Nolan H. Miller August 18, 2006 - University of Illinois

1 Notes on Microeconomic TheoryNolan H. MillerAugust 18, 2006 Contents1 The Economic DemandFunctions .. AFirstAnalysisofConsumerChoices .. ComparativeStatics .. Requirement1 Revisited:Walras What stheFunnyEqualsSignAllAbout?.. Back to Walras Law: Choice Response to a Change in Wealth .. TestableImplications .. Summary:HowDidWeGetWhereWeAre? .. Walras Law:ChoiceResponsetoaChangeinPrice .. WhyBother?.. Walras Law and Changes in Wealth: Elasticity Form .. Requirement 2 Revisited: Demand is Homogeneous of Degree Zero.. Comparative Statics of Homogeneity of Degree Zero .. Requirement3 Other Properties of the Substitution Matrix .. 27iNolan MillerNotes on Microeconomic Theoryver: Aug.

2 20063 The Traditional Approach to Consumer FromPreferencestoUtility .. SomeBasicPropertiesofUtilityFunctions .. TheUtilityMaximizationProblem(UMP).. TheIndirectUtilityFunctionandItsProperti es .. Roy The Indirect Utility Function andWelfareEvaluation .. TheExpenditureMinimizationProblem(EMP).. Properties of the Hicksian Demand Functions and Expenditure Function .. The Relationship Between the Expenditure Function and Hicksian Demand . TheSlutskyEquation .. Graphical Relationship of the Walrasian and Hicksian Demand Functions .. TheEMPandtheUMP:SummaryofRelationships .. WelfareEvaluationforanArbitraryPriceChan ge .. 834 Topics in Consumer DoesindividualWARP implyaggregateWARP?

3 So Were They Just Lying to Me When I Studied Intermediate Micro? .. ConsumptionWithEndowments ..101iiNolan MillerNotes on Microeconomic Theoryver: Aug. Consumption with Endowments: A Simple Separation Theorem .. DiscountingandPresentValue .. TheTwo-PeriodModel .. Producer Properties of the Net Supply and ProfitFunctions .. ANoteonRecoverability .. CostMinimization .. Properties of the Conditional Factor Demand and Cost Functions .. WhyDoYouKeepDoingThistoMe?.. TheGeometryofCostFunctions .. Aggregation of Supply .. AFirstCrackattheWelfareTheorems .. ConstantReturnsTechnologies .. Agricultural Household Models with Complete Markets .. 1496 Choice Under TheExpectedUtilityTheorem.

4 MillerNotes on Microeconomic Theoryver: Aug. Measuring Risk Aversion: Coefficients of Absolute and Relative Risk ComparingRiskAversion .. A Note on Comparing Distributions: Stochastic Dominance .. SomeApplications .. Insurance .. InvestinginaRiskyAsset:ThePortfolioProbl em ..1827 Competitive Markets and Partial Equilibrium PartialEquilibriumAnalysis .. Set-UpoftheQuasilinearModel .. AnalysisoftheQuasilinearModel .. A Bit on Social Cost and ComparativeStatics .. The Fundamental Welfare Theorems .. WelfareAnalysisandPartialEquilibrium .. EntryandLong-RunCompetitiveEquilibrium .. Long-RunCompetitiveEquilibrium .. Externalities and Public WhatisanExternality?.. BilateralExternalities .. Bargaining and Enforceable Property Rights: Coase s Theorem.

5 ExternalitiesandMissingMarkets .. PublicGoodsandPurePublicGoods .. MillerNotes on Microeconomic Theoryver: Aug. SimpleMonopolyPricing .. Two-Part Tariffs .. PriceDiscrimination .. Second-DegreePriceDiscrimination .. NaturalMonopolyandRamseyPricing .. FurtherTopicsinMonopolyPricing .. Multi-ProductMonopoly .. IntertemporalPricing .. MillerNotes on Microeconomic Theoryver: Aug. 2006 These notes are intended for use in courses in microeconomic theory taught at Harvard Univer-sity. Consequently, much of the structure is inherited from the required text for the course, whichis currently Mas-Colell, Whinston, and Green sMicroeconomic theory (referred to as MWG inthese notes). They also draw on material contained in Silberberg sThe Structure of Economics,aswell as additional sources.

6 They are not intended to stand alone or in any way replace the the early drafts of this document, there will undoubtedly be mistakes. I welcome commentsfrom students regarding typographical errors, just-plain errors, or other comments on how thesenotes can be made more thank Chris Avery, Lori Snyder, and Ben Sommers for helping clarify these notes andfindingmany 1 The Economic ApproachEconomics is a social sciences are concerned with the study of human you asked the next person you meet while walking down the street what defines the differencebetween economics and other social sciences, such as political science or sociology, that personwould most likely say that economics studies money, interest rates, prices, profits, and the like,while political science considers politicians, elections, etc.

7 , and sociology studies the behavior ofgroups of people. However, while there is certainly some truth to this statement, the things thatcan be fairly called economics are not so much defined by a subject matter as they are united bya common approach to problems. In fact, economists have written on topics spanning humanbehavior, from traditional studies offirm and consumer behavior, interest rates, inflation andunemployment to less traditional topics such associal choice, voting, marriage, and feature that unites these studies is a common approach to problems, which has becomeknown as the marginalist or neoclassical approach. In a nutshell, the marginalist approachconsists of four principles:1. Economic actors have preferences over allocations of the world s resources.

8 These preferencesremain stable, at least over the period of time under There are constraints placed on the allocations that a person can achieve by such things aswealth, physical availability, and social/political Given the limits in (2), people choose the allocation that they most Silberberg sStructure of Economicsfor a more extended discussion along these preferences that change can be captured by adding another attribute to the description of an on this MillerNotes on microeconomic theory : Chapter 1ver: Aug. 20064. Changes in the allocations people choose are dueto changes in the limits on available resourcesin (2).The marginalist approach to problems allows theeconomist to derive predictions about behaviorwhich can then, in principle, be tested against real world data using statistical (econometric)techniques.

9 For example, consider the problem of what I should buy when I go to the grocerystore. The grocery store isfilled with different types of food, some of which I like more and some ofwhich I like less. Principle (1) says that the trade-offs I am willing to make among the various itemsinthestorearewell-defined and stable, at least over the course of a few months. An allocation isallofthestuffthat I decide to buy. The constraints (2) put on the allocations I can buy includethe stock of the items in the store (I can t buy more bananas than they have) and the money inmy pocket (I can t buy bananas I can t afford). Principle (3) says that given my preferences, theamount of money in my pocket and the stock of items in the store, I choose the shopping cart fullof stuffthat I most prefer.

10 That is, when I walk out of the store, there is no other shopping cartfull of stuffthat I could have purchased that I would have preferred to the one I did (4) says that if next week I buy a different cart full of groceries, it is because either I haveless money, something I bought last week wasn t available this week, or something I bought thisweek wasn t available last are two natural objections to the story I told in the last paragraph, both of which pointtoward why doing economics isn t a trivial exercise. First, it is not necessarily the case that mypreferences remain stable. In particular, it is reasonable to think that my preferences this weekwill depend on what I purchased last week. For example, if I purchased chocolate chip cookieslast week, this may make me less likely to purchase them this week and more likely to purchasesome other sort of cookie.