Welcome!
Please sit in the first five rows.
It's not a big class. :)
Welcome &
Review of Econ 50
Christopher Makler
Stanford University Department of Economics
Econ 51: Lecture 1
pollev.com/chrismakler
What is an economic issue you care deeply about?
Did what we studied in Econ 50 offer a good model for this issue?
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.
Today's Agenda
Part 1: Course Overview
Part 2: Review of Econ 50
Themes of the course
Course schedule
Grading policies
Good 1 - Good 2 Space
Budget Constraints
Preferences and Utility
Optimal Choice
Demand
Three Central Themes
-
Efficiency and Equity
-
Time
-
Information
Weeks 1-3
Efficiency and Equity
Weeks 8-9
Game Theory II: Asymmetric Information
Quarter Rhythm
Weeks 5-7
Game Theory I: Perfect Information
Thursday 4/25
Midterm
Wednesday 6/12,
12:15-3:15pm
Final Exam
Week 4
Externalities
Week 10
Public Goods and Public Choice
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.
Monday
Reading and quiz for Tuesday's lecture
Thursday
Lecture; do second half of problem set exercises
Thursday & Friday
Section; office hours
Weekly Rhythm (Suggested)
Wednesday
Reading and quiz for Thursday's lecture
Tuesday
Lecture; do first half of problem set exercises
Weekend
Review material from the week
Do practice exam problems
Finish & hand in problem set
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: 5% of your grade
These are challenging, and I don't expect you to be perfect; 20% bonus given -
In-class polls: 5% of your grade.
Graded for correctness, not just completion; but 20% added to your grade. -
Homework: 20% of your grade.
Max 15 points per pset, max 100 points overall -
Exams: 70% of your grade (30% midterm, 40% final exam)
If you miss the midterm, the final counts for all 70%. Don't do this if at all possible.
Most of you will get 100% (or close) on your quizzes, pollev, and homework;
your grade will largely be determined by the exams.
So, use the quizzes, lecture, and homework to prepare for the exams!
I Know The Final Is On The Last Day of Finals Week
-
You must take final here in person unless you're traveling on Stanford business, or if you've started a summer job or internship.
-
If you have a summer job or internship, you are responsible for finding someone official to administer the test concurrently with the rest of the class. We need to know who that's going to be by Memorial Day (end of Week 8).
I'm really sorry.
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.
UCSD Videos
UCSD has video libraries for both intermediate micro and game theory...and they've let you have them for free! :) Information about how to sign up and which videos are most relevant will be posted on ED.
Review of Econ 50
pollev.com/chrismakler
When did you take Econ 50?
How well do you remember it?
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:}
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
Preferences
Definition Review:
Indifference Curves
Preferred/Dispreferred Sets
Marginal Rate of Substitution
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: }
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
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
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
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.
pollev.com/chrismakler
Find the optimal bundle for the Cobb-Douglas utility function is
u(x_1,x_2) = \ln x_1 + \tfrac{1}{4} \ln x_2
and the budget constraint is
1.2 x_1 + x_2 = 60
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've filled out the section survey.
Do the reading and the quiz -- due at 11:15am on Thursday!
Look over the summary notes for this class.
Econ 51 | 01 | Welcome and Review of Econ 50
By Chris Makler
Econ 51 | 01 | Welcome and Review of Econ 50
Welcome and Review of Econ 50
