Problem Set 6
Part I  Some practice 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.
Part II  A continuous time growth model (70 points)
So far, in the lectures and in the textbook, you have dealt with discrete time (ie, the
subscript
t
takes discrete integer values 0,1,2,3 etc.) and the dynamic equation for capital
accumulation (equation 11.3 in the textbook) is a difference equation in
K
/
N
. This excercise
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 Fall '09
 Geurrieri
 Derivative, per capita, Capital accumulation, steady state consumption

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