Exchange Rate Economics: Theories and Evidence

The new open economy macroeconomics part 2 275
price-setting firms and a fraction, v,of firms in each country can price-discriminate
across countries – referred to as PTM goods. The remaining 1 − v goods can be
freely traded across countries so firms must set a unified price for these goods and
the LOOP holds. A critical assumption,considered again later,is that consumers
are assumed to be unable to trade PTM goods across countries and therefore
cannot restore LOOP relationships. This assumption results in the home (and
correspondingly the foreign) country CPIs (equation 10.3) now being modified to:
[ ∫ n
P=
0
∫ n+(1−n)s
∫ 1/(1−θ) n
p(z) 1−θ dz + p ∗ (z) 1−θ dz + sf ∗ (z) dz] 1−θ ,
n
n+(1−n)s
(11.1)
where p represents home prices and f represents foreign currency prices. Here
p(z) is the home currency price of the home produced good, p ∗ (z) is the home
currency price of a foreign PTM good, z,and f ∗ (z) is the foreign currency
price of a foreign non-PTM good.
As in the model of the previous chapter,firms operate a simple linear production
technology:
y(z) = Ah(z),(11.2)
where y(z) is the total output of the firm, h(z) is employment and A is a constant.
For PTM firms,total output is divided between output sold domestically – x(z) –
and output sold abroad – n(z). The firm hires labour domestically and the PTM
firm chooses p(z) and f (z) separately to maximise the following profit function:
π(z) = p(z)x(z) + sf (z)n(z) − (W /A)(x(z) + n(z)),(11.3)
where the firm faces a similar demand schedule to that given in equation (10.8):
[ ] v(z) −θ
c(z) = C,(11.4)
P
where v(z) is equal to either p(z), p ∗ (z) or sf ∗ (z). Given this the firm then sets
prices in the two markets as a mark-up over MC such that:
p(z) = sf (z) =
θ W
θ − 1 A ,(11.5)
where θ/1 − θ represents the mark-up. Since the elasticities of demand are same
in each market,the LOOP and PPP must hold even for PTM goods if prices are
continuously flexible. Indeed,in the flex-price world PTM has no implications for
any variable irrespective of the source of the shock. However,PTM does have an
effect when prices are set one period in advance as in the basic NOEM model.