University of Minnesota
Econ 3102: Intermediate Macroeconomics
Practice Final
1
De°nitions (10 points)
2
Short Answers (15 points)
3
Solow Growth Model (15 points)
Consider the Solow growth model studied in Chapter 6, with technology given by
Y
t
=
zF
(
K
t
; N
t
) =
zK
1
=
4
t
N
3
=
4
t
.
Capital depreciates after use at the rate
°
2
(0
;
1)
. Assume that each agent is endowed with one unit of time
°
°
h
= 1
±
and supplies their labor inelastically. Additionally, each agent saves a fraction
s
2
(0
;
1)
of their total income. The
population evolves according to
N
t
+1
= (1 +
n
)
N
t
, where
n
°
0
.
(a) Find an expression that relates capital per worker tomorrow
k
t
+1
and capital per worker today
k
t
.
(b) What is the steadystate value of capital per worker in terms of exogenous variables.
(c) Suppose that the economy is initially in a steadystate and suddenly
TFP
decreases permanently
from
z
to
z
0
. What happens to steadystate output per capita
y
°
, capital per worker
k
°
, and consumption per capita
c
°
? Plot the evolution of capital per worker from the old to the new steadystate.
(d) Suppose that
TFP
only decreases
temporarily
. Plot the impulse reponse function for the per capita capital
stock
k
as a function of time.
4
Neoclassical Growth Model (25 points)
Consider the in°nite horizon onesector growth model. The representative household (consumer) enjoys consumption
and leisure time in all periods
t
= 0, 1,
....
The household has no exogenous income but she has a °xed time
endowment
°
h
in each period to split between labor and leisure. The household is endowed with the initial capital
stock
°
k
0
>
0
.
Assume that the household±s utility function is timeseparable, and takes the form
U
(
C
0
; C
1
; :::; ‘
0
; ‘
1
; :::
) =
1
X
t
=0
±
t
u
(
C
t
; ‘
t
)
where
C
t
and
‘
t
denote consumption and leisure in period
t
,
u
(
±
;
±
) is the period utility function which is strictly in
creasing, strictly concave, twicedi/erentiable and sati°es the Inada conditions (
lim
C
t
!
0
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 Summer '10
 ECON
 Economics, Macroeconomics, Period, representative, growth model

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