Game Theory
Definition
Game theory is the study of mathematical models of
conflict and cooperation between intelligent and
rational decision makers.
Rational: each individual maximizes her expected
utility
Intelligent: individual understands situation,

ECON300
COMPARATIVE STATICS
BASICS of DIFFERENTIAL CALCULUS
EXAM Thursday Feb 26
Exam #1 will cover chapters 1-4. Exam #2 will cover chapters 6-10.
Exam will begin at 11:00 am promptly. It will end at 11:50am promptly.
A non-graphing, non-communicative ca

ECON300
SYSTEMS OF EQUATIONS
COMPARATIVE STATICS
ECONOMIC Relationships
Some relationships are functions, but not all of them
ECONOMIC relationships come in three main flavors:
1. Definitions: Are true based on definitions of concepts
Profit = Total Cost

ECON300
PRESENT VALUE (finish up)
LOG FUNCTIONS
Exponential Functions
Log function (inverse of exponential)
Present Value
Well, we divide instead of multiply:
r is the interest rate paid yearly
Value of X in 1 time period, today, is X/(1+r)
Value of X in

ECON300
1. THE DIFFERENTIAL
2. MORE DERIVATIVES
Differential
Its a way to approximate the change of
a function using the derivative
DERIVATIVE slope of tangent line at a particular
point on the function
DIFFERENTIAL movement along the tangent line
to esti

ECON300
2/5/15
Functions 3
Roots of a quadratic function (2
nd
order)
+ + =0
Two ways to find them:
1.Play around with factors of a and c to see if
you can calculate b
OR
2. Use the quadratic formula:
S
Rules of Exponents
0
x =1
1
x =x
-1
x =1/x
a b
b a

ECON300
2/3/15
FUNCTIONS 2
Outline of first two weeks
Properties of functions (2.1, 2.2)
Types and Rules of functions (2.3)
Exponential and Logarithmic Functions (3)
Hidden chapter 0 in back of the book!
Average Rate of Change
Slope of line connecting

ECON300
1/29/14
FUNCTIONS
ASTS tutor for ECON300
- Service is free
- Tutoring is appointment based
- One-on-one or small-group tutoring available
- All requests are made through the Tutorial
Coordinator at ChrisHne DuchouqueJe at
cduchou@umd.edu
Tutor(s)

ECON300
BASICS of DIFFERENTIAL CALCULUS
Midterm
Average/Median around 15.5/25 = 62%
Please review your responses Identify
what you DO know but made a silly error,
and what you DONT know and seek
assistance in understanding those concepts.
th
Midterm #2 is

Problem Set 6 Solutions
December 4, 2015
1
1.1
Question One
Part A
Find the local max and local min for the function
y=
FOC:
1 3
x x2 8x + 2
3
dy
= x2 2x 8 = 0
dx
(x 4)(x + 2) = 0
x = -2 or x = 4
SOC:
d2 y
= 2x 2
dx2
d2 y
x = 2 : 2 = 6 < 0
dx
d2 y
x=4: 2

Y= f(X) or Y = f(X,W)
Functions map every X (or X and W) with a single Y
The set (S) of all possible Xs (or combination of inputs)
is called the DOMAIN
eg: Sx = cfw_X|X>0 read as The set of all Xs such that
X is greater than zero
The set of all possibl

NAME:
UID:
Section:
UMCP ECON 300 - Methods and Tools for Economic Analysis
UMBC ECON 490 - Analytical Methods in Economics Spring 2016 - FINAL EXAM
Prof. Montgomery
SOLUTIONS
PART A: Each question is worth 1 or 1.5 points. Provide the choice that best an

ECON 300 Fall 2016
Professor Montgomery
Problem Set #1 (September 9)
Ricky Kapoor Section 0101
See work attached
1.)
3
(a)
x
(b)
8
x 2 or
x2 y2
(c)
(d)
x
1
11
2
y
17
x2
7
2
2.)
(a) Fixed Cost Function F ( C )=600
Variable Cost Function V (C )=5 c
Total Co

ECON300: Methods and Tools of
Economic Analysis
Spring 2015
Dr. Nicholas Montgomery
Oce Hours and contact info
Prof. Montgomery
TYD4118M
Mon 1-4
Ian Chadd (101, 104, 105)
TYD4128
Mon 11-12
Thr 9-10:30
Wed 11-12
Hector Lopez Carbajal (102, 103, 106)
TYD411

Why do we use calculus?
Economics generally assumes
Rational optimizers.
Consumers maximize utility
Producers maximize profits
MLB owners maximize profits and wins
Political parties maximize election wins
You maximize some combination
grades and fun
Wh

7/2/2014
Decision Making
Under Uncertainty
1
Uncertainty
Consumers and firms are usually uncertain about the
payoffs from their choices
Example 1: A farmer chooses to cultivate either apples or
pears
When he makes the decision, he is uncertain about th

Constrained Optimization
Constraints
Limited budget
Limited revenue
Limited hours to work
.
Scarce resources create constraints
Constrained optimization
Includes an objective function and constraints
Choose variables (x1,x2) to maximize (or minimize)
a

Extreme Values of
Univariate Functions
Economic models determine optimal
outcomes, consumption, interest rates,
Calculate maximum value to identify
Highest profit
Highest utility
Highest tax revenue
Calculate minimum value to identify
Lowest cost
L

Multivariate Calculus
Multivariate calculus
Calculus with single variable (univariate)
y f ( x)
Calculus with many variables (multivariate)
y f ( x1 , x2 ,., xn )
Partial derivatives
With single variable, derivative is change in y in
response to an inf

7/14/2013
Basics of Differential Calculus
Why differential calculus?
Models explain economic behavior with system of
equations
What happens if a variable changes?
Comparative statics determines marginal change in
economic behavior
How does change in t

7/5/2013
Exponential and Logarithmic
Functions
Modeling growth
Exponential functions
Constant percentage growth per unit time
Logarithmic functions
Inverse of exponential functions
1
7/5/2013
Growth of money
Interest rate r
Value of Xt after 1 time

6/30/2014
Introduction to Probability
1
Examples
1) Which of the following outcomes is more likely when rolling a
die 5 times?
A) 1,6,3,2,5
B) 1,1,1,1,1
2) Here are the results of 9 coin flips: HHHHHHHHH
What is the most likely outcome for the 10th coin?

Extreme Values of
Multivariate Functions
Extreme values of multivariate functions
In economics many problems reflect a need to
choose among multiple alternatives
Consumers decide on consumption bundles
Producers choose a set of inputs
Policy-makers ma

7/14/2013
Systems of Equations and
Comparative Statics
Systems of equations
Model many participants
Model many markets
Model many related variables
Solving systems of equations
Comparative statics
Find impact of change in exogenous variable on
endog

Functions
Function
A mapping from each x in X to some y in Y
f: XY
Domain is X; Range (or Co-domain) is Y
y = f(x)
Each x maps into only one y
y exists and is unique
If I know x, I can determine y
Is it a function?
y
x
No! Cant say what y is knowing

f ( x )=lim f ( x )=f (a)
Functions: f(x) is a continuous function if xlim
a
x a
Monotonicity: increasing or decreasing. Strictly monotonic: strictly increasing or decreasing.
Instantaneous Rate of Change: f ( b )f (a)/ba
Convexity: Convex if average rate

Social preference if we know how the individuals rank various allocations we would
like to use this to develop a social ranking
Few problems: manipulation- changing the order on which things are voted. Rank
order voting- manipulated by introducing new alt