Welcome &
Review of Econ 50

Christopher Makler

Stanford University Department of Economics

Econ 51: Lecture 1

Today's Agenda

Part 1: Course Overview

Part 2: Review of Econ 50

Who is the Econ 51 teaching team?

What is this course about?

When will we study each topic? 

Why is this class important?

How do we all succeed?

Good 1 - Good 2 Space

Budget Sets

Indifference Curves

Optimal Choice

Demand

 

Who

Chris Makler

  • B.A.: Humanities, Yale
  • Ph.D.: Economics, Penn
    (search & matching theory)
     
  • 10 years in the education technology industry
     
  • Teaching Econ 50 & 51 since 2015
     
  • Office: Landau Econ Building, Room 144

Welcome to Econ 50!

Frank Wolak

Director of Undergraduate Studies

wolak@stanford.edu

Welcome to the Econ Major!

Joanne DeMarchena

Undergraduate Student Service Officer

jdemar@stanford.edu

TA Intros

Econ Department Peer Advising

Other Resources

VPTL Peer Tutoring

What

Three Central Themes

  • Efficiency and Equity

  • Time

  • Information

When

Weeks 1-2

Unit I: Exchange Optimization

Tuesday 10/19

Midterm (closed-book exam, in class)

Weeks 5-7

Unit III: Game Theory

Weeks 8-10

Unit IV: Asymmetric Information and Mechanism Design

Friday 12/10

Final Exam

Quarter Rhythm

Weeks 3-4

Unit II: Efficiency and Equity

Sunday 10/4-Monday 10/5

Checkpoint 1 (open-book exam, on your time)

Monday 11/1-Tuesday 11/2

Checkpoint 2

Why

How

Please be fully present in lecture.

No phones.

No tablets (except to take notes on with a stylus).

No laptops.

I'm not a monster. There will be a break in the middle of each class to connect with your digital world.

Before Lecture

  • Read the textbook and take online quizzes on the major points to be prepared for learning in lecture

Lecture

  • Presents new ideas
  • Illustrate those ideas with simple examples

After Lecture

  • Exercises for each lecture are designed to help you understand nuance
  • More complex examples and applications than in lectures; work on connecting the dots

After Each Unit

  • Exam questions will ask you to apply concepts from lecture to new situations you haven't seen before.
  • Use checkpoints to solidify your knowledge
  • Use midterm and final to demonstrate your knowledge and abilities

Grading Policy

  • This course is not graded on a curve.
    If everyone gets an A, everyone gets an A; if everyone gets a B, everyone gets a B.

  • Reading quizzes: 10% of your grade. One for each lecture; lowest 5 dropped.

  • Problem sets: 25% of your grade. One for each lecture; lowest 5 dropped.

  • Checkpoints: 15% of your grade. Higher score = 10% of grade, lower score = 5%.

  • Midterm/final: 50% of your grade. Higher score = 30% of grade, lower score = 20%.

Course Web Sites

All content is posted/linked within Canvas.

Each lecture has its own module with everything you need to know about that lecture.

Please use Ed Discussions to ask questions (not email).

Please upload your homework to Gradescope by 8am the morning after it's due.

The Small Print

  • Names and pronouns
  • Students with documented disabilities
  • Stanford University Honor Code
  • Econ Department syllabus
  • Humor gone wrong

Review of Econ 50

Good 1 - Good 2 Space

Two "Goods" : Good 1 and Good 2

\text{Bundle }X\text{ may be written }(x_1,x_2)
x_1 = \text{quantity of good 1 in bundle }X
x_2 = \text{quantity of good 2 in bundle }X
A = (40, 160)
B = (80,80)
\text{Examples:}

1

m = \text{money income}
p_1 = \text{price of good 1}
p_2 = \text{price of good 2}
\text{horizontal intercept} = \frac{m}{p_1}
\text{vertical intercept} = \frac{m}{p_2}
\text{slope of budget line} = -\frac{p_1}{p_2}

Budget Constraints

\text{Example: } p_1 = 2, p_2 = 1, m = 240

2

Preferences

Definition Review:

Indifference Curves

Preferred/Dispreferred Sets

Marginal Rate of Substitution

3

Utility Functions

u(x_1,x_2) = x_1x_2
MU_1(x_1,x_2) = \frac{\partial u(x_1,x_2)}{\partial x_1} =
MU_2(x_1,x_2) = \frac{\partial u(x_1,x_2)}{\partial x_2} =
MRS(x_1,x_2) = \frac{MU_1}{MU_2} =
MRS(40,160)=
MRS(80,80)=
u(40,160) =
u(80,80)=
\text{Example: }

4

MRS > \frac{p_1}{p_2}
MRS < \frac{p_1}{p_2}

Indifference curve is
steeper than the budget line

Indifference curve is
flatter than the budget line

Moving to the right
along the budget line
would increase utility

Moving to the left
along the budget line
would increase utility

More willing to give up good 2
than the market requires

Less willing to give up good 2
than the market requires

The “Gravitational Pull" Towards Optimality

POINT A

POINT B

5

IF...

THEN...

The consumer's utility function is "well behaved" -- smooth, strictly convex, and strictly monotonic

The indifference curves do not cross the axes

The budget line is a simple straight line

The optimal consumption bundle will be characterized by two equations:

MRS = \frac{p_1}{p_2}
p_1x_1 + p_2x_2 = m

More generally: the optimal bundle may be found using the Lagrange method

Optimal Choice

6

Optimal Choice

Otherwise, the optimal bundle may lie at a corner,
a kink in the indifference curve, or a kink in the budget line.
No matter what, you can use the "gravitational pull" argument!

  1. Write an equation for the tangency condition.
  2. Write an equation for the budget line.
  3. Solve for \(x_1^*\) or \(x_2^*\).
  4. Plug value from (3) into either equation (1) or (2).
u(x_1,x_2) = x_1x_2

Solving for Optimality when Calculus Works

p_1 = 2, p_2 = 1, m = 240
x_1^*(p_1,p_2,m)
x_2^*(p_1,p_2,m)

(Gross) demand functions are mathematical expressions
of endogenous choices as a function of exogenous variables (prices, income).

(Gross) Demand Functions

u(x_1,x_2) = x_1x_2
p_1x_1 + p_2x_2 = m

8

x_1^*(p_1,p_2,m) = \frac{a}{a+b}\times \frac{m}{p_1}

For a Cobb-Douglas utility function of the form

Special Case: The “Cobb-Douglas Rule"

u(x_1,x_2) = x_1^ax_2^b

The demand functions will be

x_2^*(p_1,p_2,m) = \frac{b}{a+b}\times \frac{m}{p_2}

That is, the consumer will spend fraction \(a/(a+b)\) of their income on good 1, and fraction \(b/(a+b)\) of their income on good 2.

This shortcut is very much worth memorizing! We'll use it a lot in the next few weeks in place of going through the whole optimization process.

9

Functional forms for utility functions:

u(x_1,x_2) = av(x_1) + bv(x_2)
u(x_1,x_2) = v(x_1) + x_2
u(x_1,x_2) = \min\left\{\frac{x_1}{a},\frac{x_2}{b}\right\}

1. Weighted average of some common
"one-good" utility function \(v(x)\):

2. "Quasilinear": one good enters linearly
(in this case \(x_2\)), another nonlinearly:

3. Perfect complements:
not used as often, but helpful

v(x) = \ln x
v(x) = \sqrt{x}
v(x) = x
v(x) = x^2
u(x_1,x_2) = a \ln x_1 + b \ln x_2
u(x_1,x_2) = a \sqrt{x_1} + b\sqrt{x_2}
u(x_1,x_2) = ax_1 + bx_2
u(x_1,x_2) = ax_1^2 + bx_2^2

Cobb-Douglas (decreasing MRS)

Weak Substitutes (decreasing MRS)

Perfect Substitutes (constant MRS)

Concave (increasing MRS)

To Do Before Next Class

Be sure you're signed up for a section.

Do the reading and the quiz -- due at 10:45am on Thursday!

Look over the summary notes for this class.

Econ 51 - Fall 21 - Lecture 1

By Chris Makler

Econ 51 - Fall 21 - Lecture 1

Welcome and Review of Econ 50

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