Exchange Rate Economics: Theories and Evidence

254 The new open economy macroeconomics part 1
The variable F is a riskless real bond denominated in the consumption commodity
good (this is assumed to be the only traded asset in the model and therefore
equals C) and τ denotes lump sum taxes. The government is assumed to balance
its budget:
τ t + M t − M t−1
P t
= 0,(10.5)
and in the absence of government spending this means that all seignorage revenues
are returned to the public in the form of transfers. By maximising (10.2) subject to
the nominal budget constraint the following expression may be obtained
∫ 1
0
p(z)c(z)dz = Z ,(10.6)
where Z is any fixed total nominal expenditure on goods. It can be demonstrated
that for any two goods z and z ′ :
c(z ′ ) = c(z)
[ ] p(z) θ
p(z ′ ,(10.7)
)
which indicates that relative consumption depends only on relative prices,which
is intuitive enough given that preferences are assumed to have a CES form. By
substituting (10.7) into (10.6) and using (10.3) the representative agents’ demand
for good z is given by:
[ ] p(z) −θ
c j Z j [ ] p(z) −θ
(z) =
P P = C j . (10.8)
P
By integrating demand for good z across all agents (taking a population weighted
average of home and foreign demands) and making use of the LOOP for
individual prices and absolute PPP (which combined mean that for any good
z, p(z)/P = p ∗ (z)/P ∗ ) a constant-elasticity demand curve for the output of the
(monopolistic) consumer–producer may be obtained as:
[ ] p(z) −θ
y(z) = C w ,(10.9)
P
where C w (= nC +(1−n)C ∗ ) is aggregate global consumption. 2 This relationship
implies that output is demand determined in this model and,as we shall see in
more detail later,with price stickiness and marginal cost given,an exchange rate
depreciation increases marginal revenue and results in an expansion of output.
As is standard in this kind of model,the representative agent must decide on her
optimal choice of consumption,money holdings,labour supply and optimal price.