《微观经济学microeconomics》英文版课件.ppt

1、 ECON501 Lecture Note 1ECON501 Lecture Note 1 Preference and ChoicePreference and ChoiceStructureStructureo Preference relationPreference relationo Choice rulesChoice ruleso The link between preference and choiceThe link between preference and choicePreference RelationsPreference Relationso The Rati

2、onal PreferenceThe Rational Preferencen CompletenessCompletenessn TransitivityTransitivityo Utility FunctionUtility Functionn Definition:a function u is a utility function Definition:a function u is a utility function representing preference relation ifrepresenting preference relation if n A prefere

3、nce relation can be represented by a A preference relation can be represented by a utility function only if it is rationalutility function only if it is rational)()(yuxuyxChoice RulesChoice Ruleso A choice structure A choice structure n Budget setsBudget setsn A choice ruleA choice ruleo The weak ax

4、iom of revealed preference(WARP):if The weak axiom of revealed preference(WARP):if x is revealed at least as good as y,then y cannot be x is revealed at least as good as y,then y cannot be revealed preferred to xrevealed preferred to xBBC)(B)(,(CThe Link Between Preference and ChoiceThe Link Between

5、 Preference and Choiceo If the preference relation is rational,then the If the preference relation is rational,then the choice structure satisfies the weak axiom.choice structure satisfies the weak axiom.o If the choice structure satisfies the WARP and If the choice structure satisfies the WARP and

6、includes all subsets of X of up to three elements,includes all subsets of X of up to three elements,then there is a corresponding rational preference then there is a corresponding rational preference relation.relation.ECON501 Lecture Note 2ECON501 Lecture Note 2 Consumer Theory 1Consumer Theory 1(Te

7、xtbook Chapter 2 and 3)(Textbook Chapter 2 and 3)StructureStructureConsumer Choice(Chapter 2)Consumer Choice(Chapter 2)o Budget setBudget seto WalrasianWalrasian demand function demand functiono Comparative staticsComparative staticso The weak axiom of revealed preference and the law The weak axiom

8、of revealed preference and the law of demand of demand Preference(Chapter 3)Preference(Chapter 3)o The basic properties of preferenceThe basic properties of preferenceo Existence of utility functionExistence of utility functionThe Budget setThe Budget seto CommoditiesCommoditieso The physical constr

9、aints and the consumption setThe physical constraints and the consumption seto The economic constraint:The economic constraint:o The The WalrasianWalrasian budget set(Definition 2.D.1)budget set(Definition 2.D.1)o Convexity of Convexity of WalrasianWalrasian budget set:proof budget set:proofwxpxppxL

10、L.11:,wpxRxBLwp,.,10:LlforxRxRXlLConsumers ChoiceConsumers Choiceo The consumers problem:to choose a consumption The consumers problem:to choose a consumption bundle x from the bundle x from the WalrasianWalrasian budget set.budget set.WalrasianWalrasian Demand Function Demand FunctionAssumption:Ass

11、umption:o It is homogeneous of degree of zero(Definition It is homogeneous of degree of zero(Definition 2.E.1):individuals choice depends only on the set 2.E.1):individuals choice depends only on the set of feasible points.of feasible points.o It satisfies It satisfies WalrasWalras law(Definition 2.

12、E.2):the law(Definition 2.E.2):the consumer fully expends his wealth.consumer fully expends his wealth.o Exercise 2.E.1Exercise 2.E.1),(wpxComparative Statics Wealth EffectsComparative Statics Wealth Effectso The consumers Engel function The consumers Engel function o The wealth effectThe wealth eff

13、ecto Normal goods and inferior goods Normal goods and inferior goods),(wpx),(/),(wpxDorwwpxwlComparative Statics Price EffectsComparative Statics Price Effectso The demand curve(Figure 2.E.2)The demand curve(Figure 2.E.2)o The offer curve(Figure 2.E.3 and 2.E.4)The offer curve(Figure 2.E.3 and 2.E.4

14、)o The price effect The price effect),(/),(wpxDorwwpxwlThe Weak Axiom of Revealed PreferenceThe Weak Axiom of Revealed Preferenceo(Definition 2.F.1)The(Definition 2.F.1)The WalrasianWalrasian demand function demand function satisfied the weak axiom of revealed preference if:satisfied the weak axiom

15、of revealed preference if:o Intuition:Figure 2.F.1Intuition:Figure 2.F.1),(),(),(),(wwpxpwpxwpxandwwpxpIfThe Implication of WARPThe Implication of WARPo Two effects of price change:substitution effect and Two effects of price change:substitution effect and income effectincome effecto(SlutskySlutsky)

16、compensated price changes)compensated price changeso Proposition 2.F.1:The Proposition 2.F.1:The WalrasianWalrasian demand function demand function satisfied the WARP if and only if:for any satisfied the WARP if and only if:for any compensated price change from initial(compensated price change from

17、initial(p,wp,w)to(p,)to(p,w)=(p,w)=(p,px(p,wpx(p,w),we have),we haveo The law of demandThe law of demand),(),(00),(),()(wpxwpxwhenwithwpxwpxppBasic Properties of PreferenceBasic Properties of Preferenceo Rational(Definition 3.B.1)Rational(Definition 3.B.1)o Monotone(Definition 3.B.2)Monotone(Definit

18、ion 3.B.2)o Local Local nonsatiatednonsatiated(Definition 3.B.3)(Definition 3.B.3)o Convex(Definition 3.B.4)Convex(Definition 3.B.4)o Homothetic(Definition 3.B.6)Homothetic(Definition 3.B.6)o QuasilinearQuasilinear(Definition 3.B.7)(Definition 3.B.7)o Continuous(Definition 3.C.1)Continuous(Definitio

19、n 3.C.1)Existence of A Utility FunctionExistence of A Utility Functiono Proposition 3.C.1:suppose that the rational Proposition 3.C.1:suppose that the rational preference relation on X is continuous,then there preference relation on X is continuous,then there is a continuous utility function that re

20、present is a continuous utility function that represent this preferencethis preference )(xuECON501 Lecture Note 3ECON501 Lecture Note 3 Consumer Theory 2Consumer Theory 2(Textbook Chapter 3)(Textbook Chapter 3)StructureStructureo Utility Maximization ProblemUtility Maximization Problemn Utility maxi

21、mizationUtility maximizationn WalrasianWalrasian demand function demand functionn Indirect utility functionIndirect utility functiono Expenditure Minimization ProblemExpenditure Minimization Problemn Expenditure minimizationExpenditure minimizationn Expenditure functionExpenditure functionn Hicksian

22、Hicksian demand function demand functionUtility Maximization ProblemUtility Maximization Problemo The problem:The problem:o The The LagrangianLagrangian for the consumers constrained for the consumers constrained optimization:optimization:o First order condition:First order condition:o Solution:Solu

23、tion:WalrasianWalrasian demand function demand functionwpxtsxuMaxx.)(0wpxpxxuorppxxuxxullklkl)(/)(/)(*),(*wpx)()(),(wpxxuwpxLUtility Maximization-ExampleUtility Maximization-Exampleo Example 3.D.1:the transformed Cobb-Douglas Example 3.D.1:the transformed Cobb-Douglas Utility FunctionUtility Functio

24、nwxpxptsxxMax221121.ln)1(lnWalrasianWalrasian Demand Function Demand Functiono Assumption:suppose a continuous utility function Assumption:suppose a continuous utility function representing a locally representing a locally nonsatiatednonsatiated preference preference relationrelationo Properties of

25、Properties of WalrasianWalrasian demand function:demand function:1.1.It is homogeneous of degree of zeroIt is homogeneous of degree of zero2.2.It satisfies It satisfies WalrasWalras law law3.3.Convexity of preference implies convexity of Convexity of preference implies convexity of x(p,wx(p,w),stric

26、t convexity of preferences implies),strict convexity of preferences implies that that x(p,wx(p,w)is single-valued)is single-valuedo ProofProof),(wpxIndirect Utility FunctionIndirect Utility Functiono Definition:Definition:o Properties:Properties:1.1.Homogeneous of degree of zeroHomogeneous of degree

27、 of zero2.2.Strictly increasing in w and Strictly increasing in w and nonincreasingnonincreasing in p in p3.3.QuasiconvexQuasiconvex in p and w in p and w4.4.ContinuousContinuousp ProofProof),(),(wpxuwpvExpenditure Minimization ProblemExpenditure Minimization Problemo The problem:The problem:o The f

28、irst order condition:The first order condition:o The solution:The solution:HicksianHicksian demand function demand function h(p,uh(p,u)uxutspxMinx)(.0uxuppxxuxxuklkl)(/)(/)(*Expenditure FunctionExpenditure FunctionoExpenditure function Expenditure function oProperties:Properties:1.1.Homogeneous of d

29、egree of one in pHomogeneous of degree of one in p2.2.Strictly increasing in u and Strictly increasing in u and nondecreasingnondecreasing in p in p3.3.Concave in pConcave in p4.4.Continuous in p and uContinuous in p and upProofProofuxutspxMinupex)(.),(HicksianHicksian Demand Function Demand Functio

30、noPropertiesProperties1.1.Homogenous of degree of zero in pHomogenous of degree of zero in p2.2.No excess utilityNo excess utility3.3.Convexity/uniqueness Convexity/uniqueness pProofProofpExample 3.E.1:Example 3.E.1:HicksianHicksian demand function and demand function and expenditure function for th

31、e Cobb-Douglas utility expenditure function for the Cobb-Douglas utility functionfunctionECON501 Lecture Note 4ECON501 Lecture Note 4Consumer Theory 3Consumer Theory 3StructureStructureo Duality Duality n Identities of Duality(p.60)Identities of Duality(p.60)n HicksianHicksian Demand and Expenditure

32、 Function Demand and Expenditure Function(p.68)(p.68)n WalrasianWalrasian Demand and Indirect Utility Demand and Indirect Utility Function(p.73)Function(p.73)n HicksianHicksian and and WalrasianWalrasian Demand(p.71)Demand(p.71)n Summary of Duality(p.75)Summary of Duality(p.75)o Welfare Evaluation(p

33、.80)Welfare Evaluation(p.80)DualityDualityo Let xLet x*be the solution to the utility maximization be the solution to the utility maximization problemproblemo Then xThen x*is also the solution to the expenditure is also the solution to the expenditure problemproblem *.)(*),(wpxtsxuMaxwpvx*)(.*),(uxu

34、tspxMinupexIdentities of DualityIdentities of Dualityo The identities(p.60)The identities(p.60),(,(),(),(,(),(),(,(),(,(wpvphwpxupepxuphuupepvwwpvpeHicksianHicksian Demand and Expenditure Function Demand and Expenditure Functiono Proposition 3.G.1(p.68):Proposition 3.G.1(p.68):ProofProofLlforpupeuph

35、upeuphllp,.,1/),(),(),(),(WalrasianWalrasian Demand and Indirect Utility Demand and Indirect Utility FunctionFunctiono Roys identity(Proposition 3.G.4,p.73):Roys identity(Proposition 3.G.4,p.73):ProofProofwwpvpwpvwpxll/),(/),(),(The Compensated Law of Demand(p.62)The Compensated Law of Demand(p.62)o

36、(Proposition 3.E.4)The(Proposition 3.E.4)The HicksianHicksian demand function demand function satisfies the compensated law of demand:for all p satisfies the compensated law of demand:for all p and pand pProofProof0),(),()(uphuphppThe The HecksianHecksian and and WalrasianWalrasian Demand Demand Fun

37、ction Function o(Proposition 3.G.3,p.71)The(Proposition 3.G.3,p.71)The SlutskySlutsky Equation EquationProofProof),(),(),(),(),(),(),(),(wpxwpxDwpxDuphDwpxwwpxpwpxpuphwppklklklRelationship between the UMP and the EMPRelationship between the UMP and the EMP),(wpx),(wpx),(wpxSlutsky Equation),(wpx),(u

38、ph),(upe),(wpv),(),(upeuphpRoys identity),(,(upepvu),(,(wpvpew),(,(),(upepxuph),(,(),(wpvphwpxWelfare EvaluationWelfare Evaluationo The equivalent variation(EV)The equivalent variation(EV)o The compensating variation(CV)The compensating variation(CV)wupeupeupewppEV),(),(),(),(10001010),(),(),(),(010

39、11110upewupeupewppCVECON501 Lecture Note 5ECON501 Lecture Note 5Producer Choice 1Producer Choice 1StructureStructureo Technology and Production SetTechnology and Production Seto Profit Maximization ProblemProfit Maximization ProblemDefinition of Production Set(p.128)Definition of Production Set(p.12

40、8)o Production set:Production set:o Transformation function:Transformation function:o Transformation frontier:Transformation frontier:o The marginal rate of transformation:The marginal rate of transformation:0)(:yFyY)(yF0)(:yFykllkyyFyyFyMRT/)(/)()(Technologies with Distinct Inputs and Outputs Techn

41、ologies with Distinct Inputs and Outputs(p.129)(p.129)o Production function:Production function:o The marginal rate of technical substitution of input The marginal rate of technical substitution of input l for input kl for input kkllkzzfzzfzMRTS/)(/)()(00)(:),(:)(zandzfqqzYzfProperties of Production

42、 Set(p.130)Properties of Production Set(p.130)o NonemptyNonemptyo ClosedClosedo No free lunchNo free luncho Possibility of inactionPossibility of inactiono Free disposalFree disposalo IrreversibilityIrreversibilityo Return to scale:Return to scale:nonincreasingnonincreasing,nondecreasingnondecreasin

43、g,constantconstanto AdditivityAdditivity(free entry)(free entry)o ConvexityConvexityProfit Maximization(p.135)Profit Maximization(p.135)o Problem:Problem:o The first order condition:The first order condition:o Alternative way:single-output technologyAlternative way:single-output technology0)(.yFtsyp

44、MaxylkklllMRTpporyyFp*)(kllkllzwwMTRSorwzzfpCOFzwzpfMax/*)(.)(0Profit FunctionProfit Functiono Profit function:Profit function:o Properties:(p.138)Properties:(p.138)1.1.Homogeneous of degree of one in pHomogeneous of degree of one in p2.2.Convex in pConvex in p3.3.NondecreasingNondecreasing in outpu

45、t price,and in output price,and nonincreasingnonincreasing in input price in input price*)(*)(wzzpfpypDemand function(supply function)Demand function(supply function)oProperties:(p.138)Properties:(p.138)1.1.Homogeneous of degree of zero in pHomogeneous of degree of zero in p2.2.If Y is convex,then I

46、f Y is convex,then y(py(p)is convex set for all p;if)is convex set for all p;if Y is strictly convex,then Y is strictly convex,then y(py(p)is single value)is single value3.3.HotellingHotelling Lemma:Lemma:)(pypppy/)()(The Law of Supply(p.138)The Law of Supply(p.138)pThe law of supply:quantities resp

47、ond in the same The law of supply:quantities respond in the same direction as price changedirection as price changeProofProof0)(yyppECON501 Lecture Note 6ECON501 Lecture Note 6Producer Choice 2Producer Choice 2StructureStructureo Cost Minimization ProblemCost Minimization Problemo Duality:Production

48、 Function and Cost FunctionDuality:Production Function and Cost FunctionCost Minimization Problem(p.139)Cost Minimization Problem(p.139)o ProblemProblemo First order condition:First order condition:o Conditional factor demand function Conditional factor demand function o Cost functionCost functiono

49、Example:the Cobb-Douglas production function Example:the Cobb-Douglas production function qzftszwMinz)(.0qzfMRTSwworzzfwlkklll*)(*)(),(qwz),(),(qwzwqwcCost Function(p.141)Cost Function(p.141)oPropertiesProperties1.1.NondecreasingNondecreasing in q in q2.2.Homogeneous of degree of one in wHomogeneous

50、 of degree of one in w3.3.Concave in wConcave in w4.4.Continuous in wContinuous in w5.5.If f(.)is homogeneous of degree of one,then c(.)If f(.)is homogeneous of degree of one,then c(.)is homogeneous of degree of one in qis homogeneous of degree of one in qConditional Factor Demand FunctionConditiona