SBP Working Paper Series STATE BANK OF PAKISTAN

M 1
t
current period, t
1 .
Pt
After some algebraic manipulation, we get
M
P
i i
t
=
t1
t
M
P
t
t
1
M
t Pt
The budget constraint faced by each household is
c
i
t
inv
i
t
t
t
t
t
(17)
i
i
Bt
i k i Bt
1
= kt
rt
wt
ht
t
(18)
R P
P
and the capital accumulation constraint,
i i
i
k
t 1
= inv
t
(1
) kt
(19)
The right hand side of equation (18) shows household’s income, which consist of wage earning
rental income
i
k i
r k
, total return from bond holdings Bt
1
t t
Pt
w h i
, t t
and profit
t
from owning the intermediate
good producing firms. On the other hand, the left hand side of equation (18) shows households
i
i
expenditures on consumption c
t
, physical assets investment inv
t
and financial assets
i
B
t
investment/borrowing .
R P
t
t
By combining budget constraint, capital accumulation constraint and equation of motion for real balances,
we get the following new budget constraint for the household:
c k
i
t
B
M
B
1
M
i i
i i
i t t i k i
i t1
t1
t
t
t
kt
rt
wt
ht
kt
t
Rt
Pt
Pt
Pt
P
t
1 = (1 )
(20)
t
Pt
The household maximizes the utility function in equation (13) subject to constraint in equation (20) with
i i i i
i
respect to c
t
, h
t
, M
t
, B
t
and kt
1
. After some simplification, we get the following first order
conditions for the household:
1
=
c
i
t
A
w
t
(21)
1 1 k
= Et
(1 r 1
)
i
i t
ct
ct
1
(22)
1 R
t
= E
i t i
ct
t1ct
1
(23)
1 1 D
= E
i t i
i
c
t ct
1
t1
M
t
/ Pt
(24)
Pt
where
t
=
P
is gross inflation.
t1
M
17