ECON 311: Mathematical Economics
Assignment 4
(Due date: December 4 before 5pm)
Question 1:
Suppose that the Central Bank adjusts ination by moving interest rate according to
the following rule:
it = it1 + (t )
We assume that the eect of interest rate on
Final Examination
Term: Fall
Year: 2013
Student Name:
Student Identication Number:
Course Abbreviation and Number: ECON 311
Course Title: Mathematical Economics
Section(s): 001
Instructor(s): Pierre Chauss
e
Date of Exam: December 5, 2013
Exam Period Star
ECON 311: Mathematical Economics
Assignment 1
(Solution)
Question 1: Prove the Youngs Theorem:
f (x)
f (x)
=
,
xi xj
xj xi
using the denition of derivatives
f (x)
f (xi + xi , xi ) f (x)
= lim
,
xi 0
xi
x i
where x is a n 1 vector and xi is the (n 1) 1 ve
ECON 311: Mathematical Economics
Assignment 2
(Due date: October 11 in class)
Question 1:
A monopoly can sell its output to two markets. The demands for the two markets are:
p1 = 200 2q1
p2 = 400 4q2
and the cost function is:
C = 2(q1 + q2 )2
a) Find p1 ,
ECON 311: Mathematical Economics
Midterm
(Fall 2013, Solution)
Question 1 (15% or 12 minutes): True, False or Uncertain.
For each of the following statement, tell me whether it is always true, always false or
uncertain. The latter means that it is false i
ECON 311: Mathematical Econometrics
Assignment 1
(Solution)
Question 1: (25%) Consider the following production function:
y = f (x1 , x2 )
In chapter 11, they mention the following result:
=
d ln(x2 /x1 )
f1 f2 (f1 x1 + f2 x2 )
% change in input ratio x1
ECON 311: Mathematical Economics
Assignment 2
(Solution)
Question 1: (6 points each: 4 for trying 2 for the right answer)
Consider a model of two-plant monopoly monopoly. The demand is a function of the
total production (q1 + q2 ), where q1 is produced in
ECON 311: Mathematical Economics
Midterm Exam (Solution)
Question 1: Short questions (35%)
Each of the following questions can be answered very quickly. If you spend too much time on them,
you are probably on the wrong track. If you need a theorem, you do
ECON 311: Mathematical Economics
Assignment 2
(Due date: October 14 before 5pm)
Question 1:
Suppose that consumers are not contrained by their income. Instead, they are constrained by the quantity of goods they can consume. Typically, each consumer solves
ECON 311: Mathematical Econometrics
Assignment 1
(Solution)
Question 1: Verify graphically whether these functions are quasiconvex or quasiconcave (assume that
xi > 0):
a) f (x) = x2 ln(x1 )
Answer
The level curve is c = x2 ln(x1 ) for a given constant c.
ECON 311: Mathematical Economics
Assignment 3
(Solution)
Question 1:
Consider the following utility maximization problem:
max U (x1 , x2 ) = ax1 + bx2
x1 ,x1
subject to
I p 1 x1 p 2 x2
T t1 x1 t2 x2
x1
x2
0
0
0
0
The rst inequality is the budget constrain
Y + a1 Y + a2 Y = b
with
a1 = (G B ), a2 = (G B ), b = (A F )
We assume that G = 2, B = 2, A = 100, and F = 0.
case 1: 2 > ( = .5 and = 0.2)
ddot(Y) + 2Y + 0.8Y = 20
5
10
Y(t)
15
20
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ECON 311: Mathematical Economics
Assignment 4
(Due on November 26 in class)
There are 5 points per question and a total of 23 questions. Therefore, the
total is 115 (It is brought back to 100 after by dividing by 1.15).
Question 1:
Consider the following
ECON 311: Mathematical Economics
Assignment 2
(Solution)
Question 1:
A monopoly can sell its output to two markets. The demands for the two markets are:
p1 = 200 2q1
p2 = 400 4q2
and the cost function is:
C = 2(q1 + q2 )2
a) Find p1 , p2 , q1 , and q2 tha
ECON 311: Mathematical Economics
Assignment 3
(Due date: November 8 in class)
Question 1:
a) We want to compute the change of consumer surplus, using the Hicksian demand
obtained by minimizing the expenditure subject to the utility being xed at a
certain
ECON 311: Mathematical Economics
Assignment 3
(Due date: November 8 in class)
Question 1:
a) We want to compute the change of consumer surplus, using the Hicksian demand
obtained by minimizing the expenditure subject to the utility being xed at a
certain
ECON 311: Mathematical Economics
Assignment 4
(Due date: November 29 in class)
Question 1:
Consider the multiplicator-accelerator model of Samuelson:
Yt = Ct + It + G0
Ct = mYt1
It = (Ct Ct1 )
(1)
(2)
(3)
where m if the propensity to consume, is the coeci
ECON 311: Mathematical Economics
Assignment 4
(Solution)
Question 1:
Consider the multiplicator-accelerator model of Samuelson:
Yt = Ct + It + G0
Ct = mYt1
It = (Ct Ct1 )
(1)
(2)
(3)
where m if the propensity to consume, is the coecient of acceleration an
ECON 311: Mathematical Economics
Midterm
(Fall 2012: Solution)
Question 1 (15% or 12 minutes): True, False or Uncertain.
For each of the following statement, tell me whether it is always true, always false or
uncertain. The latter means that it is false i
ECON 311: Mathematical Econometrics
Assignment 1
(Due date: September 27 in class)
Question 1: Prove the Youngs Theorem:
f (x)
f (x)
=
,
xi xj
xj xi
using the denition of derivatives
f (xi + xi , xi ) f (x)
f (x)
= lim
,
xi 0
xi
x i
where x is a n 1 vecto
Suggested problems for the second edition
1. Calculus for functions of n-variables (Chapter 11)
Analysis of functions through dierentiation.
Problems: 1, 3, 5, 7, 10(a, b, c, d, g, h) (pages 541 and 542)
2. Unconstrained optimization (Chapter 12)
Maximiza