ECON475 HW #8 Answers = =
1.
+ - 1- + 1-
=
Steady-state value
For the following cases, draw diagrams. Best way to do is giving values and looking at what happens, then analyzing mathematically. a. -, -1 , - lim
<
Thus there is no converge to the steady s
ECON475 HW #3 Answers
Theorem 3.5 Suppose that: (a) the domain of is an interval (finite or infinite) in (b) is a local maximum of , and is the only critical point of on . (c) Then, is the global maximum of f on .
Proof1 We will show that if is not the gl
ECON475 HW #1 Answers 1. , the sequence 1
Theorem 5.1 As . Furthermore, lim
converges to a limit denoted by the symbol
1
.
Proof Let /
1/ , 1
; so
. As lim 1
1
gets larger and goes to infinity, so does lim . Letting
. (r is fixed.) Since .
1
1
, we find l
ECON475 HW #0 Answers (P) A feasible allocation is Pareto Optimal if there is no other feasible allocation such that ; and for some . (WP) A feasible allocation allocation such that is Weak Pareto Optimal if there is no other feasible .
1. Given the defin
Middle East Technical University Department of Economics ECON 475-Introduction to Mathematical Economics Fall 2009-2010 Problem Set 2 Ebru Voyvoda and Ozlem Tonguc 1. Suppose at time t=0, you borrow 100,000 TL at a fixed interest rate i = 5% per year. You
Middle East Technical University Department of Economics
ECON 475-Introduction to Mathematical Economics Fall 2009-2010 Problem Set 1
Ebru Voyvoda and Ozlem Tonguc 1. In the Theory of the Firm, we consider the total cost, C to be a function of output leve
ANSWERS PAMPHLET
201
Solutions are A3.8
1, e1
1 2
i
i
3 1 , 2 2 e1 ei
i
3 . 2 i sin 1). 2 i. ) e2 .
e(cos 1 2 i sin )
e e2 A3.9 ez1 ez2 1 z1 (z1 1 3 z 3! 1 1 4 z 4! 1 1 ez1 (z1
z2 i
i 2 i
cos
e2 e
e2 (cos(
i sin(
z2 1 2! z2 )
z3 1 3! z2 1 2! z1 z2
1 z2 2
ANSWERS PAMPHLET
151
2 c1 b) y y 2 k1 24.15
y(0) 2, c2 9y y(0) 2, k2 y y y 0;
c1 ; 1, so y r2 k1 ,
1 3.
1 9 1 y
y(0) e (2 cos 3t 0, r y y(0)
t
c1 3i.
3c2 . sin 3t). 3k1 sin 3t 3k2 cos 3t.
k1 cos 3t
k2 sin 3t,
3k2 .
1 3
2 cos 3t
sin 3t.
e t (c1 cos t e t