Lyon
1.
Econ 6320
Second Exam
Name_
Minimize:
S.t:
[email protected]
w, x , n
+
f(x) - y = 0
f , C2 Hf negative definite
L(x, 8, w, y) = w @ x ! 8(f(x) ! y)
a. Show that if the Hessian of f, the production function, is negative definite, then the
Hessian of the Lagra
Lyon
Nov.17, 1999
1.
Econ 6320
Third Exam
Name_
A monopolist has two independent markets, such as a home market and a foreign
market. The firm attempts to maximize profits, but only has limited information about
demand and costs. We write the profit funct
Lyon
Dec. 17, 1998
1.
Econ 6320
Final Exam
Name_
This is another version of the wheat storage problem. It is still incomplete, but is
complicated enough for a test question. We start the problem at t = 0 with the harvest,
which takes place instantaneously
Lyon
Oct. 25, 1999
Econ 6320
Second Exam
Name_
1.
Let the domain of f be n .Using Taylors Theorem show that if D f(xo) = 0 and
+
o
D2 f(x) is negative definite at each x , n
+ then f(x ) is a strict (unique) global
maximum.
2.
The cost minimization proble
Lyon
Dec.17, 1999
Econ 6320
Final Exam
Name_
1.
Let the solution to a mining problem have y*(0) > 0, and x*(T*) > 0, where the
symbols are the same as used in your homework assignment. Draw a possible time path
of T*(t), and explain mathematics and the ec
Lyon
Econ 6320
Third Examination
Name_
1.
The model:
(1)
dF/dt = f(F) - h
f(0) = 0,
(2)
dn/dt = g(B)
g(0) = 0, gN(B) > 0
(3)
Ps = S(h, n, w, F)
Sh > 0 , S n < 0 , S w > 0 , S F < 0
(4)
Pd = D(h)
DN(h) < 0
(5)
R = R(F)
RN(F) < 0
(6)
Pd = Ps + R
(The fish m