Lyon
August 26, 2008
Econ 7350
Final Exam
Name_
_
1. Information about the cost function for a price-taker firm can be found from the constrained
minimization problem:
Min:
Subj. to:
C
C = wT x
x 3 w 3 +
+
f ( x ) y 0 y and exogenous f C 2
xi 0 i = 1, 2,
Lyon
Aug. 28, 2007
Econ 7350
Final Exam
a33
1.
2.
3.
a35
a 37
Let A be a 7x7 symmetric negative definite matrix. Show that a53
a 73
a55
a 75
a 57 < 0 .
a 77
Explain.
Using the fact that if two vectors, u and v, are orthogonal then u T v = 0 , show
that th
Lyon
August 29, 2006
Econ 7350
Final Exam
Name_
1. This is a utility maximization problem with a time horizon of three years where the individual starts with
a fixed supply of a non-perishable consumption good. The individual may be on a deserted island w
Lyon
Econ 7350
First Exam
August 18, 2008
DO NOT USE A CALCULATORDO NOT HAVE A CALCULATOR ON YOUR DESK
1. Define:
Y =C+I
C = a + bY cr
I = d + eY fr
M s = M 0 + mY hr
where all parameters are positive, and 0 < 1 b e < 1 .
a. What are the endogenous variab
Lyon
Aug. 20, 2007
Econ 7350
First Exam
Name_
x2 9
.
x3
a. Identify the domain, image space and target space of f.
b. Is f a continuous function? Explain.
1. Let y = f ( x ) =
2. Given that y = f ( x ) = e x and
d ln( y )
df
= e x derive the rule for
. Ex
Lyon
Econ 7350
First Exam
August 21, 2006
DO NOT USE A CALCULATORDO NOT HAVE A CALCULATOR ON YOUR DESK
1. Using y = e x and x = ln ( y ) prove that ln (u a v b ) = a ln (u ) + b ln (v ) .
2. Let A = [a1a 2 a 3a 4 ] be a 4 4 matrix where a 4 = a1 + 2a 2 .
Lyon
Oct. 5, 2004
1.
Econ 7360
First Exam
Name_
Let f*(") be the solution function for the problem of maximizing f(x, ") with x endogenous and "
exogenous. Let f , C2 and strictly concave, and let D2 f(x) be nonsingular at the solution with x , 3.
x
Let "