Advanced Microeconomics (ES30025)


 Monica Spencer
 1 years ago
 Views:
Transcription
1 Advanced Microeconoics (ES3005) Advanced Microeconoics (ES3005) Matheatics Review : The Lagrange Multiplier Outline: I. Introduction II. Duality Theory: Co Douglas Exaple III. Final Coents I. Introduction The siplest ethod of solving a constrained axiization or constrained iniization prole is y the Lagrange ultiplier ethod. In what follows we illustrate the ethod y considering, firstly, the consuer s proles of axiizing (CoDouglas) utility suject to a udget constraint, therey yielding the consuer s Marshallian deand function. We then, secondly, consider the consuer s prole of iniizing expenditure suject to a (Co Douglas) utility constraint, therey yielding the consuer s ( Hicks) Copensated deand function. We also allude to duality of the two proles and coent on the interpretation of the Lagrange Multiplier itself. II. Duality Theory: CoDouglas Exaple Marshallian Deand Functions The Marshallian deand function is otained y axiizing utility suject to a udget constraint. Thus: ax x, st Ax x + () Solution: ax { x,,λ} Lg Ax x + λ( x ) () Ax x x λ 0 (3) ( ) Ax x λ 0 (4) λ x 0 (5) Dividing (3) y (4):
2 x Advanced Microeconoics (ES3005) Ax ( ) Ax x λ λ ( ) x x ( ) x (6) Rearrange (5): x (7) Sustitute (7) in (6): x x (8) Thus: x p p p (9) ( ) The consuer s Marshallian deand functions are thus: x x ( ) (0) Recall that the Marshalian deand function easures the overall change in deand when the price of a good changes and the price of other goods and consuer incoe is held constant. Optiized utility is:
3 Advanced Microeconoics (ES3005) u u x (, ) A( x ) ( ) u A p ( ) u A ( ) p () Note that the udget constraint is satisfied: x + x p + p ( ) () Copensated Deand Function The consuer s Copensated deand function is otained y iniizing expenditure suject to a utility constraint. Thus: in x, x + st Ax u (3) Solution: in { x,,λ} Lg x + + θ u Ax ( ) (4) p x θax x 0 (5) θ ( ) Ax x 0 (6) θ u Ax x 0 (7) Dividing (5) y (6) yields: 3
4 Advanced Microeconoics (ES3005) θax θ x ( ) Ax ( ) x (8) Rearrange (7): u Ax (9) Sustitute in (9) in (8): x x + x x u Ax ( ) u ( ) ( ) x u ( ) u ( ) (0) Raising every ter y the power () yields: x ( ) u () Sustitute equation () into (9): 4
5 Advanced Microeconoics (ES3005) u Ax ( ) u ( ) ( ) x u ( ) ( ) ( ) u A ( ) ( ) u () u u The consuer s ( Hicks) Copensated deand functions are thus: x h x h ( ) u u (3) Recall that the ( Hicks) Copensated deand functions easure the change in deand following a change in price holding the price of the other good and the consuer s real incoe (vis. His aility to enjoy a particular level of utility) constant. Thus, the (Hicks) Copensated deand function easures the ownprice sustitution effect. Note that the utility constraint is satisfied: h A( x ) h ( ) A Ax u ( ) u u (4) Note that iniized expenditure is given y: h x h + h h Thus: ( ) u + p u (5) 5
6 Advanced Microeconoics (ES3005) h p u ( ) + h p u h p u h p u + (6) III. Final Coents Interpretation of the Lagrange Multiplier The Lagrange ultiplier easures the arginal effect of a relaxation in the constraint on the consuer s ojective function. Thus, the Lagrange ultiplier in the first prole, λ in the first prole easures the arginal effect on utility of a relaxation in the udget constraint and ay therefore e interpreted as the consuer s arginal utility of incoe. The Lagrange ultiplier in the second prole, θ, easures the arginal effect on expenditure on a relaxation in the utility constraint. SecondOrder Conditions Note that we have not explored the secondorder conditions to confir that we have indeed found the utility axiizing and cost iniizing choices for the consuer. We will generally assue that secondorder conditions are satisfied in Lagrange ultiplier constrained optiization proles. Duality Note the duality of the prole. Set the constraint level of utility u in the consuer s (Hicks) Copensated deand function (3) equal to the Marshallian axiized utility u in equation (): 6
7 x Advanced Microeconoics (ES3005) ( ) p x u p A ( ) p x A ( ) p x + ( ) ( )+ ( ) ( ) ( ) ( p ) p (7) This is the level of deand deterined y the Marshallian deand function (0). A siilar result occurs if we set the udget constraint in the consuer s Marshallian deand function (0) equal to the (Hicks) Copensated iniized expenditure, h in Equation (6): x h p x x x u u u u (8) This is the level of deand deterined y the (Hicks) Copensated deand function (3). 7
Factor Model. Arbitrage Pricing Theory. Systematic Versus NonSystematic Risk. Intuitive Argument
Ross [1],[]) presents the aritrage pricing theory. The idea is that the structure of asset returns leads naturally to a odel of risk preia, for otherwise there would exist an opportunity for aritrage profit.
More informationEcon 100A: Intermediate Microeconomics Notes on Consumer Theory
Econ 100A: Interediate Microeconoics Notes on Consuer Theory Linh Bun Winter 2012 (UCSC 1. Consuer Theory Utility Functions 1.1. Types of Utility Functions The following are soe of the type of the utility
More informationConstruction Economics & Finance. Module 3 Lecture1
Depreciation: Construction Econoics & Finance Module 3 Lecture It represents the reduction in arket value of an asset due to age, wear and tear and obsolescence. The physical deterioration of the asset
More informationProblem Set 2: Solutions ECON 301: Intermediate Microeconomics Prof. Marek Weretka. Problem 1 (Marginal Rate of Substitution)
Proble Set 2: Solutions ECON 30: Interediate Microeconoics Prof. Marek Weretka Proble (Marginal Rate of Substitution) (a) For the third colun, recall that by definition MRS(x, x 2 ) = ( ) U x ( U ). x
More informationDemand  Basic Review and Examples 1
Deand  Basic Review and Exaples The Basic Deand For What exactly is a deand function? In Varian s words, a consuer s deand functions give the optial aounts of each of the goods as a function of the prices
More information1 Deriving demand function
Econoics II: Micro Fall 2009 Eercise session 2 VŠE Deriving deand function Assue that consuer s utility function is of CobbDouglass for: U (; y) = y () To solve the consuer s otiisation roble it is necessary
More informationIs PayasYouDrive Insurance a Better Way to Reduce Gasoline than Gasoline Taxes?
Is PayasYouDrive Insurance a Better Way to Reduce Gasoline than Gasoline Taxes? By Ian W.H. Parry Despite concerns about US dependence on a volatile world oil arket, greenhouse gases fro fuel cobustion,
More informationProject Evaluation Roadmap. Capital Budgeting Process. Capital Expenditure. Major Cash Flow Components. Cash Flows... COMM2501 Financial Management
COMM501 Financial Manageent Project Evaluation 1 (Capital Budgeting) Project Evaluation Roadap COMM501 Financial Manageent Week 7 Week 7 Project dependencies Net present value ethod Relevant cash flows
More informationIV Approximation of Rational Functions 1. IV.C Bounding (Rational) Functions on Intervals... 4
Contents IV Approxiation of Rational Functions 1 IV.A Constant Approxiation..................................... 1 IV.B Linear Approxiation....................................... 3 IV.C Bounding (Rational)
More informationUse of extrapolation to forecast the working capital in the mechanical engineering companies
ECONTECHMOD. AN INTERNATIONAL QUARTERLY JOURNAL 2014. Vol. 1. No. 1. 23 28 Use of extrapolation to forecast the working capital in the echanical engineering copanies A. Cherep, Y. Shvets Departent of finance
More informationMATHEMATICAL MODELS Vol. III  Mathematical Modeling in Social and Behavioral Sciences  WeiBin Zhang
MATHEMATICAL MODELS Vol. III  Matheatical Modeling in Social and Behavioral Sciences  WeiBin Zhang MATHEMATICAL MODELING IN SOCIAL AND BEHAVIORAL SCIENCES WeiBin Zhang Ritsueikan Asia Pacific University,
More informationLecture L263D Rigid Body Dynamics: The Inertia Tensor
J. Peraire, S. Widnall 16.07 Dynaics Fall 008 Lecture L63D Rigid Body Dynaics: The Inertia Tensor Version.1 In this lecture, we will derive an expression for the angular oentu of a 3D rigid body. We shall
More informationCalculating the Return on Investment (ROI) for DMSMS Management. The Problem with Cost Avoidance
Calculating the Return on nvestent () for DMSMS Manageent Peter Sandborn CALCE, Departent of Mechanical Engineering (31) 453167 sandborn@calce.ud.edu www.ene.ud.edu/escml/obsolescence.ht October 28, 21
More informationImage restoration for a rectangular poorpixels detector
Iage restoration for a rectangular poorpixels detector Pengcheng Wen 1, Xiangjun Wang 1, Hong Wei 2 1 State Key Laboratory of Precision Measuring Technology and Instruents, Tianjin University, China 2
More informationMethod of supply chain optimization in Ecommerce
MPRA Munich Personal RePEc Archive Method of supply chain optiization in Ecoerce Petr Suchánek and Robert Bucki Silesian University  School of Business Adinistration, The College of Inforatics and Manageent
More informationReliability Constrained Packetsizing for Linear Multihop Wireless Networks
Reliability Constrained acketsizing for inear Multihop Wireless Networks Ning Wen, and Randall A. Berry Departent of Electrical Engineering and Coputer Science Northwestern University, Evanston, Illinois
More informationThis paper studies a rental firm that offers reusable products to price and qualityofservice sensitive
MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol., No. 3, Suer 28, pp. 429 447 issn 523464 eissn 5265498 8 3 429 infors doi.287/so.7.8 28 INFORMS INFORMS holds copyright to this article and distributed
More informationLecture 4: Equality Constrained Optimization. Tianxi Wang
Lecture 4: Equality Constrained Optimization Tianxi Wang wangt@essex.ac.uk 2.1 Lagrange Multiplier Technique (a) Classical Programming max f(x 1, x 2,..., x n ) objective function where x 1, x 2,..., x
More informationExample: Suppose that we deposit $1000 in a bank account offering 3% interest, compounded monthly. How will our money grow?
Finance 111 Finance We have to work with oney every day. While balancing your checkbook or calculating your onthly expenditures on espresso requires only arithetic, when we start saving, planning for retireent,
More informationTrading Regret for Efficiency: Online Convex Optimization with Long Term Constraints
Journal of Machine Learning Research 13 2012) 25032528 Subitted 8/11; Revised 3/12; Published 9/12 rading Regret for Efficiency: Online Convex Optiization with Long er Constraints Mehrdad Mahdavi Rong
More informationHW 2. Q v. kt Step 1: Calculate N using one of two equivalent methods. Problem 4.2. a. To Find:
HW 2 Proble 4.2 a. To Find: Nuber of vacancies per cubic eter at a given teperature. b. Given: T 850 degrees C 1123 K Q v 1.08 ev/ato Density of Fe ( ρ ) 7.65 g/cc Fe toic weight of iron ( c. ssuptions:
More information5.7 Chebyshev Multisection Matching Transformer
/9/ 5_7 Chebyshev Multisection Matching Transforers / 5.7 Chebyshev Multisection Matching Transforer Reading Assignent: pp. 555 We can also build a ultisection atching network such that Γ f is a Chebyshev
More informationPreferencebased Search and Multicriteria Optimization
Fro: AAAI02 Proceedings. Copyright 2002, AAAI (www.aaai.org). All rights reserved. Preferencebased Search and Multicriteria Optiization Ulrich Junker ILOG 1681, route des Dolines F06560 Valbonne ujunker@ilog.fr
More informationEnvelope Theorem. Kevin Wainwright. Mar 22, 2004
Envelope Theorem Kevin Wainwright Mar 22, 2004 1 Maximum Value Functions A maximum (or minimum) value function is an objective function where the choice variables have been assigned their optimal values.
More informationA Gas Law And Absolute Zero Lab 11
HB 040605 A Gas Law And Absolute Zero Lab 11 1 A Gas Law And Absolute Zero Lab 11 Equipent safety goggles, SWS, gas bulb with pressure gauge, 10 C to +110 C theroeter, 100 C to +50 C theroeter. Caution
More informationADJUSTING FOR QUALITY CHANGE
ADJUSTING FOR QUALITY CHANGE 7 Introduction 7.1 The easureent of changes in the level of consuer prices is coplicated by the appearance and disappearance of new and old goods and services, as well as changes
More informationEarnings and Community College Field of Study Choice in Canada
DISCUSSION PAPER SERIES IZA DP No. 1156 Earnings and Counity College Field of Study Choice in Canada Brahi Boudarbat May 2004 Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor
More informationDISCUSSION PAPER. Is PayAsYouDrive Insurance a Better Way to Reduce Gasoline than Gasoline Taxes? Ian W.H. Parry. April 2005 RFF DP 0515
DISCUSSION PAPER April 25 R DP 515 Is PayAsYouDrive Insurance a Better Way to Reduce Gasoline than Gasoline Taxes? Ian W.H. 1616 P St. NW Washington, DC 236 223285 www.rff.org Is PayAsYouDrive
More informationEvaluating Inventory Management Performance: a Preliminary DeskSimulation Study Based on IOC Model
Evaluating Inventory Manageent Perforance: a Preliinary DeskSiulation Study Based on IOC Model Flora Bernardel, Roberto Panizzolo, and Davide Martinazzo Abstract The focus of this study is on preliinary
More informationANSWER KEY 1 BUDGETS
ANSWER KEY 1 BUDGETS W & L INTERMEDIATE MICROECONOMICS PROFESSOR A. JOSEPH GUSE (1) Draw the budget set for the following paraeters. =, p beer = 1, p pizza =. The units for the two goods are pints and
More informationLecture L9  Linear Impulse and Momentum. Collisions
J. Peraire, S. Widnall 16.07 Dynaics Fall 009 Version.0 Lecture L9  Linear Ipulse and Moentu. Collisions In this lecture, we will consider the equations that result fro integrating Newton s second law,
More informationTopic 2 Solving Equations
Topic 2 Solving Equations Introduction: When you are given the value of a variable and an algebraic expression then you can evaluate the expression. For example, If you are told that x = 6 then the value
More information9 Multiplication of Vectors: The Scalar or Dot Product
Arkansas Tech University MATH 934: Calculus III Dr. Marcel B Finan 9 Multiplication of Vectors: The Scalar or Dot Product Up to this point we have defined what vectors are and discussed basic notation
More informationNote on a generalized wage rigidity result. Abstract
Note on a generalized age rigidity result Ariit Mukheree University of Nottingha Abstract Considering Cournot copetition, this note shos that, if the firs differ in labor productivities, the equilibriu
More informationOnline Appendix I: A Model of Household Bargaining with Violence. In this appendix I develop a simple model of household bargaining that
Online Appendix I: A Model of Household Bargaining ith Violence In this appendix I develop a siple odel of household bargaining that incorporates violence and shos under hat assuptions an increase in oen
More informationA Gas Law And Absolute Zero
A Gas Law And Absolute Zero Equipent safety goggles, DataStudio, gas bulb with pressure gauge, 10 C to +110 C theroeter, 100 C to +50 C theroeter. Caution This experient deals with aterials that are very
More informationEconomics 326: Marshallian Demand and Comparative Statics. Ethan Kaplan
Economics 326: Marshallian Demand and Comparative Statics Ethan Kaplan September 17, 2012 Outline 1. Utility Maximization: General Formulation 2. Marshallian Demand 3. Homogeneity of Degree Zero of Marshallian
More informationImperfect Competition: Monopoly
Ierfect Coetition: Monooly New Toic: Monooly Q: What is a onooly? A onooly is a fir that faces a downward sloing deand, and has a choice about what rice to charge an increase in rice doesn t send ost or
More informationSOME APPLICATIONS OF FORECASTING Prof. Thomas B. Fomby Department of Economics Southern Methodist University May 2008
SOME APPLCATONS OF FORECASTNG Prof. Thoas B. Foby Departent of Econoics Southern Methodist University May 8 To deonstrate the usefulness of forecasting ethods this note discusses four applications of forecasting
More informationPhysics 211: Lab Oscillations. Simple Harmonic Motion.
Physics 11: Lab Oscillations. Siple Haronic Motion. Reading Assignent: Chapter 15 Introduction: As we learned in class, physical systes will undergo an oscillatory otion, when displaced fro a stable equilibriu.
More informationLEASING, LEMONS, AND MORAL HAZARD
LEASING, LEMONS, AND MORAL HAZARD by Justin P. Johnson Johnson Graduate School of Manageent Cornell University Sage Hall Ithaca, NY 14853 jpj25@cornell.edu and Michael Waldan Johnson Graduate School of
More informationAnalysis of the purchase option of computers
Analysis of the of coputers N. Ahituv and I. Borovits Faculty of Manageent, The Leon Recanati Graduate School of Business Adinistration, TelAviv University, University Capus, RaatAviv, TelAviv, Israel
More informationPayAsYouDrive (PAYD): A case study into the safety and accessibility effects of PAYD strategies
J. Zantea, D.H. van Aelsfort, M.C.J. Blieer, P.H.L. Bovy 1 PayAsYouDrive (PAYD): A case study into the safety and accessibility effects of PAYD strategies J. Zantea MSc Goudappel Coffeng BV P.O. Box
More informationPrivacy, Exposure and Price Discrimination
Privacy, Exposure and Price Discriination Luc Wathieu 1 Harvard usiness School, Soldiers Field, oston, M 02163 (eail) lwathieu@hbs.edu (Tel) 6174951016 Subitted for presentation at the first QME conference
More information2141375 Measurement and Instrumentation. Analog Electrical Devices and Measurements
2141375 Measureent and Instruentation nalog Electrical Devices and Measureents nalog Devices: Current Measureents Force on a conductor I conductor is placed in a unifor agnetic field B T, at an angle
More informationLinear Programming Notes V Problem Transformations
Linear Programming Notes V Problem Transformations 1 Introduction Any linear programming problem can be rewritten in either of two standard forms. In the first form, the objective is to maximize, the material
More informationEnergy performance of windows based on net energy gain
Energy perforance of windows based on net energy gain Svend Svendsen, Professor, Technical University of Denark; ss@byg.dtu.dk, www.byg.dtu.dk Jesper Kragh, ssistant Professor, Technical University of
More informationMultiClass Deep Boosting
MultiClass Deep Boosting Vitaly Kuznetsov Courant Institute 25 Mercer Street New York, NY 002 vitaly@cis.nyu.edu Mehryar Mohri Courant Institute & Google Research 25 Mercer Street New York, NY 002 ohri@cis.nyu.edu
More informationThe individual neurons are complicated. They have a myriad of parts, subsystems and control mechanisms. They convey information via a host of
CHAPTER 4 ARTIFICIAL NEURAL NETWORKS 4. INTRODUCTION Artificial Neural Networks (ANNs) are relatively crude electronic odels based on the neural structure of the brain. The brain learns fro experience.
More informationCooperative Caching for Adaptive Bit Rate Streaming in Content Delivery Networks
Cooperative Caching for Adaptive Bit Rate Streaing in Content Delivery Networs Phuong Luu Vo Departent of Coputer Science and Engineering, International University  VNUHCM, Vietna vtlphuong@hciu.edu.vn
More informationJournal of International Economics
Journal of International Econoics 84 (2011) 26 36 Contents lists available at ScienceDirect Journal of International Econoics journal hoepage: www.elsevier.co/locate/jie Good jobs, bad jobs, and trade
More informationENZYME KINETICS: THEORY. A. Introduction
ENZYME INETICS: THEORY A. Introduction Enzyes are protein olecules coposed of aino acids and are anufactured by the living cell. These olecules provide energy for the organis by catalyzing various biocheical
More informationPage 1. Algebra 1 Unit 5 Working with Exponents Per
Algera 1 Unit 5 Working with Exponents Nae Per Ojective 1: Siplifying Expressions with Exponents (Powers INSIDE parentheses) Exponents are a shortcut. They are a quicker way of writing repeated ultiplication.
More informationVectors & Newton's Laws I
Physics 6 Vectors & Newton's Laws I Introduction In this laboratory you will eplore a few aspects of Newton s Laws ug a force table in Part I and in Part II, force sensors and DataStudio. By establishing
More informationReconnect 04 Solving Integer Programs with Branch and Bound (and Branch and Cut)
Sandia is a ultiprogra laboratory operated by Sandia Corporation, a Lockheed Martin Copany, Reconnect 04 Solving Integer Progras with Branch and Bound (and Branch and Cut) Cynthia Phillips (Sandia National
More informationPlane Trusses. Section 7: Flexibility Method  Trusses. A plane truss is defined as a twodimensional
lane Trusses A plane truss is defined as a twodiensional fraework of straight prisatic ebers connected at their ends by frictionless hinged joints, and subjected to loads and reactions that act only at
More information1 Interest rates and bonds
1 Interest rates and bonds 1.1 Copounding There are different ways of easuring interest rates Exaple 1 The interest rate on a oneyear deposit is 10% per annu. This stateent eans different things depending
More information4.4 The Simplex Method: NonStandard Form
4.4 The Simplex Method: NonStandard Form Standard form and what can be relaxed What were the conditions for standard form we have been adhering to? Standard form and what can be relaxed What were the
More informationDynamic Placement for Clustered Web Applications
Dynaic laceent for Clustered Web Applications A. Karve, T. Kibrel, G. acifici, M. Spreitzer, M. Steinder, M. Sviridenko, and A. Tantawi IBM T.J. Watson Research Center {karve,kibrel,giovanni,spreitz,steinder,sviri,tantawi}@us.ib.co
More information10.1 Systems of Linear Equations: Substitution and Elimination
726 CHAPTER 10 Systems of Equations and Inequalities 10.1 Systems of Linear Equations: Sustitution and Elimination PREPARING FOR THIS SECTION Before getting started, review the following: Linear Equations
More informationInsurance Spirals and the Lloyd s Market
Insurance Spirals and the Lloyd s Market Andrew Bain University of Glasgow Abstract This paper presents a odel of reinsurance arket spirals, and applies it to the situation that existed in the Lloyd s
More informationFinancial Risk: Credit Risk, Lecture 1
Financial Risk: Credit Risk, Lecture 1 Alexander Herbertsson Centre For Finance/Departent of Econoics School of Econoics, Business and Law, University of Gothenburg Eail: Alexander.Herbertsson@econoics.gu.se
More informationA Continuum Modeling Approach to Congestion Management of Transportation System in an Urban City
The University of Hong Kong A Continuu Modeling Approach to Congestion Manageent of Transportation Syste in an Urban City S.C. Wong Departent of Civil Engineering The University of Hong Kong Eail: hhecwsc@hkucc.hku.hk
More informationThe Research of Measuring Approach and Energy Efficiency for Hadoop Periodic Jobs
Send Orders for Reprints to reprints@benthascience.ae 206 The Open Fuels & Energy Science Journal, 2015, 8, 206210 Open Access The Research of Measuring Approach and Energy Efficiency for Hadoop Periodic
More informationWe are going to delve into some economics today. Specifically we are going to talk about production and returns to scale.
Firms and Production We are going to delve into some economics today. Secifically we are going to talk aout roduction and returns to scale. firm  an organization that converts inuts such as laor, materials,
More informationPREDICTION OF MILKLINE FILL AND TRANSITION FROM STRATIFIED TO SLUG FLOW
PREDICTION OF MILKLINE FILL AND TRANSITION FROM STRATIFIED TO SLUG FLOW ABSTRACT: by Douglas J. Reineann, Ph.D. Assistant Professor of Agricultural Engineering and Graee A. Mein, Ph.D. Visiting Professor
More informationExtendedHorizon Analysis of Pressure Sensitivities for Leak Detection in Water Distribution Networks: Application to the Barcelona Network
2013 European Control Conference (ECC) July 1719, 2013, Zürich, Switzerland. ExtendedHorizon Analysis of Pressure Sensitivities for Leak Detection in Water Distribution Networks: Application to the Barcelona
More informationAlgebra (Expansion and Factorisation)
Chapter10 Algebra (Expansion and Factorisation) Contents: A B C D E F The distributive law Siplifying algebraic expressions Brackets with negative coefficients The product (a + b)(c + d) Geoetric applications
More informationCalculation Method for evaluating Solar Assisted Heat Pump Systems in SAP 2009. 15 July 2013
Calculation Method for evaluating Solar Assisted Heat Pup Systes in SAP 2009 15 July 2013 Page 1 of 17 1 Introduction This docuent describes how Solar Assisted Heat Pup Systes are recognised in the National
More informationα α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =
More informationA New HighFrequency Fluorescent Lamp Model
A New HighFrequency Fluorescent ap Model Thoas J. Ribarich and John J. Ribarich International Rectifier Power IC Group 33 Kansas St., El Segundo, CA, 945438 Tel.: (31)76887 Fax: (31)768846 as presented
More informationSINGLE PHASE FULL WAVE AC VOLTAGE CONTROLLER (AC REGULATOR)
Deceber 9, INGE PHAE FU WAE AC OTAGE CONTROER (AC REGUATOR ingle phase full wave ac voltage controller circuit using two CRs or a single triac is generally used in ost of the ac control applications. The
More informationInternational Journal of Management & Information Systems First Quarter 2012 Volume 16, Number 1
International Journal of Manageent & Inforation Systes First Quarter 2012 Volue 16, Nuber 1 Proposal And Effectiveness Of A Highly Copelling Direct Mail Method  Establishent And Deployent Of PMOSDM Hisatoshi
More informationMetric of Carbon Equity: Carbon Gini Index Based on Historical Cumulative Emission per Capita
ADVANCES IN CLIMATE CHANGE RESEARCH 2(3): 134 140, 2011 www.cliatechange.cn DOI: 10.3724/SP.J.1248.2011.00134 POLICY FORUM Metric of Carbon Equity: Carbon Gini Index Based on Historical Cuulative Eission
More informationImagine that a wall of your house is hit on one occasion by a boy on a skateboard and on another by a large juggernaut.
A Resource for Freestanding Matheatics Qualifications Iagine that a wall of your house is hit on one occasion by a boy on a skateboard and on another by a large juggernaut. Suppose both had a speed of
More informationExperiment 2 Index of refraction of an unknown liquid  Abbe Refractometer
Experient Index of refraction of an unknown liquid  Abbe Refractoeter Principle: The value n ay be written in the for sin ( δ +θ ) n =. θ sin This relation provides us with one or the standard ethods
More informationSAMPLING METHODS LEARNING OBJECTIVES
6 SAMPLING METHODS 6 Using Statistics 66 2 Nonprobability Sapling and Bias 66 Stratified Rando Sapling 62 6 4 Cluster Sapling 64 6 5 Systeatic Sapling 69 6 6 Nonresponse 62 6 7 Suary and Review of
More informationMathematics. (www.tiwariacademy.com : Focus on free Education) (Chapter 5) (Complex Numbers and Quadratic Equations) (Class XI)
( : Focus on free Education) Miscellaneous Exercise on chapter 5 Question 1: Evaluate: Answer 1: 1 ( : Focus on free Education) Question 2: For any two complex numbers z1 and z2, prove that Re (z1z2) =
More informationMachine Learning Applications in Grid Computing
Machine Learning Applications in Grid Coputing George Cybenko, Guofei Jiang and Daniel Bilar Thayer School of Engineering Dartouth College Hanover, NH 03755, USA gvc@dartouth.edu, guofei.jiang@dartouth.edu
More informationGovernment Control of the Media
Governent Control of the Media Scott Gehlbach and Konstantin Sonin Septeber 2008 Abstract We present a foral odel of governent control of the edia to illuinate variation in edia freedo across countries
More informationNumber Who Chose This Maximum Amount
1 TASK 3.3.1: MAXIMIZING REVENUE AND PROFIT Solutions Your school is trying to oost interest in its athletic program. It has decided to sell a pass that will allow the holder to attend all athletic events
More informationChapter 5. Principles of Unsteady  State Heat Transfer
Suppleental Material for ransport Process and Separation Process Principles hapter 5 Principles of Unsteady  State Heat ransfer In this chapter, we will study cheical processes where heat transfer is
More informationAn Indian Journal FULL PAPER. Trade Science Inc. The research on green logistic network planning in manufacturing workshops ABSTRACT KEYWORDS
[Type text] [Type text] [Type text] ISSN : 09747435 Volue 10 Issue 17 BioTechnology 2014 An Indian Journal FULL PAPER BTAIJ, 10(17), 2014 [96249631] The research on green logistic network planning in
More informationModeling operational risk data reported above a timevarying threshold
Modeling operational risk data reported above a tievarying threshold Pavel V. Shevchenko CSIRO Matheatical and Inforation Sciences, Sydney, Locked bag 7, North Ryde, NSW, 670, Australia. eail: Pavel.Shevchenko@csiro.au
More informationA Strategic Approach to Software Protection U
Â Â Strategic pproach to Software Protection U OZ SHY University of Haifa, Israel and Stockhol School of Econoics, Sweden ozshy@econ.haifa.ac.il JCQUESFRNCË OIS THISSE CORE, Universite Catholique de Louvain,
More informationELECTRIC ENERGY ECONOMICS
ELECTRIC ENERGY ECONOMICS The cost to the consuer for electric energy can be roughly apportioned according to Generation 60% Transission 0% Distribution 20% Adinistrative/Profit 0% Econoics drives the
More informationSemiinvariants IMOTC 2013 Simple semiinvariants
Seiinvariants IMOTC 2013 Siple seiinvariants These are soe notes (written by Tejaswi Navilarekallu) used at the International Matheatical Olypiad Training Cap (IMOTC) 2013 held in Mubai during AprilMay,
More informationExercise 4 INVESTIGATION OF THE ONEDEGREEOFFREEDOM SYSTEM
Eercise 4 IVESTIGATIO OF THE OEDEGREEOFFREEDOM SYSTEM 1. Ai of the eercise Identification of paraeters of the euation describing a onedegreeof freedo (1 DOF) atheatical odel of the real vibrating
More informationGlobal Production Sharing and Rising Inequality: A Survey of Trade and Wages
Global Production Sharing and Rising Inequality: A Survey of Trade and Wages Robert C. Feenstra Departent of Econoics University of California, Davis and National Bureau of Econoic Research Gordon H. Hanson
More informationConstrained Least Squares
Constrained Least Squares Authors: G.H. Golub and C.F. Van Loan Chapter 12 in Matrix Computations, 3rd Edition, 1996, pp.580587 CICN may05/1 Background The least squares problem: min Ax b 2 x Sometimes,
More informationOptimal ResourceConstraint Project Scheduling with Overlapping Modes
Optial ResourceConstraint Proect Scheduling with Overlapping Modes François Berthaut Lucas Grèze Robert Pellerin Nathalie Perrier Adnène Hai February 20 CIRRELT2009 Bureaux de Montréal : Bureaux de
More information[1] Diagonal factorization
8.03 LA.6: Diagonalization and Orthogonal Matrices [ Diagonal factorization [2 Solving systems of first order differential equations [3 Symmetric and Orthonormal Matrices [ Diagonal factorization Recall:
More informationModeling Nurse Scheduling Problem Using 01 Goal Programming: A Case Study Of Tafo Government Hospital, KumasiGhana
Modeling Nurse Scheduling Proble Using 01 Goal Prograing: A Case Study Of Tafo Governent Hospital, KuasiGhana Wallace Agyei, Willia ObengDenteh, Eanuel A. Andaa Abstract: The proble of scheduling nurses
More informationEndogenous Market Structure and the Cooperative Firm
Endogenous Market Structure and the Cooperative Fir Brent Hueth and GianCarlo Moschini Working Paper 14WP 547 May 2014 Center for Agricultural and Rural Developent Iowa State University Aes, Iowa 500111070
More informationJournal of Economics and International Finance
Journal of Econoics and International Finance Volue 8 Nuber January, 014 Volue ISSN 1993833 7 Nuber 8 August 015 ISSN 006981 ABOUT JEIF The Journal of Econoics and International Finance (JEIF) is published
More informationThe Mathematics of Pumping Water
The Matheatics of Puping Water AECOM Design Build Civil, Mechanical Engineering INTRODUCTION Please observe the conversion of units in calculations throughout this exeplar. In any puping syste, the role
More informationResearch Article MultiItem Multiperiodic Inventory Control Problem with Variable Demand and Discounts: A Particle Swarm Optimization Algorithm
e Scientific World Journal, Article ID 16047, 16 pages http://dx.doi.org/10.1155/014/16047 Research Article MultiIte Multiperiodic Inventory Control Proble with Variable Deand and Discounts: A Particle
More informationHOMEWORK 4 SOLUTIONS. All questions are from Vector Calculus, by Marsden and Tromba
HOMEWORK SOLUTIONS All questions are from Vector Calculus, by Marsden and Tromba Question :..6 Let w = f(x, y) be a function of two variables, and let x = u + v, y = u v. Show that Solution. By the chain
More informationThe Economics of Payment Card Fee Structures: What Drives Payment Card Rewards? Fumiko Hayashi November 2008; Revised March 2009 RWP 0807
The Econoics o Payent Card Fee tructures: What Drives Payent Card Rewards? Fuiko ayashi Noveer 008; Revised March 009 RWP 0807 TE ECONOMIC OF PYMENT CRD FEE TRUCTURE: WT DRIVE PYMENT CRD REWRD? Fuiko
More information