Economics 101A  Section 1
Mykyta Bilyi and Jing Li
1
Unconstrained Optimization
In this class we will study economic problems from the perspective of consumers and from the perspective of producers. For our study of consumers we will usually maximize the
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Section 3.2
Mean of a Distribution
The mean of a probability distribution
P(x) over a finite set of numbers x
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Section 5.4
Operations on Random Variables
Question: How to compute the distribution of Z = f(X,Y)?
Examples:
Introduction to probability
Stat 134
FAll 2006
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Sections 1.11.3
12/3/2006
Probability as Proportion
Suppose there are 20 people taking Stat 134.
There are 7
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Sections 1.6
12/3/2006
Multiplication rule for 3 Events
The Multiplication rule for two events says:
P(AB) =
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Sections 1.41.5
12/3/2006
Three draws from a magic hat.
12/3/2006
draws3from
a magic
hat.hat:
SpaceThree
of
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Section 5.2
Joint Desity
The density function f(x,y) for a pair of RVs X
and Y is the density of probability
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Section 3.1
X is the sum of two dice.
X
(
) =7
X
(
) =5
X
(
) =5
X
(
) =5
Probability
distribution
histogram
Module 2 Study Guide
Section I
1. What are the general underlying factors behind supply and demand in a
typical product market?
Competition is a key factor for both buyers and sellers. Buyers, who
represent the demand curve, seek out good deals in order t
1. How are the concepts of scarcity, efficiency, and equity related?
Scarcity is the natural condition of all things: people have unlimited wants,
but there is a limited quantity of the things they want. As a result, not
everyone can get everything he wan
1. The process by which a firm transforms capital, land, labor, and
entrepreneurship into consumer goods and services is production.
2. Accounting profit measures revenue against expenditures, to include the
depreciation that results from using capital. E
1
2
3
4
Section I
Why is the demand for resources such as labor and capital said to
be a derived demand?
The demand for labor and capital is derived from the demand for
the goods and services they produce. The more demand for those
goods and services, the
Module 7 study guide
1
2
3
Section I
Explain the meaning of externalities, including
external costs and external benefits. Give examples.
Externalities are costs and benefits to production that
accrue outside of the firm. For example, energy
production ha
1
2
Module 6 Review Questions
Section I
Explain how increasing competition impacts supply in a market
and what its effect is.
First off, competition arises when the market has room for many
firms and when people see that existing firms in an industry are
Module 1 Review Questions
1. What does economics study?
Economics studies the production and consumption of finite resources.
Scarcity exists because all resources are finite, and not everyone can have as
much as they want of everything they want.
2. What
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Section 2.5
Sampling with replacement
Suppose we have a population of size N with
G good elements and B bad e
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Section 2.1
Toss a coin Binomial
100, whatsDistribution
the chance of 60
?
P(a sequence with 60 ) =
(#of sequ
Economics 101A  Section 2
Mykyta Bilyi and Jing Li
1
Implicit Function Theorem (IFT)
I. Univariate case. Consider an equation f (p, x) = 0 and a point (p0 , x0 ) that solves this equation.
In the most common case for this class the equation is your F.O.C
Economics 101A  Section 4
Mykyta Bilyi and Jing Li
1
Preferences: Introduction
Economists often call upon utility functions to help describe behavior. In particular, they model
agents as utility maximizers. However, none of us actually take a set of feas
Economics 101A  Section 5
Mykyta Bilyi and Jing Li
1
Marginal Rate of Substitution (MRS)
Denition: In the case of two goods the slope of an indierence curve is called the marginal rate
of substitution or MRS. It represents the amount units of good x2 tha
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Sections 6.4
Do taller people make more money?
Question: How can this be measured?

Ave (height)
wage at 19
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Sections 6.5
Bivariate Normal
Let (X,Y) be independent Normal variables.
1
( x2 + y2 )
1
2
The joint density
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Section 5.1
Uniform distribution in an area
Y
Sample space is D.
D
Outcomes are points in D with
random coord
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Section 4.5
Cumulative Distribution Function
Definition: For a random variable X, the function
F(x) = P(X x),
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Section 4.1
Examples of Continuous Random
Variables
Example 1:
X  The distance traveled by
a golfball hit b
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Sections 6.16.2
# of Heads in a Random # of Tosses
Suppose a fair die is rolled and let N be the number
on t
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Sections 6.3
Conditional density
Example: (X,Y) uniform in the
unit disk centered at 0.
Question:
Answer:
Que
Introduction to probability
Stat 134
FAll 2005
Berkeley
Lectures prepared by:
Elchanan Mossel
Yelena Shvets
Follows Jim Pitmans
book:
Probability
Section 3.4
Different types of Distributions
Finite distribution take only finitely many values.
Examples of
Module 4 review questions
1
2
3
4
Explain the law of demand. What makes the inverse relationship
between supply and demand nearly universal?
The law of demand states that as the price of something increases,
the quantity demanded will decrease, while if t