Exchange rate dynamics, asset market structure and the role of the ...

structure in the model is relatively standard in the literature. Home and foreign agents can
trade in one non-contingent bond, B t that pays out one unit of home-produced intermediate
goods in period t + 1. I denote by B t the quantity and by R t the price of the bond purchased
by home agents at the end of period t:The representative consumer faces the following budget
constraint in each period t:
P t C t + P H;t R t B t = P H;t B t 1 + P t w t h t + t (4)
where P t is the price index of the consumption bundle, de…ned below, P H;t is the price
of home produced intermediate goods and w t is the real wage. In addition to the wage,
the representative household receives dividends, t , from holding a share in the equity of
domestic …rms. All domestic …rms are wholly owned by domestic agents and equity holding
within these …rms is evenly divided between domestic households. When optimising, the
representative household takes the ‡ow of dividends as given.
The maximization problem of the Home representative agent consists of maximizing (1)
subject to (4), along with the usual transversality condition:
lim
T !1 E t
TY
R s B t+T = 0 (5)
s=1
in determining the optimal pro…le of consumption and bond holding and the labour supply
schedule. The corresponding Lagrange multiplier is:
max
C t;h t;B t; t
L = E t
1
X
s=t
s
U(C s ; (1
PH;s
h s )) + s B s 1 + w s h s +
s P H;s
C s R s B s
P s P s
Using …rst order conditions for optimal consumption, labour e¤ort and bond holdings one
can derive the static e¢ ciency condition for the consumption-labour choice as well as the
consumption Euler equation:
U C (C t ; (1
h t )) P H;t
P t
P s
(6)
U h (C t ; (1 h t ))
U C (C t ; (1 h t )) = w t (7)
= ( ~ C t ; ~ h t ) 1 R t
E t
U C (C t+1 ; (1
h t+1 )) P H;t+1
P t+1
In equilibrium, the household and average per capita levels of consumption and e¤ort are
(8)
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