CONCORDIA UNIVERSITY
Department of Economics
ECON 222/4 SECTIONS A, B and BB
STATISTICAL METHODS II
WINTER 2016 ASSIGNMENT 2 (SOLUTIONS)
Due: Monday, March 14, before 3:00pm
1. (38marks)Apopulationisassumedtofollowthebehaviour
are unknown population para
Economics 325/4 B: Winter 2014 Midterm 1
Instructions: You have 50 minutes. There are a total of 100 marks. Use your time
wisely.
1. Consider
3 4
x 3 for x > 0:
4
i) [10 Marks] Find the elasticity, slope, and rst-order Taylor series f (x) when x = 1.
ii)
CONCORDIA UNIVERSITY
Department of Economics
ECON 222/4 SECTIONS A, B and BB
STATISTICAL METHODS II
WINTER 2016 ASSIGNMENT 3
Due: Monday, April 4, before 3:00pm
1.(22marks)Aresearcherwantstofindthelinkbetweenthepriceofahouseanditsimportantcharacteristics.
ECON 301
Winter 2016
Assignment # 2
Due on or before Monday April 11 in Class
Identify the choice that best completes the statement or answers the
question.
_ 1. In Ozone, California, people all have the same tastes and they all like hot tubs.
Nobody want
Economics 325/4 A: Fall 2014 Midterm 2
Instructions: You have 50 minutes. There are a total of 100 marks. Use your time wisely.
1. Consider
r
1
; for x > 0:
ex2
i) [15 marks] Simplify f (x) ; nd the rst-order condition for f (x) ; and solve. Show that you
Economics 325/4 A: Fall 2014 Midterm 1
Instructions: You have 50 minutes. There are a total of 100 marks. Use your time wisely.
1. Consider
1
3
f (x) = 1 + x 2 2 10 2 x for x > 0:
i) [15 Marks] Calculate f 0 (x) and simplify f 0 (x) so that x only appears
Economics 325/2 A: Fall 2013 Midterm 2
Instructions: You have 45 minutes. There are a total of 100 marks. Use your time
wisely.
1. Consider the function
4 5
x 4 for x > 0:
5
i) [20 marks] Find the rst-order condition and solve. Determine if your solution
Economics 325 Fall 2013: Midterm 3
Instructions: There are a total of 100 marks. You have 45 minutes. Use your time wisely.
1. Consider the function
2
y = f (x1 ; x2 ) = ln
2
e2x1 +2x2
x1
(ex2 +7 )
2
(ex2 )
!
:
;x
;x
i) [10 marks] Simplify f (x1 ; x2 ) :
Economics 325/4 B: Winter 2014 Midterm 2
Instructions: You have 50 minutes. There are a total of 100 marks. Use your time
wisely.
1. Consider the function
1
x
f (x) = ln (e )
(ex
1
2
for x > 0:
1 )x 1
i) [10 marks] Simplify f (x) ; nd the rst-order condit
Economics 325 Fall 2011: Midterm 3
Instructions: You have 45 minutes. There are 3 questions each worth 30 marks for a
total of 90 marks. Use your time wisely.
1. Consider the function
y = f (x1 ; x2 ) = 2x2
1
x1 x2 + 2x2
2
7x1
2x2 + 20:
;x
;x
i) [8 marks]
Economics 325/a Fall 2011: Midterm 2
Instructions: You have 45 minutes. There are 3 questions each worth 30 marks for a total
of 90 marks. Use your time wisely.
1. Consider the function
3
4 5
f (x) = 8x 4 x 4 for x > 0.
5
i) [18 marks] Find the rst-order
Economics 325 Fall 2014 Midterm 3 (50 Minutes/100 Marks)
1. Consider the system of equations
4x1 + 2x2 + x3
2x1 + 2x2 + x3
x1 + x2 + x3
= 0
= 2
= 0:
i) [10 marks] If these are written in matrix notation as Ax = b; what are A; x; andhb? Calculate
det [A] u
1
Univariate Calculus
1. Exponents.
xa xb
xa
= xa b
xb
a
and (xy) = xa y a
= xa+b and
b
(xa )
= xab
1
x a =
and x0 = 1
xa
f (x) = xa =) f 0 (x) = axa
(a) Non-Integer Exponents. For any
i. xa ea ln(x) for x > 0:
ii. xa > 0:
iii. Example: 0:755 2:31 1:914 >
Economics 325/2 A: Fall 2015 Midterm 2
Instructions: You have 50 minutes. There are a total of 100 marks. Use your time wisely.
1. Consider the function
f (x) = xx e
2x
for x > 0:
i) [14 marks] Find the rst-order condition and solve. Show that f (x) is gl
Economics 325/4 B: Winter 2016 Midterm 2: (50 Minutes 100 Marks)
1.i) [10 marks] Find the demand for labour as a function the real wage w when the production function is
5 3
5 4
Q = f (L) = L 5 + L 5 :
4
3
ii) [10 Marks] If f (x) and g (x) have elasticiti
CONCORDIA UNIVERSITY
Department of Economics
ECON 222/4 SECTIONS A, B and BB
STATISTICAL METHODS II
WINTER 2016 ASSIGNMENT 1 (SOLUTIONS)
Due: Monday, February 15, before 3:00 pm
1. (4marks)Simplifythefollowingexpressions.
a. Find
1
2x dx
3
0
1
1
x4
1
2x
Economics 325/2 A: Fall 2016 Midterm 1: (50 Minutes 100 Marks)
1. i) [15 marks] Consider the function
1
2 3
f (x) = 2x 2 + x x 2 for x > 0.
3
Find the first-order condition and solve. Show that your solution yields a global maximum.
Find the elasticity of
Economics 325/2 A: Fall 2016 Midterm 2: (50 Minutes 100 Marks)
1. Consider the function
f (x) = x2x ex for x > 0.
i) [15 marks] Find the first-order condition for f (x) and solve. Show that your solution yields
a global minimum. ii) [10 Marks] Using a mon
Economics 325/2 A: Fall 2013 Midterm 1
Instructions: You have 45 minutes. There are a total of 100 marks. Use
your time wisely.
1. i) [15 marks] Consider the function
1
x2
f (x) =
2x 2 x for x > 0:
2
Find the rst-order condition for minimizing f (x). Show
Economics 325 Winter 2011: Midterm 3
Instructions: You have 45 minutes. There are 3 questions each worth 30 marks for a
total of 90 marks.
1. Consider
5
y = f (x1 , x2 ) = x2 + 2x1 x2 4x2 + 11x1 + 10x2 .
2
2 1
i) [14 marks] Find the rst-order conditions a
Economics 325/B: Winter 2011 Midterm 1
Instructions: You have 45 minutes. There are 3 questions each worth 30
marks for a total of 90 marks.
1. i) [18 marks] Consider the function
2 3
x 2 for x > 0:
3
1
f (x) = 2x 2 + x
Find f 0 (x) and show that f (x) is
Economics 325/4 B: Winter 2014 Midterm 3 (50 Minutes/100 Marks)
1. i) [15 marks] Given
4
1
x1
5
;x =
;b =
1
4
x2
10
h
i
1
calculate det [A] ; det AT A
A ; A 1 and A 1 b: Calculate x1 ; x2 in Ax = b using Cramer
s
rule. Show that A is negative denite using
Economics 325/2 A: Fall 2015 Midterm 3
Instructions: You have 50 minutes. There are a total of 100 marks. Use your time wisely.
1. i) [10 marks] Consider
y = f (x1 ; x2 ) =
1 T
x Ax + bT x where x =
2
x1
x2
;A =
3
2
2
2
;b =
2
4
:
Calculate xT Ax and bT x
1
Matrix Algebra
1. Vector Multiplication: a
b = a1 b1 + a2 b2 +
1 n
+ an bn :
n 1
(a) Examples:
3
5
3
4
=3
5+4
3
3 = 27 and
2
3
5
4 3 5 = JUNK.
6
4
2. Matrix Multiplication.
(a) First check dimensions: A
B:
m n
r s
i. If n 6= r =) AB is undened.
ii. If n
Economics 325/A: Fall 2011 Midterm 1
Instructions: You have 45 minutes. There are 3 questions each worth 30
marks for a total of 90 marks.
1. i) [20 marks] Consider the function
v
u
2 !2
u 2
3
1
3 5
+ x x 3 for x > 0.
f (x) = 3t2x 3
5
x
Simplify f (x) .
Economics 325/a Fall 2012: Midterm 2
Instructions: You have 45 minutes. There are 4 questions each worth 25 marks for a total
of 100 marks. Use your time wisely.
1. Consider
p
eln(x2 )
f (x) = q
x
(ex 1 )
for x > 0:
1
i) [10 marks] Simplify f (x) ; nd the
Economics 325/b Winter 2013: Midterm 2
Instructions: You have 50 minutes. There are 4 questions worth a total of 100 marks. Use
your time wisely.
1. Consider
f (x) = xe
x2
2
+x
; for x > 0:
i) [18 marks] Find the rst-order condition for f (x) and solve. F
Economics 325/4 B: Winter 2013 Midterm 1
Instructions: You have 50 minutes. There are 3 questions each worth 30 marks for a total
of 90 marks. Use your time wisely.
1. i) [15 marks] Consider the function
1
f (x) = 2x 2
2 3
x2
3
x for x > 0:
Find the rst-o
Economics 325/A: Fall 2012 Midterm 1
Instructions: You have 45 minutes. There are 3 questions each worth 30 marks for a total
of 90 marks.
1. Consider
3 4
x 3 for x > 0:
4
2
f (x) = 6x 3
i) [10 Marks] Find the elasticity, slope, and rst-order Taylor serie