(204A notes on OG)-P.1
Diamond economy with fiat money as store of value
• Money stock is distributed to the old at time t=1: M units
p
t
= Value of money in terms of goods = purchasing power
(if money is not valued, means p
t
= 0; inverse of price level)
M
⋅
p
t
= Aggregate value of money
m
t
=
M
⋅
p
t
/
L
t
= Per-capita money holdings of the young (end of period)
a
t
=
a
t
k
+
m
t
= Assets = Sum of money and claims on capital (a
k
)
• Question: Can we find an equilibrium with positive prices for fiat money
?
• Budget constraints:
- For the old generation in period 1, which receives fresh money:
C
21
=
(1
+
r
1
)
⋅
a
0
k
+
M
/
L
0
⋅
p
1
where
a
is invested in capital => First generation benefits if p
1
>0.
- For generations t
≥
1:
C
1
t
+
a
t
k
+
m
t
=
W
t
and
C
2
t
=
(1
+
r
t
)
⋅
a
t
−
1
k
+
p
t
p
t
−
1
m
t
−
1
- Equilibrium condition:
k
t
+
1
=
1
1
+
n
a
t
k

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