Mathematical Economics - B.S
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Lecture Notes1 Mathematical Ecnomics
Lecture Notes1 Mathematical Ecnomics Guoqiang TIAN Department of Economics Texas A&M University College Station, Texas 77843 ([email protected]) This version: August, 2020 1The most materials of this lecture notes are drawn from Chiang’s classic textbook Fundamental Methods of Mathematical Economics, which are used for my teaching and con- venience of my students in class. Please not distribute it to any others. Contents 1 The Nature of Mathematical Economics 1 1.1 Economics and Mathematical Economics . 1 1.2 Advantages of Mathematical Approach . 3 2 Economic Models 5 2.1 Ingredients of a Mathematical Model . 5 2.2 The Real-Number System . 5 2.3 The Concept of Sets . 6 2.4 Relations and Functions . 9 2.5 Types of Function . 11 2.6 Functions of Two or More Independent Variables . 12 2.7 Levels of Generality . 13 3 Equilibrium Analysis in Economics 15 3.1 The Meaning of Equilibrium . 15 3.2 Partial Market Equilibrium - A Linear Model . 16 3.3 Partial Market Equilibrium - A Nonlinear Model . 18 3.4 General Market Equilibrium . 19 3.5 Equilibrium in National-Income Analysis . 23 4 Linear Models and Matrix Algebra 25 4.1 Matrix and Vectors . 26 i ii CONTENTS 4.2 Matrix Operations . 29 4.3 Linear Dependance of Vectors . 32 4.4 Commutative, Associative, and Distributive Laws . 33 4.5 Identity Matrices and Null Matrices . 34 4.6 Transposes and Inverses . 36 5 Linear Models and Matrix Algebra (Continued) 41 5.1 Conditions for Nonsingularity of a Matrix . 41 5.2 Test of Nonsingularity by Use of Determinant . -
Cryptocurrency: the Economics of Money and Selected Policy Issues
Cryptocurrency: The Economics of Money and Selected Policy Issues Updated April 9, 2020 Congressional Research Service https://crsreports.congress.gov R45427 SUMMARY R45427 Cryptocurrency: The Economics of Money and April 9, 2020 Selected Policy Issues David W. Perkins Cryptocurrencies are digital money in electronic payment systems that generally do not require Specialist in government backing or the involvement of an intermediary, such as a bank. Instead, users of the Macroeconomic Policy system validate payments using certain protocols. Since the 2008 invention of the first cryptocurrency, Bitcoin, cryptocurrencies have proliferated. In recent years, they experienced a rapid increase and subsequent decrease in value. One estimate found that, as of March 2020, there were more than 5,100 different cryptocurrencies worth about $231 billion. Given this rapid growth and volatility, cryptocurrencies have drawn the attention of the public and policymakers. A particularly notable feature of cryptocurrencies is their potential to act as an alternative form of money. Historically, money has either had intrinsic value or derived value from government decree. Using money electronically generally has involved using the private ledgers and systems of at least one trusted intermediary. Cryptocurrencies, by contrast, generally employ user agreement, a network of users, and cryptographic protocols to achieve valid transfers of value. Cryptocurrency users typically use a pseudonymous address to identify each other and a passcode or private key to make changes to a public ledger in order to transfer value between accounts. Other computers in the network validate these transfers. Through this use of blockchain technology, cryptocurrency systems protect their public ledgers of accounts against manipulation, so that users can only send cryptocurrency to which they have access, thus allowing users to make valid transfers without a centralized, trusted intermediary. -
Course Syllabus ECN101G
Course Syllabus ECN101G - Introduction to Economics Number of ECTS credits: 6 Time and Place: Tuesday, 10:00-11:30 at VeCo 3 Thursday, 10:00-11:30 at VeCo 3 Contact Details for Professor Name of Professor: Abdel. Bitat, Assistant Professor E-mail: [email protected] Office hours: Monday, 15:00-16:00 and Friday, 15:00-16:00 (Students who are unable to come during these hours are encouraged to make an appointment.) Office Location: -1.63C CONTENT OVERVIEW Syllabus Section Page Course Prerequisites and Course Description 2 Course Learning Objectives 2 Overview Table: Link between MLO, CLO, Teaching Methods, 3-4 Assignments and Feedback Main Course Material 5 Workload Calculation for this Course 6 Course Assessment: Assignments Overview and Grading Scale 7 Description of Assignments, Activities and Deadlines 8 Rubrics: Transparent Criteria for Assessment 11 Policies for Attendance, Later Work, Academic Honesty, Turnitin 12 Course Schedule – Overview Table 13 Detailed Session-by-Session Description of Course 14 Course Prerequisites (if any) There are no pre-requisites for the course. However, since economics is mathematically intensive, it is worth reviewing secondary school mathematics for a good mastering of the course. A great source which starts with the basics and is available at the VUB library is Simon, C., & Blume, L. (1994). Mathematics for economists. New York: Norton. Course Description The course illustrates the way in which economists view the world. You will learn about basic tools of micro- and macroeconomic analysis and, by applying them, you will understand the behavior of households, firms and government. Problems include: trade and specialization; the operation of markets; industrial structure and economic welfare; the determination of aggregate output and price level; fiscal and monetary policy and foreign exchange rates. -
2020-2021 Bachelor of Arts in Economics Option in Mathematical
CSULB College of Liberal Arts Advising Center 2020 - 2021 Bachelor of Arts in Economics Option in Mathematical Economics and Economic Theory 48 Units Use this checklist in combination with your official Academic Requirements Report (ARR). This checklist is not intended to replace advising. Consult the advisor for appropriate course sequencing. Curriculum changes in progress. Requirements subject to change. To be considered for admission to the major, complete the following Major Specific Requirements (MSR) by 60 units: • ECON 100, ECON 101, MATH 122, MATH 123 with a minimum 2.3 suite GPA and an overall GPA of 2.25 or higher • Grades of “C” or better in GE Foundations Courses Prerequisites Complete ALL of the following courses with grades of “C” or better (18 units total): ECON 100: Principles of Macroeconomics (3) MATH 103 or Higher ECON 101: Principles of Microeconomics (3) MATH 103 or Higher MATH 111; MATH 112B or 113; All with Grades of “C” MATH 122: Calculus I (4) or Better; or Appropriate CSULB Algebra and Calculus Placement MATH 123: Calculus II (4) MATH 122 with a Grade of “C” or Better MATH 224: Calculus III (4) MATH 123 with a Grade of “C” or Better Complete the following course (3 units total): MATH 247: Introduction to Linear Algebra (3) MATH 123 Complete ALL of the following courses with grades of “C” or better (6 units total): ECON 100 and 101; MATH 115 or 119A or 122; ECON 310: Microeconomic Theory (3) All with Grades of “C” or Better ECON 100 and 101; MATH 115 or 119A or 122; ECON 311: Macroeconomic Theory (3) All with -
Priorities for the National Science Foundation
December 2020 Priorities for the National Science Foundation Founded in 1888, the American Mathematical Society (AMS) is dedicated to advancing the interests of mathematical research and scholarship and connecting the diverse global mathematical community. We do this through our book and journal publications, meetings and conferences, database of research publications1 that goes back to the early 1800s, professional services, advocacy, and awareness programs. The AMS has 30,000 individual members worldwide and supports mathemat- ical scientists at every career stage. The AMS advocates for increased and sustained funding for the National Science Foundation (NSF). The applications The NSF supports more fundamental research in the of advances in mathematical sciences—and done at colleges and theoretical science, 2 universities—than any other federal agency. A signif- including theory of icant increase in Congressional appropriations would mathe matics, occur help address the effects of years of high-quality grant on a time scale that proposals that go unfunded due to limited funding. means the investment Those unmet needs continue. A 2019 National Science Board report3 stated that in fiscal year 2018, “approxi- is often hard to justify mately $3.4 billion was requested for declined proposals in the short run. that were rated Very Good or higher in the merit review process.” This accounts for about 5440 declined proposals at the NSF. The U.S. is leaving potentially transformative scientific research unfunded, while other countries are making significant investments. In the next section we give an overview of our two priorities. The second, and final section offers a discussion of existing funding mechanisms for mathematicians. -
Mathematical and Physical Sciences
Overview of the Directorate for Mathematical and Physical Sciences NSF Grants Conference Hosted by George Washington University Arlington, VA, October 6-7, 2014 Bogdan Mihaila, [email protected] Program Director Division of Physics US Government NSF Vision and Goals Vision » A Nation that creates and exploits new concepts in science and engineering and provides global leadership in research and education Mission » To promote the progress of science; to advance the national health, prosperity, and welfare; to secure the national defense Strategic Goals » Transform the frontiers of science and engineering » Stimulate innovation and address societal needs through research & education » Excel as a Federal Science Agency NSF in a Nutshell Independent agency to support basic research & education Grant mechanism in two forms: » Unsolicited, curiosity driven (the majority of the $) » Solicited, more focused All fields of science/engineering Merit review: Intellectual Merit & Broader Impacts Discipline-based structure, some cross-disciplinary Support large facilities NSF Organization Chart Office of Diversity & National Science Board Director Inclusion (ODI) (NSB) Deputy Director Office of the General Counsel (OGC) Office of the NSB Office Office of International & Inspector General $482M (OIG) ($4.3M) Integrative Activities (OIIA) ($14.2M) Office of Legislative & Public Affairs (OLPA) Computer & Mathematical Biological Information Engineering Geosciences & Physical Sciences Science & (ENG) (GEO) Sciences (BIO) Engineering (MPS) (CISE) -
International Baccalaureate Diploma Programme Subject Brief Individuals and Societies: Economics—Higher Level First Assessments 2022—Last Assessments 2029
International Baccalaureate Diploma Programme Subject Brief Individuals and societies: Economics—higher level First assessments 2022—last assessments 2029 The Diploma Programme (DP) is a rigorous pre-university course of study designed for students in the 16 to 19 age range. It is a broad-based two-year course that aims to encourage students to be knowledgeable and inquiring, but also caring and compassionate. There is a strong emphasis on encouraging students MA PROG PLO RAM to develop intercultural understanding, open-mindedness, and the attitudes necessary for DI M IB S IN LANG E UDIE UAG ST LITERAT E them to respect and evaluate a range of points of view. AND URE A IN The course is presented as six academic areas enclosing a central core. Students study E E N D N DG G E D IV A O L E I W X S ID U IT O T O two modern languages (or a modern language and a classical language), a humanities G E U IS N N C N K ES TO T I A U CH EA D E A F A C L O H E T or social science subject, an experimental science, mathematics and one of the creative L Q R S O I I C P N D P G E A Y S A E R arts. Instead of an arts subject, students can choose two subjects from another area. S O S E A Y H It is this comprehensive range of subjects that makes the Diploma Programme a T demanding course of study designed to prepare students effectively for university A P G entrance. -
The Rise and Fall of Walrasian General Equilibrium Theory: the Keynes Effect
The Rise and Fall of Walrasian General Equilibrium Theory: The Keynes Effect D. Wade Hands Department of Economics University of Puget Sound Tacoma, WA USA [email protected] Version 1.3 September 2009 15,246 Words This paper was initially presented at The First International Symposium on the History of Economic Thought “The Integration of Micro and Macroeconomics from a Historical Perspective,” University of São Paulo, São Paulo, Brazil, August 3-5, 2009. Abstract: Two popular claims about mid-to-late twentieth century economics are that Walrasian ideas had a significant impact on the Keynesian macroeconomics that became dominant during the 1950s and 1060s, and that Arrow-Debreu Walrasian general equilibrium theory passed its zenith in microeconomics at some point during the 1980s. This paper does not challenge either of these standard interpretations of the history of modern economics. What the paper argues is that there are at least two very important relationships between Keynesian economics and Walrasian general equilibrium theory that have not generally been recognized within the literature. The first is that influence ran not only from Walrasian theory to Keynesian, but also from Keynesian theory to Walrasian. It was during the neoclassical synthesis that Walrasian economics emerged as the dominant form of microeconomics and I argue that its compatibility with Keynesian theory influenced certain aspects of its theoretical content and also contributed to its success. The second claim is that not only did Keynesian economics contribute to the rise Walrasian general equilibrium theory, it has also contributed to its decline during the last few decades. The features of Walrasian theory that are often suggested as its main failures – stability analysis and the Sonnenschein-Mantel-Debreu theorems on aggregate excess demand functions – can be traced directly to the features of the Walrasian model that connected it so neatly to Keynesian macroeconomics during the 1950s. -
Nine Lives of Neoliberalism
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Plehwe, Dieter (Ed.); Slobodian, Quinn (Ed.); Mirowski, Philip (Ed.) Book — Published Version Nine Lives of Neoliberalism Provided in Cooperation with: WZB Berlin Social Science Center Suggested Citation: Plehwe, Dieter (Ed.); Slobodian, Quinn (Ed.); Mirowski, Philip (Ed.) (2020) : Nine Lives of Neoliberalism, ISBN 978-1-78873-255-0, Verso, London, New York, NY, https://www.versobooks.com/books/3075-nine-lives-of-neoliberalism This Version is available at: http://hdl.handle.net/10419/215796 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative -
THE NEOLIBERAL THEORY of SOCIETY Simon Clarke
THE NEOLIBERAL THEORY OF SOCIETY Simon Clarke The ideological foundations of neo-liberalism Neoliberalism presents itself as a doctrine based on the inexorable truths of modern economics. However, despite its scientific trappings, modern economics is not a scientific discipline but the rigorous elaboration of a very specific social theory, which has become so deeply embedded in western thought as to have established itself as no more than common sense, despite the fact that its fundamental assumptions are patently absurd. The foundations of modern economics, and of the ideology of neoliberalism, go back to Adam Smith and his great work, The Wealth of Nations. Over the past two centuries Smith’s arguments have been formalised and developed with greater analytical rigour, but the fundamental assumptions underpinning neoliberalism remain those proposed by Adam Smith. Adam Smith wrote The Wealth of Nations as a critique of the corrupt and self-aggrandising mercantilist state, which drew its revenues from taxing trade and licensing monopolies, which it sought to protect by maintaining an expensive military apparatus and waging costly wars. The theories which supported the state conceived of exchange as a ‘zero-sum game’, in which one party’s gain was the other party’s loss, so the maximum benefit from exchange was to be extracted by force and fraud. The fundamental idea of Smith’s critique was that the ‘wealth of the nation’ derived not from the accumulation of wealth by the state, at the expense of its citizens and foreign powers, but from the development of the division of labour. The division of labour developed as a result of the initiative and enterprise of private individuals and would develop the more rapidly the more such individuals were free to apply their enterprise and initiative and to reap the corresponding rewards. -
Mathematical and Physical Sciences
DIRECTORATE FOR MATHEMATICAL AND $1,255,820,000 PHYSICAL SCIENCES (MPS) -$247,590,000 / -16.5% MPS Funding (Dollars in Millions) Change over FY 2018 FY 2019 FY 2020 FY 2018 Actual Actual (TBD) Request Amount Percent Astronomical Sciences (AST) $311.16 - $217.08 -$94.08 -30.2% Chemistry (CHE) 246.29 - 214.18 -32.11 -13.0% Materials Research (DMR) 337.14 - 273.78 -63.36 -18.8% Mathematical Sciences (DMS) 237.69 - 203.26 -34.43 -14.5% Physics (PHY) 310.75 - 247.50 -63.25 -20.4% Office of Multidisciplinary Activities (OMA) 60.39 - 100.02 39.63 65.6% Total $1,503.41 - $1,255.82 -$247.59 -16.5% About MPS The MPS FY 2020 Request builds on past efforts and aligns with NSF priorities for FY 2020. The programs in MPS span from individual investigator awards to large, multi-user facilities. MPS-funded science spans an enormous range as well: from the smallest objects and shortest times ever studied to distances and times that are the size and age of the universe. Individual investigators and small teams receive most awards, but centers, institutes, and facilities are all integral to MPS-funded research. The MPS FY 2020 Request is influenced by four key priorities: (1) sustaining core research programs, (2) supporting the highest priority facilities, (3) supporting early-career investigators, and (4) providing funding for targeted basic research in NSF-Wide Investments, including the NSF Big Ideas. MPS continues to support its core areas of science (astronomical sciences, chemistry, materials research, mathematical sciences, and physics) as well as thet next generation of scientists. -
Brochure on Careers in Applied Mathematics
careers in applied mathematics Options for STEM Majors society for industrial and applied mathematics 2 / careers in applied mathematics Mathematics and computational science are utilized in almost every discipline of science, engineering, industry, and technology. New application areas are WHERE CAN YOU WHAT KINDS OF PROBLEMS MIGHT YOU WORK ON? constantly being discovered MAKE AN IMPACT? While careers in mathematics may differ widely by discipline while established techniques Many different types and job title, one thing remains constant among them— are being applied in new of organizations hire problem solving. Some potential problems that someone with ways and in emerging fields. mathematicians and mathematical training might encounter are described below. Consequently, a wide variety computational scientists. Which of them do you find most intriguing, and why? of career opportunities You can easily search the • How can an airline use smarter scheduling to reduce costs of are open to people with websites of organizations and aircraft parking and engine maintenance? Or smarter pricing mathematical talent and corporations that interest to maximize profit? training. you to learn more about their • How can one design a detailed plan for a clinical trial? Building such a plan requires advanced statistical skills and In this guide, you will find answers to sophisticated knowledge of the design of experiments. questions about careers in applied mathematics • Is ethanol a viable solution for the world’s dependence and computational science, and profiles on fossil fuels? Can biofuel production be optimized to of professionals working in a variety of combat negative implications on the world’s economy and environment? environments for which a strong background • How do we use major advances in computing power to in mathematics is necessary for success.