This preview shows pages 1–2. Sign up to view the full content.
PartISomepract
ice with production functions (30 points)
For each of the following production functions :
1)
Y
AK
N
;
A
,
and
are strictly positive constants
2)
Y
A
K
1
N
1/
;
A
,
and
are strictly positive constants, and 0
1
3)
Y
K
AN
1
,and
A
BK
;
B
,
and
are strictly positive constants, and 0
1
do the following :
(a) (12 points) determine whether the production function exhibits diminishing marginal
returns to capital
(b) (12 points) determine whether the production function is CRS, DRS or IRS
(c) (6 points) if possible, express
Y
/
N
as a function of
K
/
N
In each of these questions,
show the math explicitly
and
provide extra conditions on the
constants
, if necessary, to make a determination on the nature of the production function.
(1)
(a)
F
K
AK
1
N
F
KK
1
AK
2
N
,sofor
1, the production function has diminishing
returns
(b)
F
K
,
N
AK
N
F
K
,
N
for any
0
so for
1, the production function is CRS
1, the production function is IRS
1, the production function is DRS
(c) It is possible to represent
y
(
Y
/
N
as a function of
k
(
K
/
N
in the CRS case :
y
Ak
(2)
(a)
F
K
A
1
K
N
1
F
KK
A
1
K
N
1
1
.
1
.
1
.
K
1
N
0, so this
production function always has diminishing returns
(b) Clearly
F
K
,
N
F
K
,
N
for any
0, so the production function is CRS
(c) When the production function is CRS, it can always be representated in the form
y
f
k
In this case
y
A
k
1
1/
(3)
First substitute for
A
into the production function, so
Y
K
1
B
1
N
1
(a)
F
K
1
K
1
1
B
1
N
1
F
KK
1
1
1
K
1
2
B
1
N
1
For
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/29/2009 for the course 14 14.02 taught by Professor Geurrieri during the Fall '09 term at MIT.
 Fall '09
 Geurrieri

Click to edit the document details