Quiz 2, Math for Economics II (10 pts)
New York University, Sylvester Eriksson-Bique
Show your work and justify your answers where appropriate. If you write the correct answer without sucient work,
you will receive little or no credit.
1. (2 points) Let =

785
14.4 GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE
Math for Econ II Homework Assignment 2
New York University
Due in Recitation, Friday, February 19th
rcises and Problems for Section 14.4
cises
Please write neat solutions for the problems below.

Math for Econ II Homework Assignment 1
New York University
Due in Recitation, Friday, February 12th
Please 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.
Do no

Math for Econ II Homework Assignment 2
New York University
Due in Recitation, Friday, February 19th
Please 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.
Do no

Math for Econ II Homework Assignment 3
New York University
Due in Recitation, Friday, February 26th
Please 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.
Do no

Math for Econ II Homework Assignment 3
New York University
Due in Recitation, Friday, February 26th
Please 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.
Do no

Math for Econ II Homework Assignment 8 - Solutions
New York University
Due in Recitation, Friday, April 15th
Please 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 credi

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Introduction to Differential Equations
(9.8, 9.9 in MFE book)
Math for Economics 2
Math for Economics 2
Introduction to Differential Equations(9.8, 9.9 in MFE book)
Differential equations allow us to find the general formula for a
function by using proper

Math for Econ II, Written Assignment 10 (28 points)
Due Friday, May 1
Please 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.
Write your name and recitation sect

Present and Future Values (10.3, 10.5 in e-book)
Math for Economics 2
Math for Economics 2
Present and Future Values (10.3, 10.5 in e-book)
Present vs. Future Values
The future value, B, of a payment P, is the amount to which P
would have grown (at some s

Math for Econ II Homework Assignment 7 - Solutions
New York University
Due in Recitation, Friday, April 8th
Please 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

Antiderivatives and Areas: Intro to Integration
(9.1, 9.2 in MFE book; 5.1 in Stewart)
Math for Economics II
Math for Economics II
Antiderivatives and Areas: Intro to Integration(9.1, 9.2 in MFE b
A function F is an antiderivative of f on an interval I if

Integration by parts
(9.5 in MFE book; 6.1 in e-book
Math for Economics II
Math for Economics II
Integration by parts(9.5 in MFE book; 6.1 in e-book
The Magic Formula
Product rule: If u(x) and v (x) are differentiable,
uv 0 + vu 0 = (uv )0 ,
uv 0 = (uv )0

Lecture 4b
Warm-Up Problem (Clicker)
2 |x|
.
2+x
Which one of the of the following is lim f (x)?
Suppose that f (x) =
x2
A.
B.
C.
D.
E.
1
1
0
The limit does not exist.
None of the above
Announcements
I
Quiz 3 Topics (announced on NYU Classes): Present and

Lecture 5a
Warm-up Problem (Clicker)
In which one of the following intervals is the equation
x5 x2 = 4
guaranteed to have a solution? You must be able to justify your choice
using the IVT.
A. [2, 1]
B. [3, 1]
C. [0, 2]
D. [2, 3]
E. None of the above
Annou

Worksheet 2, solutions
Multivariable optimization using Lagrange multipliers
1. Consider f (x, y) = 2xy under the constraint 5x + 4y = 100. Does f have a minimum value subject to the
constraint? Find all points which satisfy the Lagrange multiplier condit

5.4 THEOREM
Math for Econ II Homework Assignment 6 - Solutions
5-4h43
43. Using the graph ofNew
f in
Figure
?, arrange the ins5-4h47-48
following
York
University
Due
in
Recitation,
Friday,
April
1st
quantities in increasing order, from least to greatest.

The Definite Integral
(9.2, 9.3 in MFE book; 5.2 in Stewart)
Math for Economics II
Math for Economics II
The Definite Integral(9.2, 9.3 in MFE book; 5.2 in Stewart)
As we saw at the end of last section:
Rb
The definite integral a f (x) dx represents the a

Math for Econ II, Written Assignment 9 (28 points)
Due Friday, April 24
Please 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.
Write your name and recitation se

Math for Econ II, Written Assignment 7 (28 points)
Due Friday, April 10
Please 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.
Write your name and recitation se

Matrices and Systems of Equations
Munn, Math for Economics II
Munn, Math for Economics II
Matrices and Systems of Equations
Systems of equations
In the past weve solved equations like:
x + y = 5,
3x y = 7.
What about more complicated systems?
x 2y + z = 5

Multivariable Optimization: Lagrange Multipliers
(11.8 in e-book; 14.1-14.6 in MFE textbook)
Munn, Math for Economics II
Munn, Math for Economics II
Multivariable Optimization: Lagrange Multipliers (11.8 in e-book
Tools from Math for Econ 1
1
Maxes, mins,

Invertible Matrices, Determinants, and Cramers
Rule (16.1-16.8)
Munn, Math for Economics II
Munn, Math for Economics II
Invertible Matrices, Determinants, and Cramers Rule (16.1-16.8)
Consider
3x1 + 4x2 = 3
5x1 + 6x2 = 7
This is the matrix equation
3 4
5

Optimization for functions of multiple variables
(Ch. 13 in MFE textbook; Section 11.7 in e-book)
Munn, Math for Economics I
Munn, Math for Economics I
Optimization for functions of multiple variables (Ch. 13 in MFE t
Let f be a function of multiple varia

Directional derivatives, gradients, tangent planes,
and dierentials (11.4, 11.6 of Stewart)
Munn, Math for Economics II
Munn, Math for Economics II
Directional derivatives, gradients, tangent planes, and dierentials
Average rate of change in a direction
S

Examples of Historic Sites/Societies using Wordpress.com
1. Banting House NHSC: Suburbia Theme
https:/bantinghousenhsc.wordpress.com
2. The Edinburgh Historical Society: The Misty Lake Theme (my fav)
https:/edinburghistoricalsociety.org
3. Ewecross Histor

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IZA DP No. 8916
Severe Air Pollution and Labor Productivity
Teng Li
Haoming Liu
Alberto Salvo
March 2015
Forschungsinstitut
zur Zukunft der Arbeit
Institute for the Study
of Labor
Severe Air Pollution and Labor Productivity
Teng Li

PARTICULATE POLLUTION AND THE
PRODUCTIVITY OF PEAR PACKERS*
Tom Chang
Joshua Graff Zivin
Tal Gross
Matthew Neidell
February 2014
Abstract
We study the effect of outdoor air pollution on the productivity of indoor workers at a pear-packing
factory. We focu

How Can Trade Liberalization Be Conducive to a Better Environment?
A Survey of the Literature
Savas Alpay
Department of International Trade
Beykent University
Beykent, 34500 Istanbul, Turkey
Abstract
This article surveys trade and the environment literat