Notes on microeconomics

Intermediate Microeconomic Theory

Undergraduate Lecture Notes

by Oz Shy

University of Haifa November 1997–January 1998 File=Micro16 Revised=2000/06/19 22:18

Contents
Remarks v

I
1

Semester ℵ

1

Consumer Theory 2 1.1 Major Issues 2 1.2 Budget Constraints 2 1.3 Preferences and Utility Functions 2 1.4 Indifference Curves 3 1.5 The consumer’s utility maximization problem 1.6Demand functions 5 1.7 Elasticity 6 1.8 Compensated demand 9 1.9 Slutski decomposition 10 1.10 Revealed preferences 10 1.11 Indexes 11 1.12 Consumer surplus 13 1.13 Commodity Endowment 15 1.14 Labor supply 17 1.15 Saving & Loans 18 Uncertainty Models 21 2.1 The Expected Utility Hypothesis 21 2.2 Defining risk aversion 21 2.3 Insurance 22 2.4 Consumer equilibrium: optimal insurance level 2.5 Freeentry competitive insurance industry 23 2.6 Diversification of portfolios to reduce risk 24 Producer Theory 25 3.1 The Production Function 25 3.2 Properties of CRS production functions 3.3 Short-run Production Function 27 3.4 Cost Functions 27 3.5 Profit Maximization 30

4

2

23

3

26

Remarks
• Notes prepared during the 1st semester at the University of Haifa, Nov.97–Jan.98(Tash-Nach) • For a Syllabus see a separate handout in Hebrew (summarized by the present Table of Content) • Texts: 1. Blumental, Levhari, Ofer, & Sheshinski, 1971. Price Theory. Academon Press. 2. Varian H, 1987, Intermediate Microeconomics, W.W. Norton • Lecture is 3 × 45 minutes (given nonstop once a week

Department of Economics, University of Haifa (June 19, 2000) ozshy@econ.haifa.ac.il

Part ISemester ℵ

Lecture 1 Consumer Theory
1.1 Major Issues • Characterizing the behavior of a competitive optimizing consumer • Deriving consumer demand functions from utility maximization • Consumer problem is divided into “objective” problem (the budget — determined by prices and income); and “subjective” problem (preference, or like) • Major assumption: consumers are competitive (take prices &income as given). • Why focusing on 2 goods? 1.2 Budget Constraints • Define the commodity space as R + • Define a bundle as a pair (x, y). • px x + py y ≤ I (set) =⇒ y = • Drawing: Intercepts • Slope = − px py • Income changes, price changes • Effects of pure inflation λpx , λpy , and λI 1.3 Preferences and Utility Functions
I px I py I py px py x

−

and

Let A, B, & C denote bundles (e.g.,A = (x0 , y0 ), B = (x1 , y1 ), etc.) • In economics, a consumer is a preference ordering over bundles (subjective) • Define a preference ordering of a consumer (a) Completeness: Either A (b) Transitive: A B and B B or B C =⇒ A as a binary relation on R + satisfying: C

A for all A, B ∈ R +

• In most of our analysis we assume that a consumer’s preference ordering satisfies monotonicity: where(x, y0 ) (x0 , y0 ) for all x ≥ x0 ; and (x0 , y) (x0 , y0 ) for all y ≥ y0 ; and (x, y) (x0 , y0 ) for all x > x0 and y > y0

Consumer Theory

3

• Theorem: Under the 3 axioms, there exists a function U , called utility function, U : R + → R satisfying (x0 , y0 ) (x1 , y1 ) if and only if U (x0 , y0 ) U (x1 , y1 ) 1.4 Indifference Curves • An indifference curve for a given utility level U0 isthe set of all bundles, (x, y) ∈ R + yielding U (x, y) = U0 • Properties of indifference curves: (a) Never intersect (b) Monotonicity ⇒ downward sloping • Rate of Commodity Substitution: RCS(x, y) = Sy,x = • Marginal Utility: MU(x, y)x = • Proposition: RCS(x, y) = −
def def

dy dx

U0

∂U (x, y) ∂x

and

MU(x, y)y = MU(x, y)x MU(x, y)y
def

def

∂U (x, y) ∂y

Proof 1: Define theimplicit function F (x, y(x) = U (x, y) − U0 = 0. Then, by the implicit function Theorem ∂y(x) MUx (x, y) ∂F (x, y)) =− = − ∂U∂x = − (x,y) ∂x ∂x MUy (x, y)
∂y ∂U (x,y)

Proof 2: Totally differentiating U (x, y) = U0 yields MUx dx + MUy dy = dUo = 0 =⇒ MUx (x, y) dy =− dx MUy (x, y)

• Demonstration of various preferences (utility function) 1. Non-monotonic: (a) Bliss point (b) Non-monotonic...