Intermediate Microeconomics:
Competitive Market
February 27, 2012
Competitive Market
A competitive market is when:
rms are too small to aect price, they are price takers
there is free entry and exit of rms
prices are known, transaction costs are low
Profi
Intermediate Microeconomics:
Information
February 9, 2012
Information
So far we have assumed that individuals have all the information
necessary to make decisions
However, reality is that people have dierent information sets
We are going to look at what h
Intermediate Microeconomics:
Production and Costs
February 19, 2012
Production
A production function is the relationship by which inputs are
combined to produce output.
Production requires inputs, such as Labour and Machines. We
will denote labour with L
Chapter 1
Introduction
I. Defining Social Psychology
A. What is Social psychology
B. What Social Psychology is Not
1. Folk wisdom (common sense explanations)
2. Sociology
3. Personality
4. Philosophy
II Social influence is at the heart of Social Psycholog
Research Methods
I. Goals of Psychological Research
A. Description
B. Theory Building
1. Theory
2. Hypothesis
C. Causal Analysis
D. Application
II. Major Types of Research
A. Observational
1. Participant observation or non-participant
2. Archival research
Social Perception
Non-Verbal Behavior
I.
Facial Expressions
A.
1.
Are 6 universal types of emotions
2.
Factors that decrease decoding accuracy
a. Affect blends
b. People often appear less emotional than they
are.
c. Cultural differences
B.
Other Channels
Homework 4
Due Wednesday, October 10th,
1. In the kingdom of Far Far Away there are coins of values 1, 2 and 3 dollars. In how
many ways can the people of Far Far Away change n dollars?
Hint:
1
=
1 + x + x2
1
3i
+
2
6
n=0
1
3i
2
2
n
+
1
3i
2
6
1
3i
+
2
2
Homework 4
Due Wednesday, October 10th,
1. In the kingdom of Far Far Away there are coins of values 1, 2 and 3
dollars. In how many ways can the people of Far Far Away change n
dollars?
Hint:
1
=
1 + x + x2
3i
1
+
2
6
n=0
1
3i
2
2
n
+
1
3i
2
6
1
3i
+
2
2
Homework 3 solutions
1. Label the couples 1, 2, ., n. Let AS be the set of all congurations
in which the couples in set S sit in front of each other. There are
n
possible seats for these couples. Also we have 2|S | ways to sit the
|S |
males and females o
Homework 3
Due Friday, September 28
1. Let there be n couples and 2 benches facing each other with n seats
each. In how many ways can the n couples sit on the benches such that
no two members of the same couple are facing each other? The answer
can be in
Solutions to homework 2
1.
0ikn
n
k
n
k
n
=
i
k=0 k
k
i=0
n
k
n
=
2k
= (1 + 2)n = 3n
i
k
k=0
2. We dene PATH> (n, n) as the set of paths in an n by n grid that are
strictly above the diagonal. That is, PATH> (n, n) is the set of all paths in
PATH (n, n) t
21-301 Combinatorics
Homework 2
Due: Friday, September 14
1. Show that for any n 0
0ikn
n
k
k
i
= 3n ,
where the sum goes over all integer pairs i, k such that 0 i k n.
2. In class we have dened the Cataln number Cn to be |PATHS (n, n)| and showed that
n
21-301 Combinatorics
Homework 1
Due: Wednesday, September 5
1. How many integral solutions of
x1 + x2 + x3 + x4 + x5 = 100
satisfy x1 6, x2 10, x3 3, x4 4 and x5 4?
2. Show that
n
n
k
k
=
n
2n .
k=0
3. How many ways are there of placing k 1s and 2n k 0s a
GOALS ON COMPOUND STATEMENTS
At the end of this class, you are expected to know:
How to form compound statements by correctly using the logical connectives
How to construct truth tables for compound statements
The order of logical connectives
How to trans
21-301 Combinatorics
Homework 9
Due: Monday, December 3
1. How many ways are there of k -coloring the squares of the above diagram if the group
acting is e0 , e1 , e2 , e3 where ej is rotation by 2j/4. Assume that instead of 28 squares
there are 4n 4.
Sol
21-301 Combinatorics
Homework 9
Due: Monday, December 3
1. How many ways are there of k -coloring the squares of the above diagram if the group
acting is e0 , e1 , e2 , e3 where ej is rotation by 2j/4. Assume that instead of 28 squares
there are 4n 4.
2.
21-301 Combinatorics
Homework 8
Due: Monday, November 19
1. In a take-away game, the set S of the possible numbers of chips to remove is nite.
Show that the Grundy numbers g satisfy g (n) |S | where n is the number of chips
remaining.
Solution: Observe th
21-301 Combinatorics
Homework 8
Due: Monday, November 19
1. In a take-away game, the set S of the possible numbers of chips to remove is nite.
Show that the Grundy numbers g satisfy g (n) |S | where n is the number of chips
remaining.
2. Consider the foll
21-301 Combinatorics
Homework 7
Due: Monday, November 12
1. Let rn = r(3, 3, . . . , 3) be the minimum integer such that if we n-color the edges of the
complete graph KN there is a monochromatic triangle.
(a) Show that rn n(rn1 1) + 2.
(b) Using r2 = 6, s
21-301 Combinatorics
Homework 7
Due: Monday, November 12
1. Let rn = r(3, 3, . . . , 3) be the minimum integer such that if we n-color the edges of the
complete graph KN there is a monochromatic triangle.
(a) Show that rn n(rn1 1) + 2.
(b) Using r2 = 6, s
21-301 Combinatorics
Homework 6
Due: Monday, November 5
1. Let G be a bipartite graph with bipartition A, B where |A| = |B | = n. Let m be the
number of edges of G. Show that if r 2 and
n
m/n
2
> (r 1)
n
2
(1)
then G contains a copy of K2,r . Here K2,r is
21-301 Combinatorics
Homework 6
Due: Monday, November 5
1. Let G be a bipartite graph with bipartition A, B where |A| = |B | = n. Let m be the
number of edges of G. Show that if r 2 and
n
m/n
2
> (r 1)
n
2
then G contains a copy of K2,r . Here K2,r is a b
21-301 Combinatorics
Homework 5
Due: Monday, October 29
1. Let S1 , S2 , . . . , Sm and T1 , T2 , . . . , Tm be two partitions of the set X into sets of size k .
Show that there is a set cfw_s1 , s2 , . . . , sm that is a set of distinct representatives
21-301 Combinatorics
Homework 7
Due: Monday, October 29
1. Let S1 , S2 , . . . , Sm and T1 , T2 , . . . , Tm be two partitions of the set X into sets of size k .
Show that there is a set cfw_s1 , s2 , . . . , sm that is a set of distinct representatives