite Compulsory ECON20192 Introduction to Mathematical Economics Pre-Requisite Compulsory ECON10071B Advanced Mathematics Pre-Requisite Compulsory Pre-Requisites: (ECON10071A OR ECON10071B) AND (ECON10192 OR ECON20192)ECON10071 Adv Maths and (ECON10192 Intro Math Econ or 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:• Hammond, P., and K. Sydsæter, Mathematics for Economic Analysis, Prentice Hall, 1995• Sydsæter, K., Hammond, P., Seierstad, A. and Strom, A., Further Mathematics for Economic Analysis, Prentice Hall (now in its second edition).• Sydsæter, K., Hammond, P., and Strom, A., Essential Mathematics for Economic Analysis, Prentice Hall (now in its fourth edition)• Simon, C.P. and Blume, L.E., Mathematics for Economists, W.W. Norton (paperback and hard cover)• Jehle, J., and P. Reny, Advanced Microeconomic Theory, Addison Wesley, 2 ed., 2000.• Nicholson, W., Microeconomic Theory, 9 ed., 2005.• Rubinstein, A, Lecture Notes in Microeconomic Theory, Princeton University Press, 2 ed., 2002Prerequisite: 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:• Hammond, P., and K. Sydsæter, Mathematics for Economic Analysis, Prentice Hall, 1995.Hal R. Varian, Intermediate Microeconomics a Modern Approach, 8 edition, Norton 2010. 0 0 0 For every 10 course unit credits we expect students to work for around 100 hours. This time generally includes any contact times (online or face to face, recorded and live), but also independent study, work for coursework, and group work. This amount is only a guidance and individual study time will vary.