ECON 4465
Dr. McIntyre
Problem Set #3
Market structure
Due: Friday, 26 September
2
Consider an industry with two firms, each having total costs given by Ci (yi ) = yi . The (inverse) demand curve facing
this industry is:
P (Y ) = 100 Y;
where Y = y 1 + y2
ECON 4465
Dr. McIntyre
Problem Set #2
Profit maximization exercise
1
Consider a competitve rm with production function y = [xa + x a ] a that faces factor prices w 1 and w2 respec1
2
tively. Derive this firms factor demand functions.
The firms profit func
ECON 4465
Dr. McIntyre
Problem Set #1
Practice with derivatives
Dierentiate the following expressions. Show your work and when appropriate, simplify your algebra as
much as possible.
1.
2.
3.
4.
5.
6.
7.
8.
9.
p
f (s) = 2 + 1 s2 + 3 (s + 1)
2
2
t +1
t +
Chapter 6
DYNAMIC BEHAVIOR
We now add another layer of sophistication to our analysis: dynamics. We know from our
study of intertemporal choice, that real world decisions in economics are characterized
by the fact that individuals include time in their de
Econ 4465
Prof. McIntyre
Answers to First Take-home Exam
1.
The function (x1 ; x 2 ; : : : ; x n ) is concave if its Hessian matrix
0
11 12 1n
B 21 22 2n
B
H=B .
.
@ .
.
.
1
C
C
C
A
n1 n2 nn
Pn
is negative definite. We know, however that (x1 ; x 2 ; : :
ECON 4465: Mathematical Economics
Fall 2003
Prof. McIntyre
First Take-home Exam
Instructions. This take-home exam will be due on Wednesday, October 8 at 10:20 am. The exam is worth 100 points.
Answer all the questions. You may use your text, notes, and if