ECON 401A
Hartman
Winter 2009
FIRST EXAM
Let
Y
real aggregate output
N
labor
K
capital stock
W
nominal wage rate
P
price level
C
real consumption
T
real (lump sum) taxes
I
real investment
r
interest rate measured as a percent
G
real government purchases
M
nominal money stock
1.
This problem involves a simple specification of a classical model.
Both
P
and
W
are free to vary.
Suppose that the aggregate production function is
1/2
40
YN
and that the labor supply function is
2
110
40
S
P
N
W
.
a.
Derive the demand function for labor.
Find the equilibrium level of employment,
N
, and the
equilibrium level of output,
Y
.
In equilibrium, what is the real wage,
/
WP
?
b.
Suppose that the consumption function is
4
()
1
0
5
CY T
Y T
, that the investment demand
function is
( )
90 8
I
rr
, and that the demand function for real money balances is
(,)
1
0
LYr
Y
r
.
Suppose also that government spending, taxes, and the money supply are
fixed exogenously with
100
GT
and
700
M
.
What are the equilibrium values of
r
,
P
, and
W
?
c.
Suppose that
G
and
T
increase by the same amount.
What effect does this have on the
equilibrium levels of
N
,
Y
, and
r
in this version of the model?
d.
Suppose now the money supply increases by 3% with no change in
G
or
T
.
What effect does this
have on the equilibrium levels of
N
,
Y
,
C
,
r
,
I
,
P
, and
W
?
(If possible, indicate both the direction
and percentage amount of any change.
A formal mathematical analysis is not required for this
part of the question, but you must explain how you arrive at your answer to receive full credit.)
2.
Denote the consumption, investment, and money demand functions by
C Y
T
,
I r
, and
L Y r
,
respectively, where
01
C
Y
T
'(
)
,
I
r
'( )
0
,
L
Y
/
0, and
L
r
/
0.
Suppose also that
P
is
fixed exogenously.
Suppose now that
G
and
M