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


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



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


Wednesday 6/12,

Final Exam

Week 4


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


  • 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.


Reading and quiz for Tuesday's lecture


Lecture; do second half of problem set exercises

Thursday & Friday

Section; office hours

Weekly Rhythm (Suggested)


Reading and quiz for Thursday's lecture


Lecture; do first half of problem set exercises


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


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)
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


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} =
u(40,160) =
\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





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!

  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

(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.


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.