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34 Pages

### Chiang_Ch1-3

Course: ECON 101, Spring 2011
School: Cambrian College
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Word Count: 1302

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1-4 Part Chapters 1 Introduction (set theory, algebra) Part 2 Static Analysis (matrix algebra) Part 3 Comparative Static Analysis (derivatives w/ matrix algebra) Part 4 Optimization Problems (derivatives w/ constraints w/ matrix algebra, 2nd order conditions) Objectivesformathematical economics Tounderstandmathematicaleconomicsproblemsby statingtheunknown,thedataandtheconditions...

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Cambrian College - ECON - 101
Chiang &amp; WainwrightChiangMathematical EconomicsChapter 4Linear Models and Matrix AlgebraChiang_Ch4.ppt Stephen Cooke U. Idaho1Ch. 4 Linear Models &amp; Matrix AlgebraCh.Matrixalgebra can beused:a. to express the systemof equations in acompact no
Cambrian College - ECON - 101
Ch. 5 Linear Models &amp; Matrix Algebra5.15.25.35.45.55.65.75.8ConditionsforNonsingularityofaMatrixTestofNonsingularitybyUseofDeterminantBasicPropertiesofDeterminantsFindingtheInverseMatrixCramer'sRuleApplicationtoMarketandNationalIncomeModels
Cambrian College - ECON - 101
Ch.6ComparativeStaticsandtheConceptofDerivative6.1 TheNatureofComparativeStatics6.2 RateofChangeandtheDerivative6.3 TheDerivativeandtheSlopeofaCurve6.4 TheConceptofLimit6.5 DigressiononInequalitiesandAbsoluteValues6.6 LimitTheorems6.7Continuityan
Cambrian College - ECON - 101
Chiang,Ch.7RulesofDifferentiationandTheirUseinComparativeStatics 7.1 RulesofDifferentiationforaFunctionofOneVariable 7.2 RulesofDifferentiationInvolvingTwoorMoreFunctionsoftheSameVariable 7.3 RulesofDifferentiationInvolvingFunctionsofDifferentVaria
Cambrian College - ECON - 101
Ch.8ComparativeStaticAnalysisofGeneralFunctionModels8.1 Differentials8.2 TotalDifferentials8.3 RulesofDifferentials(IVII)8.4 TotalDerivatives8.5 DerivativesofImplicitFunctions8.6 ComparativeStaticsofGeneralFunctionModels8.7 LimitationsofComparat
Cambrian College - ECON - 101
Ch.9 Optimization:ASpecialVarietyofEquilibriumAnalysis 9.1 OptimumValuesandExtremeValues 9.2 RelativeMaximumandMinimum:FirstDerivativeTest 9.3 SecondandHigherDerivatives 9.4 SecondDerivativeTest 9.5 DigressiononMaclaurinandTaylorSeries 9.6NthDer
Cambrian College - ECON - 101
ChiangCh.10ExponentialandLogarithmicFunctions10.1 The Nature of Exponential Functions10.2 Natural Exponential Functions andthe Problem of Growth10.3 Logarithms10.4 Logarithmic Functions10.5 Derivatives of Exponential andLogarithmic Functions10.6
Cambrian College - ECON - 101
Ch.11TheCaseofMorethanOneChoiceVariable 11.1TheDifferentialVersionofOptimizationConditions 11.2ExtremeValuesofaFunctionofTwoVariables 11.3QuadraticFormsAnExcursion 11.4ObjectiveFunctionswithMorethanTwoVariables [11.5SecondOrderConditionsinRelatio
Cambrian College - ECON - 101
Ch.12OptimizationwithEqualityConstraints12.112.212.312.412.5Demand12.612.712.8EffectsofaConstraintFindingtheStationaryValuesSecondOrderConditionsQuasiconcavityandQuasiconvexityUtilityMaximizationandConsumerHomogeneousFunctionsLeastCostCom
Cambrian College - ECON - 101
Ch. 13Further Topics in Optimization13.1 Nonlinear Programming and KuhnTucker Conditions13.2 The Constraint Qualification13.3 Economic Applications13.4 Sufficiency Theorems in NonlinearProgramming13.5 Maximum-value Functions and theEnvelope Theore
Cambrian College - ECON - 101
Chapter 12 OptimizationWith Equality ConstraintsEcon 130 Class Notes fromAlpha Chiang, Fundamentals of MathematicalEconomics, 3rd EditionIntroduction Previously,all choice variables wereindependent of each other. However if we are to observe the
Cambrian College - ECON - 101
Cambrian College - ECON - 101
LINEARMODELSANDMATRIXALGEBRAChapter4AlphaChiang,FundamentalMethodsofMathematicalEconomics3rdeditionWhyMatrixAlgebraAsmoreandmorecommoditiesareincludedinmodels,solutionformulasbecomecumbersome.Matrixalgebraenablestodousmanythings:providesacompac
Cambrian College - ECON - 101
LINEAR MODELS AND MATRIXALGEBRA- Part 2Chapter 4Alpha Chiang, Fundamental Methodsof Mathematical Economics3rd editionVector Operations Multiplicationof vectorsAn m x 1 column vector u, and a 1 x n row vector v,yield a product uv of dimension m
Cambrian College - ECON - 101
LINEAR MODELS ANDMATRIX ALGEBRA- Part 3Chapter 4Alpha Chiang, Fundamental Methods ofMathematical Economics3rd editionIdentity Matrix1 0 I2 = 0 1 1 0 0 0 1 0 I3 = 0 0 1 Characteristics:It is like the number 1: a(1) = (1)a=aIA = AI = AIden
Cambrian College - ECON - 101
LINEAR MODELS AND MATRIXALGEBRA- ContinuedChapter 5Alpha Chiang, Fundamental Methodsof Mathematical Economics3rd editionConditions for Nonsingularity of a Matrix Whensquareness condition is alreadymet, a sufficient condition for thenonsingulari
Cambrian College - ECON - 101
LeontiefInputOutputModelsFrom Chapter 5Alpha Chiang, Fundamental Methods ofMathematical Economics, 4th EditionBackgroundProfessor Wassily Leontief, a Nobel Prizewinner,* deals with this particular question:&quot;What level of output should each of the
Cambrian College - ECON - 101
COMPARATIVE STATICS AND THECONCEPT OF DERIVATIVEChapter 6Alpha Chiang, Fundamental Methodsof Mathematical Economics3rd editionNature of Comparative Staticsconcerned with the comparison of different equilibriumstates that are associated with differ
Cambrian College - ECON - 101
Chapter 8COMPARATIVE STATIC ANALYSIS OFGENERAL FUNCTION MODELSAlpha Chiang, Fundamental Methodsof Mathematical Economics3rd editionComparative Static AnalysisSignificance: sometimes no explicit reduced form solution can beobtained. Hence, we will
Cambrian College - ECON - 101
Chapter 9:OPTIMIZATION: A Special Varietyof Equilibrium AnalysisAlpha Chiang, FundamentalMethods of MathematicalEconomics3rd editionOptimum Values and Extreme ValuesEconomics is by and large a science of choice.common criterion of choice among al
Cambrian College - ECON - 101
Chapter 10:Exponential andLogarithmic FunctionsAlpha Chiang, FundamentalMethods of MathematicalEconomics3rd editionExponential functionsy = f (t ) = b b &gt; 1Generalized:ty = aba and c are compressing or extending agentsctExponential functions
Cambrian College - ECON - 101
Chapter 11 - Optimization:More Than One Choice VariableAlpha Chiang, Fundamentals ofMathematical Economics, 3rd EditionOne variable casez = f ( x)dz = 0dz = f '( x )dxMax: d 2 z &lt; 0Min: d 2 z &gt; 0necessary but not sufficientfor either maximum or
Cambrian College - ECON - 101
Econ 509, Introduction to Mathematical Economics IProfessor Ariell ReshefUniversity of VirginiaLecture notes based on Chiang and Wainwright, Fundamental Methods of Mathematical Economics.1Mathematical economicsWhy describe the world with mathematica
City Colleges of Chicago - ECON - Econ
Chapter 1Ten Principles of EconomicsTRUE/FALSE1.Scarcity means that there is less of a good or resource available than people wish to have.ANS: TDIF: 1REF: 1-0NAT: AnalyticLOC: Scarcity, tradeoffs, and opportunity costTOP: ScarcityMSC: Definiti
City Colleges of Chicago - ECON - Econ
Chapter 2Thinking Like An EconomistTRUE/FALSE1.Economists try to address their subject with a scientists objectivity.ANS: TDIF: 1REF: 2-1NAT: AnalyticLOC: The study of economics and definitions of economicsTOP: EconomistsMSC: Definitional2.Ec
City Colleges of Chicago - ECON - Econ
Chapter 4The Market Forces of Supply and DemandTRUE/FALSE1.Prices allocate a market economys scarce resources.ANS: TDIF: 1REF: 4-0NAT: AnalyticLOC: Markets, market failure, and externalitiesTOP: Market economiesMSC: Definitional2.In a market
City Colleges of Chicago - ECON - Econ
Chapter 5Elasticity and Its ApplicationTRUE/FALSE1.Elasticity measures how responsive quantity is to changes in price.ANS: TDIF: 1REF: 5-0NAT: AnalyticLOC: ElasticityTOP: Price elasticity of demandMSC: Definitional2.Measures of elasticity enh
City Colleges of Chicago - ECON - Econ
Chapter 6Supply, Demand, and Government PoliciesTRUE/FALSE1.Economic policies often have effects that their architects did not intend or anticipate.ANS: TDIF: 1REF: 6-0NAT: AnalyticLOC: The study of economics and definitions of economicsTOP: Pub
City Colleges of Chicago - ECON - Econ
Chapter 7Consumers, Producers, and the Efficiency of MarketsTRUE/FALSE1.Welfare economics is the study of the welfare system.ANS: FDIF: 1REF: 7-1LOC: Supply and demandTOP: WelfareNAT: AnalyticMSC: Definitional2.The willingness to pay is the m
City Colleges of Chicago - ECON - Econ
Chapter 8Application: the Costs of TaxationTRUE/FALSE1.Total surplus is always equal to the sum of consumer surplus and producer surplus.ANS: FDIF: 2REF: 8-1NAT: AnalyticLOC: Supply and demandTOP: Total surplusMSC: Interpretive2.Total surplus
City Colleges of Chicago - ECON - Econ
City Colleges of Chicago - ECON - Econ
Chapter 10ExternalitiesTRUE/FALSE1.Markets sometimes fail to allocate resources efficiently.ANS: TDIF: 2REF: 10-0NAT: AnalyticLOC: Markets, market failure, and externalitiesTOP: Market failureMSC: Interpretive2.When a transaction between a bu
City Colleges of Chicago - ECON - Econ
Chapter 11Public Goods and Common ResourcesTRUE/FALSE1.When goods are available free of charge, the market forces that normally allocate resources in our economyare absent.ANS: TDIF: 2REF: 11-0NAT: AnalyticLOC: Markets, market failure, and exter
City Colleges of Chicago - ECON - Econ
Chapter 12The Design of the Tax SystemTRUE/FALSE1.The average American pays a higher percent of his income in taxes today than he would have in the late 18thcentury.ANS: TDIF: 1REF: 12-0NAT: AnalyticLOC: The role of government TOP:Tax burdenMS
City Colleges of Chicago - ECON - Econ
Chapter 13The Costs of ProductionTRUE/FALSE1.The economic field of industrial organization examines how firms decisions about prices and quantitiesdepend on the market conditions they face.ANS: TDIF: 2REF: 13-0NAT: AnalyticLOC: Costs of producti
City Colleges of Chicago - ECON - Econ
Chapter 14Firms in Competitive MarketsTRUE/FALSE1.For a firm operating in a perfectly competitive industry, total revenue, marginal revenue, and average revenueare all equal.ANS: FDIF: 2REF: 14-1NAT: AnalyticLOC: Perfect competitionTOP: Average
City Colleges of Chicago - ECON - Econ
Chapter 15MonopolyTRUE/FALSE1.Monopolists can achieve any level of profit they desire because they have unlimited market power.ANS: FDIF: 2REF: 15-0NAT: AnalyticLOC: MonopolyTOP: MonopolyMSC: Interpretive2.Even with market power, monopolists
City Colleges of Chicago - ECON - Econ
Chapter 16Monopolistic CompetitionTRUE/FALSE1.The &quot;competition&quot; in monopolistically competitive markets is most likely a result of having many sellers in themarket.ANS: TDIF: 1REF: 16-1NAT: AnalyticLOC: Monopolistic competitionTOP: Monopolistic
City Colleges of Chicago - ECON - Econ
Chapter 17OligopolyTRUE/FALSE1.The essence of an oligopolistic market is that there are only a few sellers.ANS: TDIF: 1REF: 17-0NAT: AnalyticLOC: OligopolyTOP: OligopolyMSC: Definitional2.Game theory is just as necessary for understanding com
City Colleges of Chicago - ECON - Econ
Chapter 18The Markets For the Factors of ProductionTRUE/FALSE1.If the marginal productivity of the sixth worker hired is less than the marginal productivity of the fifth workerhired, then the addition of the sixth worker causes total output to declin
City Colleges of Chicago - ECON - Econ
Chapter 19Earnings and DiscriminationTRUE/FALSE1.A compensating differential refers to a difference in wages that arises from nonmonetary characteristics.ANS: TDIF: 2REF: 19-1NAT: AnalyticLOC: Labor marketsTOP: Compensating differentialsMSC: De
City Colleges of Chicago - ECON - Econ
Chapter 20Income Inequality and PovertyTRUE/FALSE1.The poverty line is set by the government so that 10 percent of all families fall below that line and are therebyclassified as poor.ANS: FDIF: 1REF: 20-1NAT: AnalyticLOC: The study of economics,
City Colleges of Chicago - ECON - Econ
Chapter 21The Theory of Consumer ChoiceTRUE/FALSE1.The theory of consumer choice illustrates that people face tradeoffs, which is one of the Ten Principles ofEconomics.ANS: TDIF: 1REF: 21-0NAT: AnalyticLOC: Utility and consumer choiceTOP: Consu
City Colleges of Chicago - ECON - Econ
Chapter 22Frontiers of MicroeconomicsTRUE/FALSE1.The science of economics is a finished jewel, perfect and unchanging.ANS: FDIF: 1REF: 22-0NAT: AnalyticLOC: The Study of economics, and definitions in economicsTOP: economicsMSC: Definitional2.
UNI - CS - 121
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2/24/2010Sedimentary EnvironmentsGeology 11 Principles of GeologyA. M. P. TengonciangDepartment of Physical SciencesUniversity of the Philippines, BaguioCONTINENTAL SEDIMENTARY ENVIRONMENTSALLUVIALFANBreccia,conglomerate,arkoseComposition Terr
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2/22/2011Continental/ terrestrialSedimentary EnvironmentsTransitionalMarineGeology 11 Principles of GeologyA. M. P. Tengonciang &amp; D. N. JavierDepartment of Physical SciencesUniversity of the Philippines, BaguioContinental/terrestrialdepositional
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ANGELES, GRACE ELYSSE D.Geol 11 Section: WFU201158955BS BiologyTopic: STROMBOLIAN ERUPTION
University of the Philippines Diliman - GEOL - 11
Lecture 11: Rock deformation The movements of Earth's tectonic plates creates stressesrocks subject to stress will deform (change in volume or shape of a body of rock) ways in which rocks deform are varied; which style a particular rock mass adoptsdep
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GENERAL A RTICLEAlfred Wegener From Continental Drift toPlate TectonicsA J Saigeetha and Ravinder Kumar BanyalWhat is the nature of the force or mechanism that movesmassive continents thousands of miles across? What causesviolent earthquakes to dis
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7/4/2011VolcanismGeology 11 Principles of GeologyA. M. P. Tengonciang &amp; D.D. N. javierDepartment of Physical SciencesUniversity of the Philippines, BaguioWhy does magma rise? Physical properties (temperature, composition,viscosity, relative buoyan
University of the Philippines Diliman - GEOL - 11
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University of the Philippines Diliman - GEOL - 11
Diliman Learning Resource CenterMathematics 17Second Semester AY 2010-2011Midterm Exam ReviewJanuary 17, 2011, MondayGeneral Directions. Do as indicated. Write your answers clearly and legibly. Show your complete solutions, if necessary, andbox your
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IIFifth LongExaml. T rueo r F alsei 2o0e. rnai ntocfw_a T heexpression q 1 2010 1 2011 b e s implified i .(b) T hel awo f s ines ndt he l awo f c osines lso oldt ruef or r ightt riangles.aah(c) T her ectangular( n,-n) c onverted t he p olarc
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Mathematics 17Fifth Long ExamGENERAL DIRECTION: Write the exam code of the test paper at the upper right corner of yourbluebook (front). Write your student number below the code. Show all necessary solutions and box the nalanswers. Refrain from using
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Math 17 TWHFW-71st Sem AY 2010-11Exercise 1 Part I Answer KeySolutions to Exercise Set I. Please remember that there may be (and probably are) multiple ways to go about a given problem. As long as the techniquesare valid and the computations are caref
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Math 17 TWHFW-7Ex 1 (HW 4) Part IIPlease do the exercises as indicated. Write down all nal answers on aseparate piece of paper.I. Simplify the following expressions: Consider simplest assumptions on radicandsand variables and that all divisors are no