ECON 200A: MICROECONOMICS ("DECISIONS")

Fall 2003 Tu,Th 8:00-9:50am ECON 300

Mark Machina Office: ECON 217 Hours: Wed 10:00-2:00

The topics of this course are the economic theories of consumer and producer behavior.

The texts for the 200AIB/C sequence are:

Kreps, D., A Course in Microeconomic Theory. Princeton: Princeton Univ. Press, 1990.

Mas-Colell, A., M. Whinston and J. Green ("MWG"), Microeconomic Theory, Oxford:Oxford Univ. Press, 1995.

Varian, H., Microeconomic Analysis, 3rd ed. New York: W.W. Norton & Co., 1992.

There will also be a Mathematical Handout for this course, and additional in-class handouts.

An extremely useful book of problems, designed to hone your analytical ability is:

Dixon, P., S. Bowles and D. Kendrick, Notes and Problems in Microeconomic Theory,1985, (Amsterdam: North-Holland)

Other useful readings include the relevant chapters of:

Debreu, G., Theory of Value, 1959, (New York: Wiley).

Henderson, J. and R. Quandt, Microeconomic Theory: A Mathematical Approach, 3rd ed.,1980 (New York: McGraw-Hill)

Malinvaud, E., Lectures on Microeconomic Theory, 1972 (Amsterdam: North-Holland)

Russell, R. and M. Wilkinson, Microeconomics: A Synthesis of Modern and NeoclassicalTheory, 1979, (New York: Wiley)

EXAMS: Your grade the course will be determined on the basis of two midterms (dates to bedetermined) and the final exam (Tuesday, December 9, 8-1lam).

OPTIONAL QUESTIONS: For those who would like prior practice working with the materialat a more basic level, or whose microeconomics background is not strong, there is an Econ 100Apackage available at Soft Reserve. This package contains approximately 00 practice questions,which sometimes accidentally find their way onto Econ 200A midterms and final exams. Evenonto Micro Qualifiers ...

-- -

ECONOMICS 200A COURSE OUTLINE

Fall 2003 Mark Machina

I. INTRODUCTION AND BASIC MATHEMATICAL IDEAS

a. Some Introductory IdeasDomain of Microeconomic AnalysisRole of Models in EconomicsThe Circular Flow DiagramStocks versus Flows and the Dimensions of Economic Variables

b. Elasticityc. Level Curves of Functions

d. Possible Properties of FunctionsCardinal vs. Ordinal Properties of FunctionsScale Invariance and Constant Returns to ScaleHomogeneous Functions and Euler's TheoremHomotheticityConcavity and ConvexityQuasiconcavity and QuasiconvexityAdditive and Multiplicative Separability

e. Systems of Linear Equations and Cramer's Rule

II. MATHEMATICS OF OPTIMIZATION

a. The General Structure of Optimization ProblemsObjective Functions, Control Variables, Parameters, ConstraintsSolution Functions and Optimal Value Functions

b. Unconstrained OptimizationFirst Order Condit;onsSecond Order Conditions

c. Constrained OptimizationFirst Order Conditions

LagrangiansComer Solutions

Second Order Conditions

d. Comparative Statics of SolutionFunctions - Implicit DifferentiationDifferentiation of First Order Conditions

. A RelatedApplication:ComparativeStaticsof Equilibriae. Comparative Statics of Optimal Value Functions- The Envelope Theorem

Unconstrained Case: Differentiation of the Objective FunctionConstrained Case: Differentiation of the Lagrangian

III. CONSUMER PREFERENCES AND THE UTILITY FUNCTION

a. The Choice SpaceThe Objects of ChoiceThe Relevant Time PeriodThe Issue of Divisibility

b. The Consumer's Preference RankingWeak Preference, Strict Preference and IndifferencePreferences are Defined over CommodityBundles, not Individual CommoditiesGeneral Properties of the Preference Ranking:

Completeness, Reflexivity and TransitivityContinuity

Alternative Definitions of ContinuityExample of Non-Continuous Preferences: Lexicographic Preferences

Possible Additional Properties of the Preference RankingWeak Monotonicity/Strong MonotonicityLocal NonsatiationWeak Convexity/Convexity/Strong Convexity

c. Indifference Curves and the Marginal Rate of SubstitutionBetter-Than Sets, Worse-Than Sets and Indifference SetsTypical Properties of Indifference Curves

One Through Each PointDownward Sloping and "Thin"Can't Cross

Marginal Rate of Substitution (MRS)Definition ofMRSGraphical Interpretation: Slope of the Indifference CurveConvexity of Preferences and Hypothesis of Diminishing MRS

d. Utility FunctionsRepresentation of a Preference Ranking by a Utility FunctionMonotonic Invariance of Utility FunctionsPossible Properties of a Utility Function:

Weak/Strong MonotonicityWeak/Strong QuasiconcavityHomotheticityAdditive/Multiplicative Separability

Expressing the MRS in Terms of Marginal UtilitiesMonotonic Invariance of the MRSHypothesis of Diminishing MRS

Algebraic Condition for Hypothesis of Diminishing MRSImportant Examples of Utility Functions

LinearCobb-DouglasLeontiefConstant Elasticity of Substitution (CES)

2

---

IV. UTILITY MAXIMIZATION AND DEMAND FUNCTIONS

a. Utility Maximization Subject to a Budget ConstraintGraphical IllustrationFirst Order Conditions for Utility Maximization

Two Interpretations of the First Order ConditionsMonotonic Invariance of the First Order Conditions

"Marginal Utility of Income"Second Order Conditions (Hypothesis of Diminishing MRS)Algebraic Examples: Cobb-Douglas, Leontief, LinearComer Solutions

b. Regular or "Marshallian" Demand FunctionsDefinition of Regular Demand Functions

Examples: Cobb-Douglas, Leontief, LinearGeneral Properties of Demand Functions:

Not Necessarily Nonincreasing in "Own Price"Walras' Law .

Scale Invariant in Prices and IncomeRelationship between Price Elasticities & Income Elasticity for a Good

Market Demand Functions .

c. The Indirect Utility FunctionProperties:

Increasing in Income, Nonincreasing in PricesHomogeneous Degree Zero in Prices and IncomeQuasiconvex in Prices

Utility-Income CurvesPrice Indifference CurvesEffect of Monotonic Transformation of UtilityExamples: Cobb-Douglas, Leontief, Linear

d. Compensated Demand Functions and the Expenditure FunctionThe Expenditure Minimization Problem

First Order Conditions for Expenditure MinimizationCompensated or'''Hicksian'' Demand Functions

Properties:Homogeneous Degree Zero in PricesNonincreasing in "Own Price"

Identities Linking the Marshallian and Hicksian Demand FunctionsExamples: Cobb-Douglas, Leontief, Linear

The Expenditure FunctionProperties:

Increasing in Utility, Nondecreasing in PricesHomogeneous of Degree One in PricesConcave in Prices

Identities Linking the Expenditure and Indirect Utility Functions

3

.-. ---.-...

V. COMPARATIVE STATICS OF DEMAND

a. Changes in IncomeIncome-Consumption LociEngel Curves: Definition and Graphical DerivationIncome Elasticity

Superior, Normal and Inferior GoodsIncome Elasticity and Budget SharesRelationship Between Income Elasticities of All Goods

Algebraic Derivation of the Effect of an Income ChangeRelationship Between Income Elasticities for All Goods

b. Changes in PricesPrice-Consumption LociGraphical Derivation ofMarshallian Demand CurvesOwn Price Elasticity

Price Elasticity and Budget SharesCross Price Elasticity

Gross Substitutes and Gross ComplementsAlgebraic Derivation ofthe Effect of a Price ChangeRelationship Between All Price and Income Elasticities for a Good

c. Compensated Price ChangesGraphical Illustration of a Compensated Price ChangeGraphical Illustration of a Compensated Demand CurvesAlgebraic Derivation ofthe Effect of a Compensated Price ChangeNonpositivity of Own Compensated Price EffectCompensated Cross Price Elasticity

Net Substitutes aridNet Complements

d. The Slutsky EquationExpressing Each ofthe Three Basic Changes in Terms of the Other TwoGraphical IllustrationAlgebraic FormulationGiffen Goods

e. Some Important ResultsEconomic Interpretation of the Lagrangian MultiplierRoy's Identity (Linking the Indirect Utility and Demand Functions)Relationship Between the Expenditure and Compensated Demand FunctionsA One-Line Proof of the Slutsky EquationJustification of the Two-Good Approach: The Composite Commodity Theorem

4

VI. PRODUCTION, COST AND DUALITYa. Factors of Production

The Stock-Flow DistinctionTypes of Factors and Their Income

b. Production Functions and Production SetsDefinition and Important Examples of Production Functions

Linear .

Leontief and Multi-Technique LeontiefCobb-DouglasConstant Elasticity of Substitution

Marginal Products and the Law of Diminishing Marginal ReturnsAverage Products and the Average-Marginal RelationshipReturns to ScaleTechnical Progress

Three Implications of Technical ProgressHicks-Neutral, Harrod-Neutral and Solow-Neutral Technical ProgressContinuous Technical Progress

Production Sets and Input Requirement Sets

c. Isoquants and the Marginal Rate of Technical Substitution (MRTS)Definition and General Properties of Isoquants

Examples: Linear, Cobb-Douglas, LeontiefDefinition ofMRTSExpressing MRTS in Terms of Marginal ProductsHypothesis of Diminishing MRTSElasticity of Substitution

d. The Nature of CostDefinition of CostAccounting Cost vs. Opportunity Cost of Owned Factors

Numerical ExampleCost of Entrepreneurial Ability and Definition of ''Normal Profits"Short Run versus Long Run Planning Horizons

e. Short Run Cost FunctionsExpansion Path in the Short RunGraphical Derivation ofthe Short Run Total Cost CurveAlgebraic Derivation of Short Run Total Cost Function (STC)

Examples: Linear, Leontief, Cobb-DouglasShort Run Variable Cost Function (SVC)Short Run Fixed Cost Function (SFC)Short Run Marginal Cost Function (SMC)

Relation ofSMC to Marginal Product of Labor and Wage RateShort Run Average Total Cost Function (SATC)Short Run Average Variable Cost Function (SAVC)Short Run Average Fixed Cost Function (SAFC)Average-Marginal RelationshipsEffects and Interpretation of "Changes in Fixed Capital K"

5

f. Long Run Minimization and Long Run Cost FunctionsIsocost LinesLong Run Cost Minimization

First Order Conditions and Output-Constrained Factor DemandsTwo Interpretations of the First Order Conditions

Second Order Conditions and the Hypothesis of Diminishing MRTSEquivalence to Constrained Output Maximization

The Long Run Expansion PathLong Run Total Cost Function (LTC)

Properties of LTC:Increasing in Output, Nondecreasing in Factor PricesHomogeneous of Degree One in Factor PricesConcave in Factor Prices

Examples: Linear, Leontief, Cobb-DouglasDeriving Output-Constrained Factor Demands from LTC

Long Run Marginal Cost Function (LMC)Relation of LMC to Marginal Products and Factor Prices

Long Run Average Cost Function (LAC)Returns to Scale and Long Run Average CostAverage-Marginal Relationship

Relation Between Long Run and Short Run Total, Average and Marginal Cost Curves

g. Duality Between Production and CostEquivalence of Cost Minimization and Constrained Output MaximizationConvexification of Input Requirement Sets and Competitive ProductionRecovery of Production Function and Cost Functions from Each OtherCharacterization of Cost Functions:

PositiveNondecreasing in Output and Factor PricesHomogeneous Degree One in Factor PricesConcave in Factor Prices

Relationship Between Isocost Curves (in the Factor Price Plane) and Isoquants

VII. PROFIT MAXIMIZATION AND SUPPLY

a. Long Run Profit Maximization and SupplyLong Run Profit Maximization (Graphical Illustration and Algebraic Formulation)

First Order Conditions and InterpretationSecond Order Condition (Increasing Marginal Cost)

The Long Run Supply Function ofthe FirmProperties:

Increasing in Price, Nonincreasing in Factor PricesScale Invariant in Output and Factor PricesLong Run Elasticity of Supply

Cobb-Douglas ExampleThe Long Run Profit Function

Properties:Increasing in Price, Nonincreasing in Factor Prices

6

Homogeneous of Degree One in All (Output and Factor) PricesConvex in Output and Factor Prices

Cobb-Douglas ExampleIdentity Linking the Long Run Profit and Supply Functions

b. Short Run Profit Maximization and SupplyThe Three Relevant Regions and the Shut Down Decision

Illustration in Tenns of STC and SVC CurvesIllustration in Tenns ofSATC and SAVC CurvesThe Short Run Supply Curve of the Finn

The Short Run Supply Function of the FinnProperties:

Increasing inp, Nonincreasing in (w,r)Scale Invariant in (p,w)Effects of Changes in K

Short Run Elasticity of SupplyCobb-Douglas Example

The Short Run Profit FunctionProperties

Increasing inp, Nonincreasing in (w,r)Homogeneous Degree One in (p,w,r)Convex in (p,w,r)

Effects of Changes in KCobb-Douglas Example

Identity Linking the Short Run Profit and Supply FunctionsComparison of Short Run and Long Run Profit FunctionsComparison of Short Run and Long Run Supply Elasticities

c. Factor Demand FunctionsMaximizing Profits by Choosing Optimal Input Levels

Marginal Value Product of a Factor of ProductionShort Run Factor Demand

First Order Condition for Short Run Profit MaximizationShort Run Factor Demand Functions

Nonincreasing in Own Factor PriceScale Invariant in Output Price and Prices of Variable FactorsRelation to Short Run Supply Function

Long Run Factor DemandFirst Order Conditions for Long Run Profit MaximizationLong Run Factor Demand Functions

Nonincreasing in Own Factor PriceScale Invariant in Output Price and Factor PricesRelation to Long Run Supply FunctionRelation to the Profit FunctionProperties:

Nonincreasing in Own PriceScale Invariant in (p,w,r)Symmetric Cross Factor Price Effects

7

- +-- - - -- - - - -. - -- - +---

VIII. CHOICE UNDER UNCERTAINTY

a. Objective UncertaintyObjects of Choice and Preference FunctionalsStructure of Expected Utility Preferences

Axiomatic Characterization of Expected UtilityArrow-Pratt Characterization of Comparative Risk Aversion

Risk Aversion and WealthRothschild-Stiglitz Characterization of Comparative RiskDemand for msurance

b. Subjective UncertaintyStates, Events, Outcomes and ActsProbabilistic SophisticationExpected Utility Preferences over Subjective Acts

State-Dependent Utilityc. Evidence and Alternative Models

Evidence on the mdependence AxiomNon-Expected Utility Preference Functionals

Generalized Expected Utility AnalysisEvidence on Probabilistic Sophistication and the Stability of Preferences

IX. INTERTEMPORAL CHOICE & PRODUCTION: SUPPLY AND DEMAND FOR CAPITAL

a. Supply of Labor: The Labor-Leisure Decisionmcome-Leisure Space and the Labor-LeisureDecisionFirst Order Conditions for Optimal Supply of LaborComparative Statics: mcome and Substitution EffectsBackward Bending Supply of Labor CurvesKinked Budget Lines and the Overtime Decision

b. Supply of Capital: The Consumption-Savings Decisionmtertemporal mcome and Consumption Streamsmterest Rates and Discounted Present Value of a Streammtertemporal Utility Maximization

First Order Conditions and mterpretationComparative Statics: mcome and Substitution Effects

c. Intertemporal Production: The Demand for CapitalTwo-Period IllustrationFinite-Period Production and mvestmentContinuous Time Production: When to Cut a Tree

d. Relationship between Rental Market and Sales Market for Capital

X. SPECIFICATION ANDESTIMATION OF DEMAND,COST ANDSUPPLYa. Parametric Estimation of Demand Systemsb. Parametric Estimation of Production and Cost Systems

c. Nonparametric Testing of the MaximizationHypothesis

8

ECONOMICS 200A READINGS BY TOPIC

Fall 2003 Mark Machina

I. Introduction and Basic Mathematical IdeasRequired: Math Handout, Sections A through F; Kreps Ch.lAlso suggested: MWG App.A-E; Varian Ch.26

II. Mathematics of OptimizationRequired: Mathematical Handout, Sections G through IAlso suggested: Kreps App.l; MWG App. J-L; Varian Ch.27

III. Consumer Preferences and the Utility FunctionRequired: Kreps Sect.2.1; MWG Ch.l, Sects.2A -2C,3A - 3C; Varian Sect. 7.1Also suggested: Suggested readings will be provided in an in-class handout

IV. Utility Maximization and Demand FunctionsRequired: Kreps Ch.2; MWG Sects.2D,3D; Varian Sects.7.2-7.5Also suggested: Henderson & Quandt, Sects.2.1-2.3

V. Comparative Statics of DemandRequired: MWG Sects.2E-2F, 3E-3J; Varian Chs. 8,9Also suggested: MWG ChA; Varian Ch.l 0, Henderson & Quandt, Sects.2.5-2.7

VI. Production, Cost and DualityRequired: Kreps Sect. 7.1 ; MWG Ch.5; Varian Chs.l,4,5,6Also suggested: Henderson & Quandt, ChsA,5

VII. Profit Maximization and SupplyRequired: Kreps Ch.7; MWG Ch.5; Varian Chs.2,3Required: Viner, J. (1931). "Cost Curves and Supply Curves," Zeitschrift flir

Nationalokonomie III: 23-46.Also suggested: Kreps Chs.19,20

VIII. Choice Under UncertaintyRequired: Kreps Ch.3; MWG Ch.6; Varian Ch.ll;Required: Pratt J. (1964). "Risk Aversion in the Small and in the Large," Econo-

metrica 32, 122-136.Also suggested: Rothschild, M. & J. Stiglitz (1970). "Increasing Risk: I. A Defini-

tion," Journal of Economic Theory 2, 225-243;Machina, M. (1987). "Choice Under Uncertainty: Problems Solved and Unsolved,"

Journal of Economic Perspectives, Summer 1987.

IX. Intertemporal Choice and ProductionRequired: MWG Sects.20A-20D; Varian Ch.19Also suggested: Kreps ChA, Sect.6.5; MWG Sects.19A-19B

X. Specification and Estimation of Demand, Cost and SupplyRequired: Varian Ch.12Required: Ch. 3 of Deaton & Muellbauer (1980), Economics and Consumer Behavior.

9

ECON 200A: FAMOUS OPTIMIZATION PROBLEMS

Optimization Objective Constraint Control Parameters Solution Optimal ValueProblem Function Variables Functions Function

Consumer's U(x\,...,xn) P\'XI+...+Pn,xn = 1 X),''',Xn p\,...,Pn,l x,{p\,...,Pn,/) V(p\,...,Pn,/)

Problem utility function budget constraint commodity prices and regular demand indirect utilitylevels Income functions function

Expenditure p\,x\+...+Pn,xn U(x),...,xn)= U X),''',Xn p),...,pn , U h,{p\,...,Pn, U) e(p\,...,Pn, U)Minimization expenditure level desired utility level commodity prices and compensated expenditure

Problem (' allowance ') (' Jonathan's ') levels utility level demand functions function

LaborlLeisure U(RJ) 1 = 10+ w.(168-H)R,I w,/o L(wJo):=168-R(wJo) V(wJo)

Decision utility function budget constraintleisure time, wage rate and

labor supply function indirect utilitydisposable inc. nonwage income function

Intertemporal U(c\,...,cn) L\(l +i)"(/,-c,) = 0 c),..., Cn I),...,ln, i c,{/),...,ln,i) V(/),...,ln,i)

Optimization utility function budget constraint consumption income stream and consumption indirect utilitylevels interest rate functions function

Long Run Cost w.L + r.K F(L,K) = Q L,K Q, w,r L(Q,w,r), K(Q,w,r) LTC(Q,w,r)Minimization total cost desired output factor levels desired output and output-constrained long run total

factor prices factor demands cost function

Long Run Profitp.Q -LTC(Q,w,r) Q P, w,r Q(P,w,r) 1Z(P,w,r)

Maximization none output price and long run supply long run profit(in tenns of Q) total profit output level

factor prices function function

Long Run ProfitP.F(L,K) - w.L - r.K L,K P, w, r L(P,w,r), K(P,w,r) 1Z(P,w,r)

Maximization none output price and factor demand long run profit(in tennsof L,K) total profit factor levels

factor prices functions function

Long Run Profitp.Q - w.L - r.K F(L,K)= Q Q,L,K P, w,r Q(p'w,r),L(p'w,r),K(p'w,r) 1Z(P,w,r)

Maximization output and output price and output supply & factor long run profit(in tenns of Q, L, K) total profit production function factor levels factor prices demand functions function