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A Primer on Search Models of Money
Based on Trejos and Wright (1995) “Search, Bargaining, Money, and Prices”,
Journal of Political Economy,
p.11839.
1
Environment
•
Unit measure of agents.
•
Pref: each agent has preferences over a variety of goods that can be pro
duced by a fraction
x
of the population.
q
units consumed generates utility
u
(
q
)
•
Tech: each agent can produce
q
units of one nonstorable good at cost
cq
.
Thegoodisdemandedbyfract
ion
x
of the pop.
•
E
ﬃ
cient quantity is
u
0
(
q
∗
)=
c
(i.e. MB=MC).
•
Fraction
M
of the population are endowed with 1 unit of indivisible money.
Inventory is bounded above by 1
.
•
Matching technology: It any given period the probability of matching with
another agent is
β.
Given above:
—
arrival rate of an appropriate buyer for a seller is
βMx
(meet agent
with money who likes my good)
—
” seller for a buyer is
β
(1
−
M
)
x
—
Normalize
βx
=1
.
•
Bargaining Protocol
—
When an appropriate buyer and seller meet, they bargain over
q
(the
amount of good to be traded for a unit of money
→
p
=
1
q
). In 1st
generation models,
q
,so
p
= 1 independent of
M
.
—
Nash bargaining. Can be formalized as a sequential game between
the buyer and seller a la Rubinstein (1982, Ecta).
2
Steady State Equilibrium in the TrejosWright
Model
In 3 parts:
1. taking prices as given (i.e.
q
t
=
Q
t
), determine the value of being a buyer
V
bt
(
Q
t
) or a seller
V
st
(
Q
t
)
.
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 Spring '07
 CORBAE

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