Quiz 1, Math for Economics II, Solution (10 pts)
New York University, Juan Gonzalez Paris
Note: Show all your work, clearly and in order, if you want to get full credit.
2
1. Let f (x, y) = e(x+2y) .
(a) (2 pts) Find Dv f (1, 1) where v = i + j.
(b) (2 pt
Assignment 5, Math for Economics I (28 points)
Due Friday, October 17, in recitation
Write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will
not be given any credit. Please do not forget to:
Wr
Quiz 4, Math for Economics II, Solution (10 pts)
New York University, Juan Gonzalez Paris
Note: The quiz has two problems, one in the front and other in the back. Show all your
you want to get full credit.
1 1 1 1
0 3 2 1
1. Consider the system of equat
Math for Econ II, Written Assignment 2 Solutions (28 points)
1. (4 pts) Find all unit vectors which are perpendicular to 2, 7 .
(by perpendicular, we mean that the vectors meet at a right angle)
Solution: We use the formula 2, 7 u = | 2, 7 |u| cos . If a
Homework 1 Solutions (28 points)
1. (6 pts) Residents of the town of Maple Grove who are connected to the municipal water supply are billed a fixed
amount monthly plus a charge for each cubic foot of water used. In other words, the monthly bill is a linea
Assignment 7, Math for Economics I (28 points)
Due Friday, October 31st, in recitation
Write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will
not be given any credit. Please do not forget to:
Math for Econ II, Written Assignment 1 Solutions (28 points)
1. (5 pts) Let f (x, y) =
1
2
ln(x2 + y 2 ).
(a) (2 pts) What is the domain of f ? Very briey justify your answer.
(b) (3 pts) Suppose (a, b) is in the domain of f . Show that fxx (a, b) + fyy (
Assignment 2, Math for Economics I (28 points)
Due Friday, September 19, in recitation
Write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will
not be given any credit. For especially painful com
Math for Econ II, Written Assignment 4 (28 points)
1. (4 pts) The gures below show the optimal point (marked with a dot) in three optimization problems with the
same constraint. Arrange the corresponding values of from smallest to largest. Assume > 0 in e
Assignment 4, Math for Economics I (28 points)
Due Friday, October 3rd, in recitation
Write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will
not be given any credit. Please do not forget to:
W
Assignment 1, Math for Economics I (28 points)
Due Friday, September 12, in recitation
Write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will
not be given any credit. For especially painful com
Math for Econ I, Homework Assignment 2
Due Tuesday, February 18th
New York University
Please read sections 4.6, 4.8-4.10 and 5.1-5.3.
Please write neat solutions for the problems below. Show all your work. If you only write the answer with no work you
wil
Math for Econ II, Written Assignment 3 Solutions (28 points)
1. (4 pts) Find the dierential of the following functions.
(a) (2 pts)
f (x, y) =
y
1 + xy
(b) (2 pts) P (K, L, M ) = KM eL
Solution: (a)
2
M 2
df = fx dx + fy dy =
df =
y
(1 + xy)(1) y(x)
y d
Quiz 1, Math for Economics I (10 Points)
New York University
1. Each part is worth one point.
A What is your recitation section number? Section 8
B What is your TAs name? Chen Li
C What is your TAs email address? Chen.li.1077@nyu.edu
2. This question is w
Assignment 6, Math for Economics I (28 points)
Due Friday, October 24th, in recitation
Write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will
not be given any credit. Please do not forget to:
Assignment 6, Math for Economics I (28 points)
Due Friday, March 27th, in recitation
Write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will
not be given any credit. Please do not forget to:
Wr
Quiz 2, Math for Economics I (10 Points)
New York University
1- A contract offers you the following payments: you are paid $1000 new, $3000 one year from now, and
$2000 two years from now. Assuming an annual interest rate of 7% compounded annually, what i
Midterm 2, Spring 2015
Math for Economics I - section 1
New York University
(2 pages)
Read all of the following information before starting the exam:
Show all work, clearly and in order, if you want to get full credit. A correct answer without
supporting
Exam 1, Fall 2014
Math for Economics I
New York University, Jankowski
Name:
Recitation Section:
Read all of the following information before starting the exam:
On multiple choice questions, there is no partial credit, and you are not required to show you
Assignment 2, Math for Economics I (28 points)
Write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will
not be given any credit. For especially painful computations, you may use your calculator,
Assignment 2, Math for Economics I (28 points)
Due Friday, February 13, in recitation
Write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will
not be given any credit. For especially painful comp
Assignment 1, Math for Economics I (28 points)
Due Friday, February 6, in recitation
Write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will
not be given any credit. For especially painful compu
12-3w21
0
26. Figure 12.14 shows a contour map of a hill with two
paths, A and B.
(a) On which path, A or B, will you have to climb more
Math for Econ I-Worksheet9
12, 2012 09 : 16) [ex-3]
steeply?
Selin Kalaycioglu
(b) On which path, A or B, will you pro
Math for Econ I-Worksheet 2
main Sheet: 1 Page: 1 (September 16, 2012 18 : 48) [1-4aq2-main] Selin Kalaycioglu
Job: bchap1-temp Sheet: 38 Page: 38 (August 15, 2012 10 : 14) [ex-1-4]
New York University
1. In Figure below, which shows the cost and revenue
Math for Econ I, Homework Assignment 1 Solutions
Due Tuesday, February 11th
New York University
Please read sections 4.1 through 4.5 of the textbook.
Please write neat solutions for the problems below. Show all your work. If you only write the answer with
Higher-Order Derivatives
(6.9 in MFE book; 2.2 in e-book)
Section 1, Math for Economics 1
March 5, 2015
Main author: Jankowski
Higher orderderivatives
1/7
2nd derivative
Dierentiate f (x) to get the 2nd derivative of f , written f (x).
Example: If f (x) =
A variety of essential functions
(4.6-4.10 and 10.5 in MFE book, 1.2 in e-book)
Section 1, Math for Econ 1
February 3, 2015
Section 1, Math for Econ 1
A variety of essential functions
Some basic terminology we will discuss:
Revenue, cost, prot
Compound in
Continuity
(7.8 in MFE book; 1.5 in e-book)
Section 1 spring 2015, Math for Econ 1
February 12, 2015
Main author: Jankowski
Continuity
1 / 14
Warm-up
Consider the function f graphed below.
lim f (x) and f (4) both exist, but arent equal.
x4
( lim f (x) =
Linearization and Dierentials
Munn, Math for Economics 1
Section 7.4 in MFE textbook
Munn, Math for Economics 1 Section 7.4 in MFE textbook
Linearization and Dierentials
Overview and Motivation For Today
Concepts: linearization and dierentials. They help
MATH-UA.211 Written HW 1
Due: Tuesday, September 20 or Friday, September 23 during your recitation
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Although the final answer is im
Multivariable optimization
Math for Economics I
May 8, 2014
Math for Economics I
Multivariable optimization
Let f be a function of two variables with domain D. We want to
find the largest and smallest values of f on D, if they exist.
f has an global maxim
Midterm II, Math for Economics I, Spring 2014
New York University, Dmitry Zakharov
Name:
Recitation Section:
Read all of the following information before starting the exam:
Show all your work, clearly and in order, to get full credit. A correct answer wi
Math for Economics 4, Quiz 1 (10 pts)
New York University
1. (4 pts). Find and sketch the domain of the function
f (x, y) =
1
ln(x2 + y 2 1)
Solution: we need x2 + y 2 1 > 0, and we also need ln(x2 + y 2 1) 6= 0, so x2 +
y 2 1 6= 1. Hence the domain
is th
Midterm I, Math for Economics I, Spring 2014
New York University, Dmitry Zakharov
Name:
Recitation Section:
Read all of the following information before starting the exam:
Show all your work, clearly and in order, to get full credit. A correct answer wit