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Unformatted text preview: ECONOMICS 100A: MICROECONOMICS Summer Session I 2010 Tues, Thur 8:00-10:50am Professor Mark Machina TA: Travis Brayak Office: Econ Bldg 217 Center Hall 109 Office Hrs: Tu,Th 11:30-1:30 Office: Sequoyah Hall 232 Discussion Section: Office Hours: Fri 11-1 Friday 9:00-10:50am DATE TOPIC CSB 001 TEXT / MATH HANDOUT Jun. 29 Introduction & Mathematical Review #1 Ch. 1 / Sects. A, B Jun. 29 Mathematical Review #1 (continued) Jul. 1 Consumer Preferences: Utility Functions and Indifference Curves 3.1 Jul. 1 Consumer Preferences: Utility Functions and Indifference Curves (continued) 3.2 Jul. 6 Mathematical Review #2 Jul. 6 Utility Maximization and Demand Functions Jul. 8 Utility Maximization and Demand Functions (continued) Jul. 8 Consumer Surplus and Welfare Analysis Jul. 13 Mathematical Review #3 F,G,H Jul. 13 Mathematical Review #3 (continued) F,G,H Jul. 15 (Thursday) Midterm Exam Jul. 20 Comparative Statics of Demand 4.2 Jul. 20 Comparative Statics of Demand (continued) 4.3 Jul. 22 Comparative Statics of Demand (continued) 4.4, 4.5 Jul. 22 Supply of Labor: The Labor-Leisure Decision Jul. 27 Supply of Capital: The Consumption-Saving Decision 15.4 Jul. 27 Supply of Capital: The Consumption-Saving Decision (continued) 15.4 Jul. 29 Decision Making under Risk and Uncertainty 16.1, 16.2 Jul. 29 Decision Making under Risk and Uncertainty (continued) 16.3, 16.4 Jul. 31 (Saturday) FINAL EXAM 8:00-11:00am 2/C D, E 3.3, 3.4 4.1 5.1-5.4 5.5 TBA TEXT & READINGS: Microeconomics: Theory and Applications with Calculus (UCSD Custom Edition) by Jeffrey Perloff, Addison-Wesley, 2008. There is also a Math Handout, available on the web page. You are responsible for all the material in the assigned portions of these materials. EXAMS: Grades are determined on the basis of a Midterm Exam and a Final Exam. COURSE WEB PAGE: The course web page is at: This page contains useful information and materials about the course, including the Math Handout, Old Exam Questions, and information about the exams. ECON 100A COURSE OUTLINE I. INTRODUCTION AND MATHEMATICAL REVIEW #1 a. Domain of Microeconomic Analysis b. Circular Flow Diagram c. Stocks vs. Flows and the Dimensions of Economic Variables d. Calculus Review (Math Handout, Section A) Derivatives, Partial Derivatives and the Chain Rule Approximation Formulas for Small Changes in Functions (Total Differentials) e. Elasticity (Math Handout, Section B) Absolute, Proportionate and Percentage Changes in Variables Definition of Elasticity and Examples Constant Elasticity Functions f. Level Curves of Functions (Math Handout, Section C) Definition and Graphical Illustration Algebraic Formula for a Level Curve Formula for the Slope of a Level Curve II. CONSUMER PREFERENCES: UTILITY FUNCTIONS & INDIFFERENCE CURVES a. Commodities, Commodity Bundles and Preferences Commodities are Typically Flows, not Stocks Issue of Divisibility Weak Preference, Strict Preference and Indifference Relations b. Utility Functions Preferences are defined over Commodity Bundles, not Individual Commodities Utility Functions and Total Utility Curves Important Examples: Linear, Cobb-Douglas, Leontief Marginal Utility and Marginal Utility Curves Hypothesis of Diminishing Marginal Utility Monotonic Transformations of Utility Functions c. Indifference Curves and the Marginal Rate of Substitution Deriving a Consumer’s Indifference Curves from Their Utility Function General Properties of Indifference Curves: One Through Every Commodity Bundle Downward Sloping and Can’t Cross Marginal Rate of Substitution (MRS) Graphical Interpretation: Slope of the Indifference Curve Algebraic Formula: Ratio of Marginal Utilities Hypothesis of Diminishing Marginal Rate of Substitution III. MATHEMATICAL REVIEW #2 a. Scale Properties of Functions (Math Handout, Section D) b. Solving Optimization Problems (Math Handout, Section E) General Structure of Optimization Problems First and Second Order Conditions for Unconstrained Optimization Problems First Order Conditions for Constrained Optimization Problems c. Corner Solutions and Inequality Constraints IV. UTILITY MAXIMIZATION AND DEMAND FUNCTIONS a. Utility Maximization Subject to a Budget Constraint Graphical Illustration First Order Conditions for Utility Maximization Two Interpretations of the First Order Conditions Second Order Conditions (Hypothesis of Diminishing MRS) Corner Solutions: Graphical Illustration and Algebraic Condition Indirect Utility Functions and their Properties b. Regular (“Marshallian”) Demand Curves and Demand Functions Definition of Regular Demand Functions Examples: Cobb-Douglas, Leontief, Linear General Properties of Demand Functions: Walras’ Law Scale Invariant in Prices and Income Relationship between Price Elasticities & Income Elasticity for a Good Market Demand Functions c. Consumer Surplus and Welfare Analysis Consumer Surplus Equivalent and Compensating Variation Expenditure Functions V. MATHEMATICAL REVIEW #3 a. Comparative Statics of Solution Functions (Math Handout, Section F) b. Comparative Statics of Equilibria (Math Handout, Section G) c. Comparative Statics of Optimal Value Functions (Math Handout, Section H) VI. COMPARATIVE STATICS OF DEMAND a. Income Changes Income-Consumption Locus Engel Curves: Definition and Graphical Derivation Income Elasticity Superior, Normal and Inferior Goods Income Elasticity and Budget Shares Relationship Between Income Elasticities of All Goods Algebraic Derivation of the Effect of an Income Change b. Price Changes Price-Consumption Locus Graphical Derivation of Marshallian Demand Curves Own Price Elasticity Price Elasticity and Expenditures Cross Price Elasticity Gross Substitutes and Gross Complements Algebraic Derivation of the Effect of a Price Change c. Compensated Price Changes and Compensated (“Hicksian”) Demand Functions Graphical Illustration of a Compensated Price Change Graphical Derivation of Compensated Demand Curves Algebraic Derivation of Compensated Demand Functions Algebraic Derivation of the Effect of a Compensated Price Change d. The Slutsky Equation Expressing Each of the Three Basic Changes in Terms of the Other Two Graphical Illustration Algebraic Formulation and Informal Proof Giffen Goods VII. SUPPLY OF LABOR: THE LABOR-LEISURE DECISION Income-Leisure Space and the Labor-Leisure Decision First Order Conditions for Optimal Supply of Labor Comparative Statics: Income and Substitution Effects Backward Bending Supply of Labor Curves Kinked Budget Lines and the Overtime Decision VIII. SUPPLY OF CAPITAL: THE CONSUMPTION-SAVINGS DECISION Intertemporal Income and Consumption Streams Interest Rates and Discounted Present Value of a Stream Intertemporal Utility Maximization First Order Conditions and Interpretation Comparative Statics: Income and Substitution Effects IX. DECISION MAKING UNDER RISK AND UNCERTAINTY a. Outcomes, Lotteries and Expected Value Choice over Lotteries Expected Value The St. Petersburg Paradox b. Expected Utility Two-Stage Lotteries and the Independence Axiom von Neumann-Morgenstern Utility Functions and Expected Utility c. Risk Aversion Properties of Risk Averse Preferences Arrow-Pratt Measure of Risk Aversion Risk Aversion and Wealth d. Measures of Risk Aversion e. Demand for Insurance f. Investment in a Risky Asset FAMOUS OPTIMIZATION PROBLEMS IN ECONOMICS Optimization Problem Objective Function Constraint Control Variables Parameters Solution Functions Optimal Value Function Consumer’s Problem U(x1,...,xn) utility function p1⋅x1+...+pn⋅xn = I budget constraint x1,..., xn commodity levels p1,..., pn, I prices and income xi(p1,...,pn,I) regular demand functions V(p1,...,pn,I) indirect utility function Expenditure Minimization Problem p1⋅x1+...+pn⋅xn expenditure level U(x1,..., xn) = – u desired utility level x1,..., xn commodity levels p1,..., pn , – u prices and utility level hi(p1,...,pn , – ) u compensated demand functions e(p1,...,pn , – ) u expenditure function Labor/Leisure Decision U(H,I ) utility function H, I w, I0 I = I0 + w⋅(168 – H) leisure time, wage rate and budget constraint disposable inc. nonwage income 168 – H(w, I0) labor supply function V(w, I0) indirect utility function Consumption/ Savings Decision U(c1,c2) utility function c1 , c2 I1 , I2, i c2 = I2 + (1+i)⋅(I1– c1) c1(I1, I2, i), c2(I1, I2, i) consumption income stream and consumption functions budget constraint levels interest rate V(I1, I2, i) indirect utility function Long Run Cost Minimization w⋅L + r⋅K total cost F(L,K) = Q desired output L, K factor levels Q, w, r L(Q,w,r), K(Q,w,r) desired output and output-constrained factor prices factor demand functions LTC(Q,w,r) long run total cost function Long Run Profit Maximization P⋅Q – LTC(Q,w,r) total profit none Q output level P, w, r output price and factor prices Q(P,w,r) long run supply function π (P,w,r) long run profit function P, w, r output price and factor prices L(P,w,r), K(P,w,r) factor demand functions π (P,w,r) none L, K factor levels (in terms of Q) Long Run Profit P⋅F(L,K) – w⋅L– r⋅K Maximization total profit (in terms of L and K) long run profit function ...
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