Math for Econ II, Written Assignment 2 (30 points)
Due Friday, September 18th, in recitation
Please write neat solutions for the problems below. Show all your work. If you only write the answer with n
Math for Economics II, Written Assignment 1 (30 points)
Due Friday, September 18th, in recitation
Fall 2015
Please write neat solutions for the problems below. Show all your work. If you only write th
785
14.4 GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE
Math for Econ II Homework Assignment 2
New York University
Due in Recitation, Friday, September 23
rcises and Problems for Section 14.4
cise
Math for Econ II, Written Assignment 3 (30 points)
Due Friday, October 2, in recitation
1. (5 points, review of MFE 1) A rm produces and sells two commodities. When the rm produces x tons of the
rst c
'/Price Ceilings and Price Floors
PROBLEM SET #2: UNGRADED WORKSHEET
Instructions: Answer all the questions in this worksheet. Youll use some of the answers to complete
Problem Set #2 - Selected Quest
PROBLEMS FOR SECTION 13.1
2 _ ~ .
1. The function f dened for all (x, y) by f (x, y) = *2x2 y + 4x + 4y 3 has a maxrmum
Find the corresponding values of x and y.
2. (a) The function f dened for all (x
Antiderivatives and Areas: Intro to Integration
(9.1, 9.2 in MFE book; 5.1 in Stewart)
Jankowski, Math for Economics II
March 24, 2015
Jankowski, Math for Economics II
Antiderivatives and Areas: Intro
Invertible Matrices, Determinants, and Cramers
Rule (16.1-16.8)
Jankowski, Math for Economics II
February 26, 2015
Jankowski, Math for Economics II
Invertible Matrices, Determinants, and Cramers Rule
Leontief Input-Output Model (16.9)
Jankowski, Math for Economics II
March 10, 2015
Jankowski, Math for Economics II
Leontief Input-Output Model (16.9)
Basic Setup
Consider an economy with n sectors. T
The Definite Integral
(9.2, 9.3 in MFE book; 5.2 in Stewart)
Jankowski, Math for Economics II
April 12, 2015
Jankowski, Math for Economics II
The Definite Integral(9.2, 9.3 in MFE book; 5.2 in Stewart
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
Quiz 6
MFE II, Section 006, Fall 2016
Recitation Section:
Name:
Netid:
Problem 1.(5 points.)
Solve the following initial value problem. Give your answer in explicit form.
y 0 + 9ey+3x = 0
y(0) = 0
Pro
Integration by parts
(9.5 in MFE book; 6.1 in e-book)
Jankowski, Math for Economics II
April 9, 2015
Jankowski, Math for Economics II
Integration by parts(9.5 in MFE book; 6.1 in e-book)
The Magic For
Vectors (10.2, 10.3 of Stewart)
Jankowski, Math for Economics II
February 5, 2015
Jankowski, Math for Economics II
Vectors (10.2, 10.3 of Stewart)
Foreshadowing directional derivatives: beyond fx and
Condensed Review, Functions of Several Variables
(MFE text: 11.1, 11.2, 11.3, 11.7)
Jankowski, Math for Economics I
February 1, 2015
Jankowski, Math for Economics I
Condensed Review, Functions of Seve
1. Compute the following integrals.
Z
2
dx
x+
(a)
x
Solution:
Z
Z
xex
(b)
2 1
x+
2
x2
dx =
+ 2 ln|x| + C.
x
2
dx
Solution: Let u = x2 1. Then du = 2x dx. Making the substitution, we have
Z
Z
1
1
1 2
Multivariable Optimization: Lagrange Multipliers
(11.8 in e-book; 14.1-14.6 in MFE textbook)
Jankowski, Math for Economics II
February 21, 2015
Jankowski, Math for Economics II
Multivariable Optimizat
Heres an exercise we did in class on September 20th, with solutions:
Let f (x, y) = xexy .
(a) Find f (1, 0).
Solution. Recall that f (a, b) = hfx (a, b), fy (a, b)i. So,
f (x, y) = hexy + xyexy , x2
Introduction to Dierential Equations
(9.8, 9.9 in MFE book)
December 2, 2015
Introduction to Dierential Equations(9.8, 9.9 in MFE book)
Dierential equations allow us to find the general formula for a
Present and Future Values (10.3, 10.5 in e-book)
Jankowski, Math for Economics 2
April 21, 2015
Jankowski, Math for Economics 2
Present and Future Values (10.3, 10.5 in e-book)
Present vs. Future Valu
Directional derivatives, gradients, tangent planes,
and differentials (11.4, 11.6 of Stewart)
Jankowski, Math for Economics II
February 7, 2015
Jankowski, Math for Economics II
Directional derivatives
Name
Address | phone | email
[Date]
[Name of Recruiter if you have it]
[Name of Firm]
[Firms Address]
[If you have a specific contact Dear Mr./Ms. Recruiters Name,]
[If not To the Recruiting Team,]
My
HW 7
Due Friday, March 27
Please give complete, well written solutions to the following exercises.
1. Assume an economics model where we have three industries with the following consumption matrix
0
HW 8
Due Friday, April 3
Please give complete, well written solutions to the following exercises.
1. (5 points) Find the area between the x-axis and the curve y = x3 from
x = 0 to x = 1 by finding the
785
14.4 GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE
ms for Section 14.4
14-4w27 29. grad f = (2x + 3ey )%i + 3xey%
j
adient of the function. Assume
domain on which the function
ins14-4w28-29
I
HW 3
Please give complete, well written solutions to the following exercises.
2
1. (2 pts) Find the differential of the function P (K, L, M ) = KM eL
M 2
2. (5 pts, review of MFE 1) A firm produces an
HW 4
Due Friday, February 27
Please give complete, well written solutions to the following exercises.
1. (3 pts) The figures below show the optimal point (marked with a dot)
in three optimization prob