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!
- Write an equation for the tangency condition.
- Write an equation for the budget line.
- Solve for \(x_1^*\) or \(x_2^*\).
- 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
