ECON3202/5402 S2/2015
Mathematical Economics
Assignment 5 - Solutions
Assignment Questions
1. Think about the wine storage problem we discussed in class (also problem pages 282-285
in the textbook). Assuming all the same conditions as before, but now the
ECON3202/5402 S2/2015
Mathematical Economics
Assignment 6 - Solutions
Assignment Questions
1.
z = x(y + 4) subject to x + y = 8
a) Use the Lagrange multiplier method to nd the stationary values of z.
Answer:
L = x(y + 4) + (8
x
y)
First-order conditions:
ECON3202
S2/2016
Mathematical Economics
Assignment 8 - Solutions
Due Date: 17 October, 2016 - Beginning of Week 12 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete it.
Th
ECON3202
S2/2016
Mathematical Economics
Assignment 2
Due Date: 8 August, 2016 - Beginning of Week 3 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. The hard copy is
ECON3202
S2/2016
Mathematical Economics
Assignment 9 - Solutions
Due Date: 24 October, 2016 - Beginning of Week 13 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. Th
ECON3202
S2/2016
Mathematical Economics
Assignment 2 - Solutions
Assignment Questions
1. a) Expand the following summation expressions:
i.
5
X
i1 xi
i=2
Answer:
x2 + 2 x3 + 3 x4 + 4 x5
ii.
2
X
(x i)2
i=0
Answer:
x2 + (x 1)2 + (x 2)2
P
b) Rewrite the foll
ECON3202
S2/2016
Mathematical Economics
Assignment 4 - Solutions
1. Given Q = 100 2P + 0.02Y , where Q: quantity demanded; P : price; Y : income and
given P = 20 and Y = 5000 find the:
(a) Price elasticity of demand
Answer: d = Q/P
= 1002P2+0.02Y =
Q/P
P
ECON3202
S2/2016
Mathematical Economics
Assignment 3
Due Date: 15 August, 2016 - Beginning of Week 4 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. The hard copy is
ECON3202
S2/2016
Mathematical Economics
Assignment 6
Due Date: 19 September, 2016 - Beginning of Week 9 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. The hard copy
ECON3202
S2/2016
Mathematical Economics
Assignment 5
Due Date: 12 September, 2016 - Beginning of Week 8 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. The hard copy
ECON3202
S2/2016
Mathematical Economics
Assignment 3
Assignment Questions and Solutions
1. Given the function y = 6x2 5x 4
(a) Find the difference quotient as a function of x and x
Answer:
y
f (x0 + x) f (x0 )
=
x
x
f (x0 + x) = 6(x0 + x)2 5(x0 + x) 4
f (
ECON3202
S2/2016
Mathematical Economics
Assignment 5 - Solutions
Assignment Questions
1. Suppose a wine dealer is in possession of a certain quantity (say 1 case) of wine, which
he can sell now (t = 0) for $k or store it for t periods and sell it in the f
ECON3202
S2/2016
Mathematical Economics
Assignment 8
Due Date: 17 October, 2016 - Beginning of Week 12 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. The hard copy
ECON3202
S2/2016
Mathematical Economics
Assignment 6 - Solutions
Due Date: 19 September, 2016 - Beginning of Week 9 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. T
ECON3202
S2/2016
Mathematical Economics
Assignment 9 - Solutions
Due Date: 24 October, 2016 - Beginning of Week 13 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. Th
ECON3202/5402 S2/2015
Mathematical Economics
Tutorial 8 - Extra Questions from Chapter 11
Tutorial Questions - Concavity and Convexity
i. Using (11.20) from textbook page 322 check whether the following function is concave,
convex, strictly concave or str
ECON3202/5402 S2/2015
Mathematical Economics
Tutorial 6 - Chapters 9 & 10 - Solutions
Tutorial Questions:
Chapter 9:
1. Find the stationary values of the function
1
y = x3
3
x2 + x + 10
check whether the stationary points are relative maxima, minima or in
ECON3202/5402 S2/2015
Mathematical Economics
Assignment 8 - Solutions
Assignment Questions
1. Find the following:
a)
Answer:
b)
Z
Z
4x
dx
+1
x2
4x
dx = 2 ln(x2 + 1) + c
+1
x2
Z
(2ax + b)(ax2 + bx)7 dx
Answer: Substitution rule: Let u = ax2 + bx. Then du =
ECON3202/5402 S2/2015
Mathematical Economics
Assignment 7 - Solutions
Assignment Questions
1. For the following problem:
min C = f (x1 ; x2 ; :; xn )
subject to g i (x1 ; x2 ; :; xn )
xj
ri
0
with i = 1; 2; :; m and j = 1; 2; :n
a) Write the Lagrangian fu
ECON3202/5402 S2/2015
Mathematical Economics
Assignment 4 - Solutions
Assignment Questions
1. Given the market model
Q=a
Q=
(a, b > 0)
bP
c + dP (c, d > 0)
with solutions:
P =
Q =
a+c
b+d
ad bc
b+d
Examine the comparative static properties of the equilibr
ECON3202/5402 S2/2015
Mathematical Economics
Assignment 2 - Solutions
Assignment Questions
1. a) Expand the following summation expressions:
i.
5
X
i 1
xi
i=2
Answer:
x2 +
2
x3 +
3
x4 +
4
x5
ii.
2
X
(x
i)2
i=0
Answer:
x2 + (x
1)2 + (x
2)2
P
b) Rewrite the
ECON3202 S2/2015
Mathematical Economics
Assignment 1 - Solutions
Assignment Questions
1. a) Given the market model
Qd = Qs
Qd = 18
Qs =
4P
6 + 5P
nd P and Q (Use fractions rather than decimals)
Answer:
By substitution we get 18 4P = 6 + 5P or 9P = 24. Thu
ECON3202
S2/2016
Mathematical Economics
Assignment 1 - Solutions
Assignment Questions
1. a) Given the market model
Qd = Qs
Qd = 18 4P
Qs = 6 + 5P
find P and Q (Use fractions rather than decimals)
Answer:
By substitution we get 18 4P = 6 + 5P or 9P = 24. T
ECON3202
S2/2016
Mathematical Economics
Assignment 1
Due Date: 1 August, 2016 - Beginning of Week 2 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. The hard copy is
ECON3202
S2/2016
Mathematical Economics
Assignment 7
Due Date: 10 October, 2016 - Beginning of Week 11 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. The hard copy
ECON3202
S2/2016
Mathematical Economics
Assignment 1
Due Date: 1 August, 2016 - Beginning of Week 2 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. The hard copy is
ECON3202
S2/2016
Mathematical Economics
Assignment 7 - Solutions
Due Date: 10 October, 2016 - Beginning of Week 11 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. Th
ECON3202
S2/2016
Mathematical Economics
Assignment 4
Due Date: 22 August, 2016 - Beginning of Week 5 Lecture
Submission Procedure for Assignments
Students must submit a hard copy of their assignment. You will have one week to complete
it. The hard copy is
ECON3202
S2/2016
Mathematical Economics
Lecture 5
1
Comparative Statics of General-Function Models
Given
F1 (x, y, w; z) = 0
F2 (x, y, w; z) = 0
F (x, y, w; z) = 0
3
y
w
we want to solve x
z , z and z
Step 1: Start by determining whether the Jacobian |J
ECON3202
S2/2016
Mathematical Economics
Lecture 8
1
Optimization - The case of more than one choice
variables
1.1
Review: Extreme values of a function of ONE variable
Condition
First-order necessary condition
Second-order necessary condition
Second-order
ECON3202
S2/2016
Mathematical Economics
Lecture 3
1
Summary of Lecture 2
1.1
1)
2)
3)
4)
5)
6)
HOW TO INVERT A MATRIX:
calculate the determinant |A|
calculate the minors |Mij |
calculate cofactors |Cij |
construct the cofactor matrix C
get the adjugate ma