Exchange Rate Economics: Theories and Evidence

102 The flexible price monetary approach
set aside money in period t to satisfy all of their purchases in t+1. This is rationalised
by thinking of the representative agent as a household with two individuals,one
specialising in production and the other in consumption. In period t the producer
sells her output and in period t +1 the consumer spends the proceeds of that output.
At the end of t +1 the household’s producer and consumer only get together again
after markets have closed.
Specifically,assume that the total outstanding stock of the home and foreign
money are M t and Mt
∗ (these are assumed to evolve according to a first-order AR
process,known to agents),P t is the home price of y and Pt
∗ is the foreign price
of y ∗ . The current values of y, y ∗ , M and M ∗ are known in advance so domestic
(and foreign) residents know in advance how much home and foreign money is
needed to finance current consumption plans. The cash-in-advance constraints for
the home agent have the following form:
and
m 1t−1 ≥ P t C t ,(4.24)
m ∗ 1t−1 ≥ P ∗
t C t ,(4.24 ′ )
where m 1 and m1 ∗ denote,respectively,the domestic agent’s holdings of home
and foreign money. These constraints imply that agents have to set aside at least
as much money as they plan to spend on purchases of goods. However,given
that there is no uncertainty about how much money will be required to finance
period-t purchases,these constraints will be binding (i.e. agents don’t hold excess
money balances) in the presence of a positive nominal interest rate. The binding
cash-in-advance constraints are:
and
m 1t = P t C t (4.25)
m ∗ 1t = P ∗
t C t . (4.25 ′ )
By adding the two monies into the respective consolidated budget constraint,
the Euler equation in the presence of a cash-in-advance constraint can be
demonstrated to be:
S t P ∗
t
P t
= u∗ c t
u ct
. (4.26)
This expression is not our desired result since it does not feature money. To
introduce money into (4.26) we note that the adding-up constraints for the two