Exchange Rate Economics: Theories and Evidence

174 Currency substitution and portfolio balance models
In common with model 1,the country is assumed to produce a traded good,is
small in relation to world trade,and equation (7.11) holds. In contrast to model 1,
however,the domestic economy produces,in addition to the traded good,a nontraded
good. The relative price of traded to non-traded goods, P T /P N ,governs
production decisions and since (7.11) holds this may be written as q = S/P N ,
where q is the real exchange rate. Thus we have:
Y T = Y T (q),
Y N = Y N (q),
Y T
q > 0,(7.17)
Y N
q < 0,(7.18)
where Y N denotes the demand for non-traded goods and the partial derivatives
denote the effect of an increase in the real exchange rate on production. Thus an
increase in the real exchange rate leads to an increased in production of the traded
good and decreased production of the non-traded good. The demand for each
good,denoted as C T and C N ,depends upon q and real wealth:
C T = C T (q, w), C T q < 0, C T w > 0,(7.19)
C N = C N (q, w), C N q > 0, C N w > 0,(7.20)
where the partial derivatives indicate that an increase in the real exchange rate
results in reduced consumption of the traded good and increased consumption of
the non-traded good,and an increase in real wealth results in an increase in the
demand for both goods. The accumulation of foreign money,in turn,is given by
the difference between the consumption and production of traded goods:
Ṁ ∗ = CA = Y T (q) − C T (q, w) (7.21)
Since prices are assumed to by fully flexible in model 2,equilibrium in the market
for non-traded goods will hold continuously and is given by:
Y N (q) = C N (q, w). (7.22)
The assumed values of the partials for Y N and C N implies a specific relationship
between w and q. In particular,a rise in real wealth must be accompanied by a fall
in the real exchange rate:
q = q(w), q w < 0 (7.23)
On substitution of (7.23) into (7.21) we can obtain a further expression for the
accumulation of foreign money in terms of the value of assets:
Ṁ ∗ = f (w) (7.24)
The change in real wealth is given by
ẇ = Ṁ + Ṁ ∗ ,(7.25)