Homework 2
May 5, 2016
1. In an economy with 2 goods x1 , x2 sold at positive prices p1 , p2 , a
consumer has wealth w and a utility function of the form
u(x1 ; x2 ) =
1
+ x2
x1
(a) Write the Lagrange
Optimization Theory for Economics
SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/15
Chapter 5
Optimization with Mixed Constraints
2/15
Introduction
The analysis for optimization with
Optimization Theory for Economics
SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/19
Chapter 6
Envelope Theorem
2/19
Optimization in Parametric Form
In economics, it is often the case
Optimization Theory for Economics
SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/31
Chapter 9
Optimization Over Time Under
Uncertainty
2/31
Introduction
In the last chapter, we discus
ECON 200: Spring 2015
Assignment 1, due on Friday, April 3.
1. Consider the following function:
8 2
< x (sin x1
f (x) =
:
1); x 6= 0
:
0; x = 0
Can you show that this function is everywhere dierentiab
ECON 200: Spring 2014
Assignment 1, due on Friday March 31.
Note: To check the definiteness of a symmetric matrix, you can use the following Proposition:
Let A be an n n symmetric matrix, and let Ak b
Homework 2
The deadline for this homework is May 12th, before the class.
1. In an economy with 2 goods x1 , x2 sold at positive prices p1 , p2 , a consumer has wealth
w and a utility function of the f
Optimization Theory for Economics
SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/53
Chapter 7
Optimization under Uncertainty
2/53
Introduction
Agents in the real economy usually have
Optimization Theory for Economics
SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/31
Chapter 10
Optimization Over Infinite Horizons
2/31
Introduction
Often there is no natural way to s
Optimization Theory for Economics
Dr. SHI Fei and Dr. SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/1
Chapter 3
Optimization with Equality Constraints
2/1
Introduction
In Chapter 2,
ECON 200: Spring 2015
Assignment 3, due on June 19.
1 A consumer lives for two periods. Income in period 1 is sure and equal to Y1 . The
income Y2 in period 2 can be random. If he saves S from his per
Optimization Theory for Economics
SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/34
Chapter 8
Optimization Over Time
2/34
Introduction
In this chapter, we discuss the situations where
Optimization Theory for Economics
SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/48
Organizational Stuff
This course is specially designed for second-year undergraduate
students at A
Optimization Theory for Economics
SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/50
Chapter 4
Optimization with Inequality
Constraints
2/50
Introduction
In this chapter, we turn to th
Optimization Theory for Economics
Dr. SHI Fei and Dr. SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/1
Chapter 6
Envelope Theorem
2/1
Optimization in Parametric Form
In economics, it
Optimization Theory for Economics
Dr. SHI Fei and Dr. SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/52
Chapter 3
Optimization with Equality Constraints
2/52
Introduction
In Chapter 2
Optimization Theory for Economics
SHI Fei and SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/42
Organizational Stuff
This course is ONLY required for Chinese students. Foreign
student
Optimization Theory for Economics
Dr. SHI Fei and Dr. SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/1
Chapter 2
Unconstrained Optimization
2/1
Introduction
In this chapter, we study
Optimization Theory for Economics
Dr. SHI Fei and Dr. SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/1
Notes on
the economic meaning of multipliers
2/1
Example 1: The Invisible Hand i
ECON
200: Spring 2014
1 A consumer lives for two periods. Income in period 1 is sure and equal to Y1 . The
income Y2 in period 2 can be random. If he saves S from his period-1 income, he gets
total re
Optimization Theory for Economics
Dr. SHI Fei and Dr. SHI Hao
Department of Economics
Shanghai Jiao Tong University
1/9
Chapter 1 Continued
2/9
Chapter 1 (Continued)
Continuity, dierentiability, conca
ECON 200: Spring 2015
Assignment 3, due on June 19.
1 A consumer lives for two periods. Income in period 1 is sure and equal to Y1 . The
income Y2 in period 2 can be random. If he saves S from his per
Homework#2
Due on May 22th, before the class
1. In an economy with 2 goods x1 , x2 sold at positive prices p1 , p2 , a
consumer has wealth w and a utility function of the form
u(x1 ; x2 ) =
1
+ x2
x1
1. What are benefits of involving suppliers in design and prototyping?
Despiteitshighertoolingcostsandlongerleadtimes,itcoulddrasticallyreducetheproblems
associatedwithbringinganewmodelintoproductiona
2016 Spring 1EC208
Homework Assignment #2 Due on April 26th
1.
Access the dataset associated with this homework. The temperature and winning times among a
sample of male and female runners of the New
Homework 2
May 5, 2016
1. In an economy with 2 goods x1 , x2 sold at positive prices p1 , p2 , a
consumer has wealth w and a utility function of the form
u(x1 ; x2 ) = !
1
+ x2
x1
(a) Write the Lagran
Spring 2016 EC208
Homework Assignment #3
1. Use the information below to answer all the parts of this question.
Random Variable
Distribution
Let X represent the Sulphur content Uniformlydistributed
of
ECON 200: Spring 2016
Assignment 1, due on Friday, April 1.
1. Consider the following function:
f (x) =
8 2
< x (sin x1 ! 1); x 6= 0
:
:
0; x = 0
Can you show that this function is everywhere dierenti
EC208Spring 2016
Homework Assignment #1
Due on March 22nd
1.
a.
b.
c.
d.
e.
f.
2.
Using your knowledge of data types, classify the data that would be gathered from each of
thefollowing questions as no
Spring 2016 1EC208
Homework Assignment #4 Due on June 7th
1. Use the data in Question 1 of HW4 Dataset.xlsx to perform this
regression analysis.
An Associated Press release reported on a group of evan