...on Mathematics for Economists Chien-Fu CHOU September 2006 Contents Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7 Lecture 8 Lecture 9 Lecture 10 Static Economic Models and The Concept of Equilibrium Matrix Algebra Vector Space and Linear Transformation Determinant, Inverse Matrix, and Cramer’s rule Differential Calculus and Comparative Statics Comparative Statics – Economic applications Optimization Optimization–multivariate case Optimization with equality constraints and Nonlinear Programming General Equilibrium and Game Theory 1 5 10 16 25 36 44 61 74 89 1 1 Static Economic Models and The Concept of Equilibrium Here we use three elementary examples to illustrate the general structure of an economic model. 1.1 Partial market equilibrium model A partial market equilibrium model is constructed to explain the determination of the price of a certain commodity. The abstract form of the model is as follows. Qd = D(P ; a) Qd : Qs : P: a: Qs = S(P ; a) Qd = Qs , quantity demanded of the commodity quantity supplied to the market market price of the commodity a factor that affects demand and supply D(P ; a): demand function S(P ; a): supply function Equilibrium: A particular state that can be maintained. Equilibrium conditions: Balance of forces prevailing in the model. Substituting the demand and supply functions, we have D(P ; a) = S(P ; a). For a given a, we can solve this last equation to obtain the equilibrium price P ∗ as a...
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...constructors. The conversion from class to basic type is indeed not that easy as it cannot be done using constructors. for this conversion we need to define an overloaded casting operator. This is usually referred to as a conversion function. The syntax for this is as follows: operator typename(){….} The above function shall convert a class type data to typename. A conversion function must follow the following 3 rules: a. It cannot have a return type b. It has to be declared inside a class. c. It cannot have any arguments. (ii)File pointers: we need to have file pointers viz. input pointer and output pointer. File pointers are required in order to navigate through the file while reading or writing. There are certain default actions of the input and the output pointer. When we open a file in read only mode, the input pointer is by default set at the beginning. When we open a file in write only mode, the existing contents are deleted and the file pointer is attached in the beginning. C++ also provides us with the facility to control the file pointer by ourselves. For this, the following functions are supported by stream classes: seekg(), seekp(), tellg(), tellp(). (iii) Function prototyping is used to describe the details of the function. It tells the compiler about the number of arguments, the type of arguments, and the type of the return values. It some what provides the compiler with a template that is used when declaring and defining a function. When a function is invoked...
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...Trigonometry Schaum’s Easy Outline: Business Statistics Schaum’s Easy Outline: Principles of Accounting Schaum’s Easy Outline: Applied Physics Schaum’s Easy Outline: Biology Schaum’s Easy Outline: Biochemistry Schaum’s Easy Outline: Molecular and Cell Biology Schaum’s Easy Outline: College Chemistry Schaum’s Easy Outline: Genetics Schaum’s Easy Outline: Human Anatomy and Physiology Schaum’s Easy Outline: Organic Chemistry Schaum’s Easy Outline: Physics Schaum’s Easy Outline: Programming with C++ Schaum’s Easy Outline: Programming with Java Schaum’s Easy Outline: Basic Electricity Schaum’s Easy Outline: Electromagnetics Schaum’s Easy Outline: Introduction to Psychology Schaum’s Easy Outline: French Schaum’s Easy Outline: German Schaum’s Easy Outline: Spanish Schaum’s Easy Outline: Writing and Grammar SCHAUM’S Easy OUTLINES PRINCIPLES OF ECONOMICS Based on Schaum’s O u t l i n e o f T h e o r y a n d P ro b l e m s o f Principles of Economics (Second Edition) b y D o m i n i c k S a l v a t o r e , Ph.D. and E...
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...1 The Science of Macroeconomics Questions for Review 1. Microeconomics is the study of how individual firms and households make decisions, and how they interact with one another. Microeconomic models of firms and households are based on principles of optimization—firms and households do the best they can given the constraints they face. For example, households choose which goods to purchase in order to maximize their utility, whereas firms decide how much to produce in order to maximize profits. In contrast, macroeconomics is the study of the economy as a whole; it focuses on issues such as how total output, total employment, and the overall price level are determined. These economy-wide variables are based on the interaction of many households and many firms; therefore, microeconomics forms the basis for macroeconomics. 2. Economists build models as a means of summarizing the relationships among economic variables. Models are useful because they abstract from the many details in the economy and allow one to focus on the most important economic connections. 3. A market-clearing model is one in which prices adjust to equilibrate supply and demand. Market-clearing models are useful in situations where prices are flexible. Yet in many situations, flexible prices may not be a realistic assumption. For example, labor contracts often set wages for up to three years. Or, firms such as magazine publishers change their prices only every three to four years. Most macroeconomists believe...
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...assume that there is no production and the economy is a pure exchange economy. There are 2 individuals and 2 goods, who will exhaust the goods together. Naturally they will consume until (MRS x,y )A = (MRS x,y )B. But we don't know beforehand what will be the exact equilibrium. But if we know the initial distribution, we can define the boundary within which the equilibrium solution will lie. 2. Thus the initial distribution of goods and their relative bargaining strengths will determine the equilibrium position. This general equilibrium determines not only the final distribution of goods but also the rates of exchange or relative prices. Note that however, we can't determine absolute prices from here, we can only determine relative prices. Show that in PC, General Equilibrium can exist 1. This ca be shown using the fact that under PC, relative prices which A is facing will be same as relative prices which B is facing and hence MRS x,y for both will be same. General Equilibrium of Production 1. We assume that all labor is homogenous, receives equal wages, total quantity of each factor (L and K) is fixed, the production function is continuous and twice differentiable and the technology is given which together with factor endowments limits the production possibilities. Naturally the equilibrium condition is (MRTS L,K)X = (MRTS L,K)Y. Show that in PC, General Equilibrium can exist file:///C:/Users/user/Documents/micro%20economy.html 1/134 7/7/2014 Evernote Export 1. This...
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...Op"erations Research This page intentionally left blank Copyright © 2007, 2005 New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved. No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher. All inquiries should be emailed to rights@newagepublishers.com ISBN (13) : 978-81-224-2944-2 PUBLISHING FOR ONE WORLD NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com PREFACE I started my teaching career in the year 1964. I was teaching Production Engineering subjects till 1972. In the year 1972 I have registered my name for the Industrial Engineering examination at National Institution of Industrial Engineering, Bombay. Since then, I have shifted my field for interest to Industrial Engineering subjects and started teaching related subjects. One such subject is OPERATIONS RESEARCH. After teaching these subjects till my retirement in the year 2002, it is my responsibility to help the students with a book on Operations research. The first volume of the book is LINEAR PORGRAMMING MODELS. This was published in the year 2003. Now I am giving this book OPERATIONS RESEARCH, with other chapters to students, with a hope that it will help them to understand...
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...User SONPR:Job EFF01417:6264_ch01:Pg 0:23907#/eps at 100% *23907* Fri, Nov 9, 2001 11:52 AM part I Introduction User SONPR:Job EFF01417:6264_ch01:Pg 1:21266#/eps at 100% *21266* Fri, Nov 9, 2001 11:52 AM C H A P T E R The Science of Macroeconomics The whole of science is nothing more than the refinement of everyday thinking. — Albert Einstein 1 O N E 1-1 What Macroeconomists Study Why have some countries experienced rapid growth in incomes over the past century while others stay mired in poverty? Why do some countries have high rates of inflation while others maintain stable prices? Why do all countries experience recessions and depressions—recurrent periods of falling incomes and rising unemployment—and how can government policy reduce the frequency and severity of these episodes? Macroeconomics, the study of the economy as a whole, attempts to answer these and many related questions. To appreciate the importance of macroeconomics, you need only read the newspaper or listen to the news. Every day you can see headlines such as INCOME GROWTH SLOWS, FED MOVES TO COMBAT INFLATION, or STOCKS FALL AMID RECESSION FEARS. Although these macroeconomic events may seem abstract, they touch all of our lives. Business executives forecasting the demand for their products must guess how fast consumers’ incomes will grow. Senior citizens living on fixed incomes wonder how fast prices will rise. Recent college graduates looking for jobs hope that the economy...
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...User SONPR:Job EFF01417:6264_ch01:Pg 0:23907#/eps at 100% *23907* Fri, Nov 9, 2001 11:52 AM part I Introduction User SONPR:Job EFF01417:6264_ch01:Pg 1:21266#/eps at 100% *21266* Fri, Nov 9, 2001 11:52 AM C H A P T E R The Science of Macroeconomics The whole of science is nothing more than the refinement of everyday thinking. — Albert Einstein 1 O N E 1-1 What Macroeconomists Study Why have some countries experienced rapid growth in incomes over the past century while others stay mired in poverty? Why do some countries have high rates of inflation while others maintain stable prices? Why do all countries experience recessions and depressions—recurrent periods of falling incomes and rising unemployment—and how can government policy reduce the frequency and severity of these episodes? Macroeconomics, the study of the economy as a whole, attempts to answer these and many related questions. To appreciate the importance of macroeconomics, you need only read the newspaper or listen to the news. Every day you can see headlines such as INCOME GROWTH SLOWS, FED MOVES TO COMBAT INFLATION, or STOCKS FALL AMID RECESSION FEARS. Although these macroeconomic events may seem abstract, they touch all of our lives. Business executives forecasting the demand for their products must guess how fast consumers’ incomes will grow. Senior citizens living on fixed incomes wonder how fast prices will rise. Recent college graduates looking for jobs hope that the economy...
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...Cornell University, Ithaca, NY, USA Alfred Kobsa University of California, Irvine, CA, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen TU Dortmund University, Germany Madhu Sudan Microsoft Research, Cambridge, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max Planck Institute for Informatics, Saarbruecken, Germany Richard Hull Jan Mendling Stefan Tai (Eds.) Business Process Management 8th International Conference, BPM 2010 Hoboken, NJ, USA, September 13-16, 2010 Proceedings 13 Volume Editors Richard Hull IBM Research, Thomas J. Watson Research Center 19 Skyline Drive, Hawthorne, NY 10532, USA E-mail: hull@us.ibm.com Jan Mendling Humboldt-Universität zu Berlin, Institut für Wirtschaftsinformatik Unter den Linden 6, 10099 Berlin, Germany E-mail: contact@mendling.com Stefan Tai Karlsruhe Institute of Technology (KIT) Englerstraße 11, Gebäude 11.40, 76131 Karlsruhe, Germany E-mail: stefan.tai@kit.edu Library of Congress Control Number: 2010933361 CR Subject Classification (1998): D.2, F.3, D.3, D.1, D.2.4, F.2 LNCS Sublibrary: SL 3 – Information Systems and Application, incl. Internet/Web and HCI ISSN ISBN-10 ISBN-13 0302-9743 3-642-15617-7 Springer...
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...intensive. We have adopted a strategy to minimize the notational burden within each individual chapter at the cost of being, at times, inconsistent in our use of symbols across chapters. We list here a set of symbols regularly used with their specific meaning. At times, however, we have found it more practical to use some of the listed symbols to represent a different concept. In other instances, clarity required making the symbolic representation more precise (e.g., by being more specific as to the time dimension of an interest rate). Roman Alphabet a Amount invested in the risky asset; in Chapter 14, fraction of wealth invested in the risky asset or portfolio AT Transpose of the matrix (or vector)A c Consumption; in Chapter 14 only, consumption is represented by C, while c represents ln C ck Consumption of agent k in state of nature θ θ CE Certainty equivalent CA Price of an American call option CE Price of a European call option d Dividend rate or amount ∆ Number of shares in the replicating portfolio (Chapter xx E The expectations operator ek Endowment of agent k in state of nature θ θ f Futures position (Chapter 16); pf Price of a futures contract (Chapter 16) F, G Cumulative distribution functions associated with densities: f, g Probability density functions K The strike or exercise price of an option K(˜) Kurtosis of the random variable x x ˜ L A lottery L Lagrangian m Pricing kernel M The market portfolio k M Uθ Marginal utility of agent k in state θ p Price of an arbitrary...
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...CONVERSION FACTORS FROM ENGLISH TO SI UNITS Length: 1 ft 1 ft 1 ft 1 in. 1 in. 1 in. 1 ft2 1 ft2 1 ft2 1 in.2 1 in.2 1 in.2 1 ft3 1 ft3 1 in.3 1 in.3 1 in. 1 in.3 1 ft/min 1 ft/min 1 ft/min 1 ft/sec 1 ft/sec 1 in./min 1 in./sec 1 in./sec 3 0.3048 m 30.48 cm 304.8 mm 0.0254 m 2.54 cm 25.4 mm 929.03 10 4 m2 929.03 cm2 929.03 102 mm2 6.452 10 4 m2 6.452 cm2 645.16 mm2 28.317 10 3 m3 28.317 103 cm3 16.387 10 6 m3 16.387 cm3 0.16387 0.16387 10 mm 10 4 m3 5 3 Coefficient of consolidation: Force: 1 in.2/sec 1 in.2/sec 1 ft2/sec 1 lb 1 lb 1 lb 1 kip 1 U.S. ton 1 lb 1 lb/ft 1 lb/ft2 1 lb/ft2 1 U.S. ton/ft2 1 kip/ft2 1 lb/in.2 1 lb/ft3 1 lb/in.3 1 lb-ft 1 lb-in. 1 ft-lb 1 in.4 1 in.4 6.452 cm2/sec 20.346 103 m2/yr 929.03 cm2/sec 4.448 N 4.448 10 3 kN 0.4536 kgf 4.448 kN 8.896 kN 0.4536 10 3 metric ton 14.593 N/m 47.88 N/m2 0.04788 kN/m2 95.76 kN/m2 47.88 kN/m2 6.895 kN/m2 0.1572 kN/m3 271.43 kN/m3 1.3558 N · m 0.11298 N · m 1.3558 J 0.4162 0.4162 106 mm4 10 6 m4 Area: Stress: Volume: Unit weight: Moment: Energy: Moment of inertia: Section modulus: Hydraulic conductivity: 0.3048 m/min 30.48 cm/min 304.8 mm/min 0.3048 m/sec 304.8 mm/sec 0.0254 m/min 2.54 cm/sec 25.4 mm/sec CONVERSION FACTORS FROM SI TO ENGLISH UNITS Length: 1m 1 cm 1 mm 1m 1 cm 1 mm 1m 1 cm2 1 mm2 1 m2 1 cm2 1 mm2 1m 1 cm3 1 m3 1 cm3 1N 1 kN 1 kgf 1 kN 1 kN 1 metric ton 1 N/m 3 2 3.281 ft 3.281 10 3.281 10 39.37 in. 0.3937 in. 0.03937 in. 2 Stress: 2 3 ft ft 1 N/m2 1 kN/m2 1 kN/m2...
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...TELECOMMUNICATION SWITCHING AND NETWORKS TElECOMMUNICATION SWITCHING NffiWRKS AND THIS PAGE IS BLANK Copyright © 2006, 2005 New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved. No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher. All inquiries should be emailed to rights@newagepublishers.com ISBN (10) : 81-224-2349-3 ISBN (13) : 978-81-224-2349-5 PUBLISHING FOR ONE WORLD NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com PREFACE This text, ‘Telecommunication Switching and Networks’ is intended to serve as a onesemester text for undergraduate course of Information Technology, Electronics and Communication Engineering, and Telecommunication Engineering. This book provides in depth knowledge on telecommunication switching and good background for advanced studies in communication networks. The entire subject is dealt with conceptual treatment and the analytical or mathematical approach is made only to some extent. For best understanding, more diagrams (202) and tables (35) are introduced wherever necessary in each chapter. The telecommunication switching is the fast growing field and enormous research and development are undertaken by...
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...Cataloging-in-Publication Data Library of Congress Control Number: 2004110194 ISBN 3-540-22065-8 Springer Berlin Heidelberg New York ISBN 3-540-43450-X 2nd edition Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com ° Springer Berlin ´ Heidelberg 2000, 2002, 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Hardcover-Design: Erich Kirchner, Heidelberg SPIN 11010463 42/3130-5 4 3 2 1 0 ± Printed on acid-free paper...
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...Dragomir Krgin Managing a Corporate Bond Portfolio by Leland E. Crabbe and Frank J. Fabozzi Real Options and Option-Embedded Securities by William T. Moore Capital Budgeting: Theory and Practice by Pamela P. Peterson and Frank J. Fabozzi The Exchange-Traded Funds Manual by Gary L. Gastineau Professional Perspectives on Fixed Income Portfolio Management, Volume 3 edited by Frank J. Fabozzi Investing in Emerging Fixed Income Markets edited by Frank J. Fabozzi and Efstathia Pilarinu Handbook of Alternative Assets by Mark J. P. Anson The Global Money Markets by Frank J. Fabozzi, Steven V. Mann, and Moorad Choudhry The Handbook of Financial Instruments edited by Frank J. Fabozzi Collateralized Debt Obligations: Structures and Analysis by Laurie S. Goodman and Frank J. Fabozzi Interest Rate, Term Structure, and Valuation Modeling edited by Frank J. Fabozzi Investment Performance Measurement by Bruce J. Feibel The Handbook of Equity Style Management edited by T. Daniel Coggin and Frank J. Fabozzi The Theory and Practice of Investment Management edited by Frank J. Fabozzi and Harry M. Markowitz Foundations of Economic Value Added, Second Edition by James L. Grant Financial Management and Analysis, Second Edition by Frank J. Fabozzi and Pamela P. Peterson Measuring and Controlling Interest Rate and Credit Risk, Second Edition by Frank J. Fabozzi, Steven V. Mann, and Moorad Choudhry Professional Perspectives on Fixed Income Portfolio Management, Volume 4 edited by Frank J. Fabozzi The Handbook...
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...SUBJECT: BUSINESS STATISTICS COURSE CODE: MC-106 LESSON: 01 AUTHOR: SURINDER KUNDU VETTER: DR. B. S. BODLA AN INTRODUCTION TO BUSINESS STATISTICS OBJECTIVE: The aim of the present lesson is to enable the students to understand the meaning, definition, nature, importance and limitations of statistics. “A knowledge of statistics is like a knowledge of foreign language of algebra; it may prove of use at any time under any circumstance”……………………………………...Bowley. STRUCTURE: 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 Introduction Meaning and Definitions of Statistics Types of Data and Data Sources Types of Statistics Scope of Statistics Importance of Statistics in Business Limitations of statistics Summary Self-Test Questions Suggested Readings 1.1 INTRODUCTION For a layman, ‘Statistics’ means numerical information expressed in quantitative terms. This information may relate to objects, subjects, activities, phenomena, or regions of space. As a matter of fact, data have no limits as to their reference, coverage, and scope. At the macro level, these are data on gross national product and shares of agriculture, manufacturing, and services in GDP (Gross Domestic Product). 1 At the micro level, individual firms, howsoever small or large, produce extensive statistics on their operations. The annual reports of companies contain variety of data on sales, production, expenditure, inventories, capital employed, and other activities. These data are often field data...
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