Exchange Rate Economics: Theories and Evidence

252 The new open economy macroeconomics part 1
consider some extensions to the NOEM which have an important bearing on the
issue of exchange rate volatility.
10.1 The two-countryredux model
10.1.1 The base-line two-country model
The redux model is a two-country model and in each country there is a continuum
of consumer–producers (sometimes referred to as yeoman farmers) that
produce differentiated goods (0, n) in the home country and (n,1) in the foreign
country (the discussion here follows Obstfeld and Rogoff 1995,1996 and Lane
2001). Agents have perfect foresight and have monopoly power and,crucially,
charge a price above marginal cost. This is an important assumption in this model
because it means that output is at less than the socially optimum level and therefore
expansionary monetary policy,say,can have a permanent effect on output. In our
presentation of the model we will generally focus on the home relationships and
only introduce foreign relationships where it is helpful for the discussion. However,it
is important to bear in mind that paralleling each of the home country
relationships is usually an equivalent foreign country relationship. The preferences
of the representative home agent, j,are assumed to be given by the following
function:
(
∞∑
β s−t
U j
t =
s=t
log C j s + η (
Ms
P s
) 1−ε
− κ 2 y s(j) 2 )
,(10.1)
where β is the subjective rate of time preference (0 0) and it is (implicitly) assumed that the inter-temporal
elasticity of substitution is equal to unity (we return to this point in the final section).
As we shall see later, θ is also the price elasticity of demand facing the monopolist
producer and the reason this is assumed to be greater than unity is to be consistent
with the assumption of monopolistic competition. 1
From equation (10.1) we see that agents derive positive utility from consumption
and real money balances, M /P (because the latter reduce transactions costs),
and disutility from work,which is assumed positively related to output. More
specifically,suppose the disutility from work,l,is given by −φl and the production
function is y = Al α or,alternatively,in inverted form l = (y/A) 1/α . Then
if α = 1/2 and κ = 2φ/A 1/α we obtain the output term in equation (10.1).