Econ 600 Schroeter Fall 2006 Homework 1. A firm employs two inputs, x1 and x 2 , to produce one output y = f ( x1 , x2 ) , facing fixed prices for the output and inputs: p, w1 , and w2 . The firm's pr
Econ 600 Schroeter Fall 2008 Exam #2 Do all four problems. They will be equally weighted. Closed book, open notes. Be sure your answers are presented in a neat and well-organized manner. 1. Answer Tru
Econ 600 Schroeter Fall 2008 Homework (Note: These problems are very closely related to the problems in the required homework set from fall 2006 for which a solution outline is available on the web pa
Econ 600 Schroeter Fall 2006 Exam #1 Do all three problems. Weights: #1 - 30%, #2 - 35%, #3 - 35%. Closed book, closed notes. Be sure your answers are presented in a neat and well-organized manner. 1.
Econ 600 Schroeter Fall 2007 Exam #2 Solution Outline 1. a. True b. False. Change "for all u , v n " to "for all u , v n such that F (u ) F (v ) ." c. False. Change "strict global maximum" to "strict
Econ 600 Schroeter Fall 2007 Exam #1 Solution Outline 1. a. True. b. False. Change "negative semi-definite" to "negative definite." (Then could also add that x * is a "strict local maximum.") c. True.
Econ 600 Schroeter Fall 2008 Exam #1 Do all three problems. Weights: #1 - 30%, #2 - 35%, #3 - 35%. Closed book, closed notes. Be sure your answers are presented in a neat and well-organized manner. 1.
Econ 600
Schroeter
Fall 2010
Exam #1 Solution Outline
1. a. True.
b. True.
d. False. Change "
c. True.
2
d2
2
d2
F x * (a ); a 2 F * (a ) " to " 2 F x * (a ); a 2 F * (a ) ."
a 2
da
a
da
(
)
(
)
e. Fa
Econ 600
Schroeter
Fall 2009
Exam #1 Solution Outline
1. a. True.
b. False. Change "if and only if" to "if".
c. False. Change "strictly quasi-concave" to "strictly concave".
d. True.
e. Strictly speak
Econ 600
Schroeter
Fall 2010
Exam #2 Solution Outline
1. a. False. Change max to min.
d. False. Change to .
b. True.
c. True.
e. True.
2. Proof:
Given > 0 , want to show that there exists N such that
Econ 600
Schroeter
Fall 2009
Homework Solution
1. For the long-run problem:
(
)
(
)
*
*
p f1 x1 , x 2 w1 = 0
*
*
p f 2 x1 , x 2 w2 = 0
Note that the assumption of a negative definite Hessian for f ()
Econ600
Schroeter
Fall2007
Homework solutionoutline
1.a.Lagrangians forthetwoproblems:
L ( x l ) = F( x a ) - l g( x a )
a
i
(
L ( x l ,m ) = F( x a ) - l g( x a ) - m h x a )
a
ii
FONCsforsolutionto
Econ 600
Schroeter
Fall 2010
Homework solution outline
1. a.)
py w1 x1 w2 x 2 subject to f ( x1 , x 2 ) y = 0
max
w. r .t . y , x1 , x2
Lagrangian: L( y, x1 , x 2 ; ) = py w1 x1 w2 x 2 + ( y f ( x1 ,
Econ 600
Schroeter
Fall 2009
Exam #2 Solution Outline
1. a. False. Change "if and only if" to "only if" or change concave to quasiconcave
b. True.
c. True.
d. True.
e. False. Change "negative definite